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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 15 — Jul. 28, 2014
  • pp: 18698–18706
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Lidar extinction-to-backscatter ratio of the ocean

James H. Churnside, James M. Sullivan, and Michael S. Twardowski  »View Author Affiliations


Optics Express, Vol. 22, Issue 15, pp. 18698-18706 (2014)
http://dx.doi.org/10.1364/OE.22.018698


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Abstract

Bio-optical models are used to develop a model of the lidar extinction-to-backscatter ratio applicable to oceanographic lidar. The model is based on chlorophyll concentration, and is expected to be valid for Case 1 waters. The limiting cases of narrow- and wide-beam lidars are presented and compared with estimates based on in situ optical measurements. Lidar measurements are also compared with the model using in situ or satellite estimates of chlorophyll concentration. A modified lidar ratio is defined, in which the properties of pure sea water are removed. This modified ratio is shown to be nearly constant for wide-beam lidar operating in low-chlorophyll waters, so accurate inversion to derive extinction and backscattering is possible under these conditions. This ratio can also be used for lidar calibration.

© 2014 Optical Society of America

1. Introduction

Increasingly, backscatter lidar is being used for a variety of oceanographic measurements [1

1. J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Engineer. 53(5), 051405 (2014). [CrossRef]

]. Examples include fisheries [2

2. J. H. Churnside and J. J. Wilson, “Airborne lidar for fisheries applications,” Opt. Eng. 40(3), 406–414 (2001). [CrossRef]

, 3

3. J. H. Churnside, A. F. Sharov, and R. A. Richter, “Aerial surveys of fish in estuaries: a case study in Chesapeake Bay,” ICES J. Mar. Sci. 68(1), 239–244 (2011). [CrossRef]

], plankton layers [4

4. J. H. Churnside and P. L. Donaghay, “Thin scattering layers observed by airborne lidar,” ICES J. Mar. Sci. 66(4), 778–789 (2009). [CrossRef]

, 5

5. M. A. Montes-Hugo, A. Weidemann, R. Gould, R. Arnone, J. H. Churnside, and E. Jaroz, “Ocean color patterns help to predict depth of optical layers in stratified coastal waters,” J. Appl. Remote Sens. 5(1), 053548 (2011). [CrossRef]

], and internal waves [6

6. J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6(1), 063611 (2012). [CrossRef]

, 7

7. J. H. Churnside and L. A. Ostrovsky, “Lidar observation of a strongly nonlinear internal wave train in the Gulf of Alaska,” Int. J. Remote Sens. 26(1), 167–177 (2005). [CrossRef]

]. While these examples used airborne lidar, measurements have also been made from ships [8

8. O. A. Bukin, A. Y. Major, A. N. Pavlov, B. M. Shevtsov, and E. D. Kholodkevich, “Measurement of the lightscattering layers structure and detection of the dynamic processes in the upper ocean layer by shipborne lidar,” Int. J. Remote Sens. 19(4), 707–715 (1998). [CrossRef]

, 9

9. J. H. Churnside, V. V. Tatarskii, and J. J. Wilson, “Oceanographic lidar attenuation coefficients and signal fluctuations measured from a ship in the Southern California Bight,” Appl. Opt. 37(15), 3105–3112 (1998). [CrossRef] [PubMed]

]. More recently, the sub-surface ocean signals from a lidar in space have been investigated [10

10. J. Churnside, B. McCarty, and X. Lu, “Subsurface signals from ocean an orbiting polarization lidar,” Remote Sens. 5(7), 3457–3475 (2013). [CrossRef]

, 11

11. M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space‐based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40(16), 4355–4360 (2013). [CrossRef]

]. The breadth of these studies suggests that improved lidar inversion techniques could be generally useful.

The lidar signal from a given range in the ocean depends on two optical properties of the water. One is the volume scattering coefficient at the direct backscatter direction at that range, and the other is the total integrated attenuation of the propagation to that range and back. If the optical properties of the water do not vary with depth, the lidar signal will decay exponentially with depth, the rate of decay provides the attenuation, and the scattering parameter can then be determined. This technique can also be applied to profiles where segments of exponentially-decreasing signals can be identified, but, in general, the lidar signal alone is not enough information to unambiguously determine either the attenuation coefficient or the volume backscattering coefficient.

The lidar ratio, defined as the ratio of the lidar attenuation coefficient to the volume scattering coefficient at the lidar scattering angle of π sr, has proven to be a useful quantity for interpreting atmospheric lidar signals. For water clouds, the ratio is near 19 sr [12

12. Y. Hu, “Depolarization ratio-effective lidar ratio relation: Theoretical basis for space lidar cloud phase discrimination,” Geophys. Res. Lett. 34(11), L11812 (2007). [CrossRef]

]. For ice clouds, measurements are in the range of 29 ± 12 sr [13

13. W.-N. Chen, C.-W. Chiang, and J.-B. Nee, “Lidar ratio and depolarization ratio for cirrus clouds,” Appl. Opt. 41(30), 6470–6476 (2002). [CrossRef] [PubMed]

]. Measured values for aerosols in the atmosphere are generally higher [14

14. I. Mattis, A. Ansmann, D. Müller, U. Wandinger, and D. Althausen, “Dual-wavelength Raman lidar observations of the extinction-to-backscatter ratio of Saharan dust,” Geophys. Res. Lett. 29, 014721 (2002).

16

16. G. Pappalardo, A. Amodeo, L. Mona, M. Pandolfi, N. Pergola, and V. Cuomo, “Raman lidar observations of aerosol emitted during the 2002 Etna eruption,” Geophys. Res. Lett. 31(5), L05120 (2004). [CrossRef]

]. The models used to interpret data from a lidar on a satellite use six aerosol types with values as follows: clean continental (35 sr), clean marine (20 sr), dust (40 sr), polluted continental (70 sr), polluted dust (65 sr), and smoke (70 sr) [17

17. A. H. Omar, D. M. Winker, M. A. Vaughan, Y. Hu, C. R. Trepte, R. A. Ferrare, K.-P. Lee, C. A. Hostetler, C. Kittaka, R. R. Rogers, R. E. Kuehn, and Z. Liu, “The CALIPSO automated aerosol classification and lidar ratio selection algorithm,” J. Atmos. Ocean. Technol. 26(10), 1994–2014 (2009). [CrossRef]

]. All of these values are for a lidar wavelength of 532 nm.

Depending on beam divergence and initial beam width, the attenuation coefficient of an oceanographic lidar will generally be between the beam-attenuation coefficient, c, and the diffuse-attenuation coefficient, Kd. For an airborne lidar, this depends on the diameter of the lidar footprint on the surface and the single scattering albedo [18

18. H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. 21(16), 2996–3001 (1982). [CrossRef] [PubMed]

], but we will consider the two limiting cases in our analysis.

2. Bio-optical model

The lidar ratio is defined as [19

19. J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosol: A numerical study,” J. Atmos. Ocean. Technol. 15(4), 1043–1050 (1998). [CrossRef]

]
S=αβ(π)=αbβ˜(π),
(1)
where α is the lidar attenuation coefficient, β(π) is the volume scattering coefficient at a scattering angle of π radians, b is the scattering coefficient, andβ˜(π) is the scattering phase function at that angle. This is the only angle of interest for lidar applications, and the functional dependence will be dropped in the following development.

The model for diffuse-attenuation coefficient is (note that all optical coefficients in the following are for 532 nm unless noted)
Kd=Kdw+0.0474C0.67,
(2)
where Kdw is the diffuse-attenuation coefficient of pure sea water (0.0452 m−1) and C is the concentration of chlorophyll-a in mg m−3 [20

20. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res.: Ocean. 106(C4), 7163–7180 (2001). [CrossRef]

].

The beam attenuation is given by
c=a+b,
(3)
where a is the absorption coefficient and b is the scattering coefficient.

The absorption can be modeled as [21

21. A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26(3), 263–306 (1991). [CrossRef]

, 22

22. L. Prieur and S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26(4), 671–689 (1981). [CrossRef]

]
a=1.055(0.052+0.028C0.65),
(4)
which includes the contribution of 0.052 m−1 from pure sea water. We will use this model as published, but a value for the absorption by pure sea water of aw = 0.0448 m−1 [23

23. R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). [CrossRef] [PubMed]

], elsewhere.

A model for the scattering coefficient is [24

24. H. R. Gordon and A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery, a review,” in Lecture notes on coastal and estuarine studies (Springer Verlag, 1983), p. 114.

]
b=bw+0.30C0.62.
(5)
This equation was actually developed for a wavelength of 550 nm, but the difference is small (< 4% for C = 0.01 mg m−3 and decreasing with increasing C until it is 0 for C > 2 mg m−3) and will be neglected. The water contribution, bw = 1.7 × 10−3 m−1, is less than 10% for C > 0.01 mg m−3. A similar model, also for 550 nm, is given by [20

20. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res.: Ocean. 106(C4), 7163–7180 (2001). [CrossRef]

, 25

25. H. Loisel and A. Morel, “Light scattering and chlorophyll concentration in case 1 waters: A reexamination,” Limnol. Oceanogr. 43(5), 847–858 (1998). [CrossRef]

]
b=bw+0.416C0.766.
(6)
This more recent model will be used.

There are two main models for the scattering phase function. Petzold measured volume-scattering coefficients using a 75 nm spectral band centered at 514 nm [26

26. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripts Institution of Oceanography, 1972).

, 27

27. C. D. Mobley, Light and Water: Radiative transfer in natural waters (Academic, 1994), p. 592.

], which covers the lidar wavelength of interest. From these measurements, an average particulate phase function was estimated [28

28. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32(36), 7484–7504 (1993). [CrossRef] [PubMed]

], which has a value of 3.15 × 10−3 sr−1 at a scattering angle of π sr. A more recent model considers the particulate phase function to be a weighted sum of two separate functions that represent small and large particles and have values of 2.2 × 10−3 sr−1 and 2.2 × 10−4 sr−1, respectively [29

29. A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002). [CrossRef] [PubMed]

]. These phase functions were calculated for a wavelength of 550 nm, but are not expected to be much different at 532 nm. The result is
β˜p=2.2×103f+2.2×104(1f),
(7)
where the fraction of small particles is given by
f=0.855[0.50.25log10(C)].
(8)
The reported range of validity for this model is 0.1 mg m−3 < C < 10 mg m−3. An extrapolation of the results of [30

30. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009). [CrossRef] [PubMed]

] to the scattering angle of interest suggest a phase function given by
β˜p=0.151bbpbp,
(9)
where bbp is the particulate contribution to the backscattering coefficient. The ratio on the right side of this equation can be approximated by [20

20. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res.: Ocean. 106(C4), 7163–7180 (2001). [CrossRef]

]
bbpbp=0.002+0.01[0.50.25log10(C)].
(10)
These two models provide very similar results, and the second will be used here.

Taking all of this together, we see that the lidar ratio will be between the limiting cases of SKd, for which the attenuation is equal to Kd, and Sc, for which the attenuation is given by c. In addition to the conventional definition, we will also consider a modified definition in which the known pure-sea-water values are subtracted from both attenuation and volume backscatter coefficients. The four resulting models (Fig. 1
Fig. 1 Plot of lidar ratio, SKd (black, left vertical axis), for the limiting case of α = Kd, and Sc (red, right axis) for the limiting case of α = c. Solid lines represent the conventional definition and dashed lines the modified definition.
) are given by:
SKd=0.0452+0.0474C0.671.94×104+6.28×105[72.5log10(C)]C0.766
(11)
S'Kd=755C0.172.5log10(C)
(12)
Sc=0.0566+0.0295C0.65+0.416C0.7661.94×104+6.28×105[72.5log10(C)]C0.766
(13)
S'c=6624+470C0.1272.5log10(C).
(14)
This Fig. shows the reason for modified definition. In both limiting cases, there is much less variability of the lidar ratio with chlorophyll using the modified definition. This implies that estimated values can be used in lidar inversions to derive extinction and β(π) with much less error, especially for a broad lidar beam.

In general, the results of [18

18. H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. 21(16), 2996–3001 (1982). [CrossRef] [PubMed]

] can be used to obtain values for α between Kd and c. This would only be necessary for a rather narrow range of parameters where the spot diameter on the surface and c−1 are of the same order and the single scattering albedo is high. Note, for example, that the values for pure sea water are not too different, SKd = 233 sr and Sc = 292 sr, because the attenuation is largely a result of absorption.

3. In situ measurements

In situ measurements were collected from several stations at five different coastal and open-ocean environments selected to represent a diverse range of environments and optical values. The locations chosen were the New Jersey bight off the Northeast USA coast (1.0 < C < 8.1); the San Diego, California surf-zone (0.014 < C < 1.3); the Southern Ocean near South Georgia Island (0.046 < C < 0.71); the Ligurian Sea near Italy (0.035 < C < 1.4); and Monterey Bay, California (1.7 < C < 110). These data sets span both Case I and Case II waters. Vertical profiles were collected using a profiling package equipped with, among other instruments, a WET Labs AC-9, Seabird SBE49 CTD and a WET Labs ECO-BB3 backscattering sensor. Data from the instruments were merged together using common instrument time. After merging, all data were averaged to 1 meter depth bins. The AC-9 measures the absorption and beam attenuation of all in-water constituents except water, denoted apg and cpg, respectively. The instrument measures these parameters at nine wavelengths, although only the 532 nm channel was used here. The AC-9 was pure water calibrated before and after each cruise and corrections applied for temperature and salinity dependence as described by Twardowski et al. [31

31. M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an AC-9,” J. Atmos. Ocean. Technol. 16(6), 691–707 (1999). [CrossRef]

]. Scattering errors in the AC-9 absorption channel was corrected using the proportional correction algorithm of Zaneveld et al. [32

32. J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “Scattering error correction of reflecting-tube absorption meters,” in Proc. SPIE 2258, Ocean Optics XII, (SPIE, 1994), 44–55.

]. To obtain the total absorption and attenuation coefficients, a and c, the pure water absorption coefficients of Pope and Fry [23

23. R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). [CrossRef] [PubMed]

] were added to the corrected apg and cpg measurements. The ECO-BB3 is a three wavelength (including 532 nm) backscattering sensor with a nominal centroid angle (θ) of 124°. The volume scattering function (β) and backscattering coefficient (bb) at 532 nm were calculated from the ECO-BB3 data according to Sullivan et al. [33

33. J. Sullivan, M. Twardowski, J. Ronald, V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” in Light Scattering Reviews 7 (Springer, 2013), pp. 189–224.

]. For modeling inputs, β(π) was estimated by transforming the ECO-BB3 β(θ) values to β(π) using a transform factor based on the global particulate phase function derived by Sullivan and Twardowski [30

30. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009). [CrossRef] [PubMed]

]. Lidar attenuation, α, was estimated by c or by the Lee et al. [34

34. Z.-P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: An evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005).

] Kd model with a solar zenith angle of 0.

Chlorophyll concentration was estimated from the AC-9 data as in [34

34. Z.-P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: An evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005).

]. The chlorophyll absorption was estimated as the difference between the absorption at the chlorophyll peak wavelength (676 nm) and a nearby value (650 nm). This difference was converted to chlorophyll concentration using an in vivo specific absorption for chlorophyll, aph*(676), of 0.014 m2 mg−1. Errors in these estimates are caused by limits to the precision of the AC-9 measurements and by variability in the specific absorption. Chlorophyll specific absorption coefficients among diverse phytoplankton populations have been shown to vary between ~0.01 to 0.02 m2 mg−1 [35

35. J. M. Sullivan, M. S. Twardowski, P. L. Donaghay, and S. A. Freeman, “Use of optical scattering to discriminate particle types in coastal waters,” Appl. Opt. 44(9), 1667–1680 (2005). [CrossRef] [PubMed]

]. Overall, relative errors are expected to be less than ± 50% [36

36. A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parametrization,” J. Geophys. Res. 100(C7), 13321–13332 (1995). [CrossRef]

].

In all, 904 measurements from all depths sampled were binned by chlorophyll concentration, with five bins per decade. The mean values of S and error bars representing ± one standard deviation presented in Fig. 2
Fig. 2 Plot of lidar ratios, SKd (left panel) and Sc (right panel), calculated from in situ measurements. Black lines and symbols represent the theory and measurements using the conventional definition, and red lines and symbols using the modified definition.
were computed exclusively from the in situ measured optical properties. Estimated errors in C, not shown in the Fig., are roughly ± one bin. For each 1-m binned set of measurements, the assumption is made of a homogeneous water column with those optical properties to test the bio-optical modeling of S. Below 2 mg m−3, measured S 'Kd values are very close to the model, while SKd values are generally below the model values by as much as 30%. Above 2 mg m−3, the measured values of all four ratios tend to be higher than the model and exhibit higher variation. Most of these measurements were from Monterey Bay, and the assumption of Case I waters may not be valid for all values.

4. Lidar measurements

Data from the NOAA dual-polarization lidar from two different locations were used. The first case uses lidar data collected off the west coast of the United States, described in detail in [37

37. J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express 16(2), 1196–1207 (2008). [CrossRef] [PubMed]

], and chlorophyll concentration inferred from satellite measurements. The second uses lidar data collected in an inland fjord, described in detail in [38

38. J. H. Lee, J. H. Churnside, R. D. Marchbanks, P. L. Donaghay, and J. M. Sullivan, “Oceanographic lidar profiles compared with estimates from in situ optical measurements,” Appl. Opt. 52(4), 786–794 (2013). [CrossRef] [PubMed]

], and chlorophyll concentration inferred from in situ measurements. In both cases, the co- and cross-polarized lidar returns were added together, and the attenuation and volume backscatter of the combined signal were used to estimate the lidar ratio. The lidar footprint is relatively large for this system (D = 5 m at an altitude of 300 m), and measured attenuation coefficients were generally within about 10% of Kd estimated from satellite ocean color in the first case [39

39. M. A. Montes, J. Churnside, Z. Lee, R. Gould, R. Arnone, and A. Weidemann, “Relationships between water attenuation coefficients derived from active and passive remote sensing: a case study from two coastal environments,” Appl. Opt. 50(18), 2990–2999 (2011). [CrossRef] [PubMed]

] and from in situ measurements in the second [38

38. J. H. Lee, J. H. Churnside, R. D. Marchbanks, P. L. Donaghay, and J. M. Sullivan, “Oceanographic lidar profiles compared with estimates from in situ optical measurements,” Appl. Opt. 52(4), 786–794 (2013). [CrossRef] [PubMed]

]. Thus, SKd is most representative for our lidar. The modified lidar ratio was estimated by subtracting 0.0452 m−1 from the measured attenuation and 1.94 × 10−4 m−1 sr −1 from the volume backscatter.

For the first case, lidar data were collected from the coast out to a distance of 350 km, and include data in and around the Columbia River plume, comprising both Case I and Case II water types. These data were chosen for the relatively low chlorophyll values in the offshore flight segments. For this study, a linear fit to the log of the signal between 5 and 10 m depths was used to estimate the lidar parameters. Chlorophyll concentrations were obtained from the daily MODIS-Aqua, Level 3 binned data at 4 km resolution, noting that uncertainties in satellite chlorophyll retrievals can be as high as 40% in Case I waters. The closest chlorophyll value was matched within 10 days of each lidar measurement. This was necessary to provide enough matches for comparison, but added scatter to the data.

For the second case, lidar data were collected in East Sound, Washington during a strong diatom bloom. All of the data from this study are considered Case II. Optical properties were measured in situ with a high-depth-resolution profiling package, including a Seabird SBE-25 CTD with a dissolved oxygen sensor, a WET Labs AC-9 and AC-S, a WET Labs ECO-VSF, a WET Labs ECO-BB3, and WET Labs chlorophyll and CDOM fluorometers. The parameter Kd was again estimated from Lee et al. [34

34. Z.-P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: An evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005).

], but with depth-averaged inherent optical properties over the 5 – 10 m comparable lidar range. The nearest five lidar profiles to each cast were averaged together for comparison with the chlorophyll concentration inferred from the AC-9 absorption spectrum. Most of the lidar profiles were within a few tens of m of the in situ data with a time difference of less than two hours.

Even with the observed scatter, data show good agreement with the model (Fig. 3
Fig. 3 Plot of lidar ratio, SKd, estimated from lidar measurements. Black lines and symbols represent the theory and measurements using the conventional definition and red lines and symbols using the modified definition.
), despite the relative uncertainties in the input parameters and the application of substantial data from Case II waters. The relative difference (defined as the model value minus the measured value, normalized by the model value) had an average value of 9.0% for the conventional definition and −8.9% for the modified definition. Although close, these values are not significantly different from zero, with p-values of 0.06 and 0.09, respectively. The standard deviation of the error values was 22% for the conventional values and 34% for the modified values. The difference in the standard deviations of the relative values is a result of the lower mean values when the modified definition is used. The standard deviation of the unnormalized differences is the same for both definitions.

5. Discussion

Based on the in situ measurements, the model seems to work best in water with relatively low chlorophyll concentration. The likely reason is that the assumptions of the bio-optical models are best satisfied in oceanic waters with low chlorophyll concentration and even lower concentrations of suspended sediments, where all optically significant constituents approximately co-vary and are, to first order, driven by biological processes. Improved bio-optical models, of course, will lead to better estimates of lidar ratio.

In atmospheric lidar, the lidar ratio has been useful for inverting the signal to simultaneously obtain extinction and backscattering. The general approach is to find a range at which one of these parameters is known and proceed iteratively to other ranges. For example, one might use a point at high altitude where the scattering is dominated by molecules and can be accurately calculated from the density. For airborne oceanographic lidar, it will probably be more convenient to start from the sea surface, where the total integrated attenuation is negligible. For a series of measurements of the attenuated backscatter, γn, the values are found iteratively starting with sample number 0 at the surface as follows:
β0=γ0;α0=0β1=γ1exp(2ΔzSβ0);α1=Sβ1,βn=γnexp(2Δzm=0n1αm);αn=Sβn
(15)
where Δz is the depth between samples and S is the appropriate lidar ratio.

The measured lidar ratio has been used in the atmosphere to characterize cloud and aerosol types. This may prove to be more difficult in the ocean, where there are many more different types of scattering particles mixed together. These differences are contained within the variations of the measured values in this work, and more detailed models of lidar ratio will be required for this application.

It has also been suggested that the lidar ratio can be used in the radiometric calibration of atmospheric lidar, since the attenuation can be measured without calibration [40

40. E. J. O’Connor, A. J. Illingworth, and R. J. Hogan, “A technique for autocalibration of cloud lidar,” J. Atmos. Ocean. Technol. 21(5), 777–786 (2004). [CrossRef]

42

42. Y. Wu, C. M. Gan, L. Cordero, B. Gross, F. Moshary, and S. Ahmed, “Calibration of the 1064 nm lidar channel using water phase and cirrus clouds,” Appl. Opt. 50(21), 3987–3999 (2011). [CrossRef] [PubMed]

]. A similar technique should be possible for oceanographic lidar. The objective of calibration is to find the parameter A such that the product of A and the measured photocathode current I is an estimate of the attenuated backscatter. From the definitions of lidar ratio, we can find A from a measurement of I at depth z from
A=αISexp(2αz)A=(ααwIS'+βwI)exp(2αz)
(16)
as long as the water properties are uniform from the surface to depth z. The most favorable case is when relatively clear water is used to calibrate a wide-beam lidar. For this case, we can use S ' = 105 sr and the error introduced by not knowing the exact value of C will be less than 2% as long as C is less than 1 mg m−3.

6. Conclusions

A model of the lidar extinction-to-backscatter ratio was developed for Case 1 waters and limiting cases of broad- and narrow-beam oceanographic lidars. This model depends only on chlorophyll concentration and the well-known properties of pure sea water. A modified definition, in which the contributions from pure water are removed, was suggested to reduce the sensitivity to uncertainty in chlorophyll concentration. This reduction was greatest for the case of a wide lidar beam in waters with chlorophyll concentration below 1 mg m−3. Because chlorophyll concentration does not need to be known precisely, the lidar ratio will be useful for lidar inversions and for radiometric calibration.

The resulting model provides good agreement with both in situ and airborne lidar measurements. The differences are smaller than might be expected from the scatter in the data that were used to develop the bio-optical models. This scatter is a result of the wide variation in the size, shape, and internal structure of phytoplankton cells that can produce the same overall chlorophyll concentration. The scattering properties are particularly sensitive to these factors. Some of the differences are reduced in the lidar ratio, because scattering affects both the numerator and denominator of the ratio.

Acknowledgments

References and links

1.

J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Engineer. 53(5), 051405 (2014). [CrossRef]

2.

J. H. Churnside and J. J. Wilson, “Airborne lidar for fisheries applications,” Opt. Eng. 40(3), 406–414 (2001). [CrossRef]

3.

J. H. Churnside, A. F. Sharov, and R. A. Richter, “Aerial surveys of fish in estuaries: a case study in Chesapeake Bay,” ICES J. Mar. Sci. 68(1), 239–244 (2011). [CrossRef]

4.

J. H. Churnside and P. L. Donaghay, “Thin scattering layers observed by airborne lidar,” ICES J. Mar. Sci. 66(4), 778–789 (2009). [CrossRef]

5.

M. A. Montes-Hugo, A. Weidemann, R. Gould, R. Arnone, J. H. Churnside, and E. Jaroz, “Ocean color patterns help to predict depth of optical layers in stratified coastal waters,” J. Appl. Remote Sens. 5(1), 053548 (2011). [CrossRef]

6.

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6(1), 063611 (2012). [CrossRef]

7.

J. H. Churnside and L. A. Ostrovsky, “Lidar observation of a strongly nonlinear internal wave train in the Gulf of Alaska,” Int. J. Remote Sens. 26(1), 167–177 (2005). [CrossRef]

8.

O. A. Bukin, A. Y. Major, A. N. Pavlov, B. M. Shevtsov, and E. D. Kholodkevich, “Measurement of the lightscattering layers structure and detection of the dynamic processes in the upper ocean layer by shipborne lidar,” Int. J. Remote Sens. 19(4), 707–715 (1998). [CrossRef]

9.

J. H. Churnside, V. V. Tatarskii, and J. J. Wilson, “Oceanographic lidar attenuation coefficients and signal fluctuations measured from a ship in the Southern California Bight,” Appl. Opt. 37(15), 3105–3112 (1998). [CrossRef] [PubMed]

10.

J. Churnside, B. McCarty, and X. Lu, “Subsurface signals from ocean an orbiting polarization lidar,” Remote Sens. 5(7), 3457–3475 (2013). [CrossRef]

11.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space‐based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40(16), 4355–4360 (2013). [CrossRef]

12.

Y. Hu, “Depolarization ratio-effective lidar ratio relation: Theoretical basis for space lidar cloud phase discrimination,” Geophys. Res. Lett. 34(11), L11812 (2007). [CrossRef]

13.

W.-N. Chen, C.-W. Chiang, and J.-B. Nee, “Lidar ratio and depolarization ratio for cirrus clouds,” Appl. Opt. 41(30), 6470–6476 (2002). [CrossRef] [PubMed]

14.

I. Mattis, A. Ansmann, D. Müller, U. Wandinger, and D. Althausen, “Dual-wavelength Raman lidar observations of the extinction-to-backscatter ratio of Saharan dust,” Geophys. Res. Lett. 29, 014721 (2002).

15.

Z. Liu, N. Sugimoto, and T. Murayama, “Extinction-to-backscatter ratio of asian dust observed with high-spectral-resolution lidar and Raman lidar,” Appl. Opt. 41(15), 2760–2767 (2002). [CrossRef] [PubMed]

16.

G. Pappalardo, A. Amodeo, L. Mona, M. Pandolfi, N. Pergola, and V. Cuomo, “Raman lidar observations of aerosol emitted during the 2002 Etna eruption,” Geophys. Res. Lett. 31(5), L05120 (2004). [CrossRef]

17.

A. H. Omar, D. M. Winker, M. A. Vaughan, Y. Hu, C. R. Trepte, R. A. Ferrare, K.-P. Lee, C. A. Hostetler, C. Kittaka, R. R. Rogers, R. E. Kuehn, and Z. Liu, “The CALIPSO automated aerosol classification and lidar ratio selection algorithm,” J. Atmos. Ocean. Technol. 26(10), 1994–2014 (2009). [CrossRef]

18.

H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. 21(16), 2996–3001 (1982). [CrossRef] [PubMed]

19.

J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosol: A numerical study,” J. Atmos. Ocean. Technol. 15(4), 1043–1050 (1998). [CrossRef]

20.

A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res.: Ocean. 106(C4), 7163–7180 (2001). [CrossRef]

21.

A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26(3), 263–306 (1991). [CrossRef]

22.

L. Prieur and S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26(4), 671–689 (1981). [CrossRef]

23.

R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). [CrossRef] [PubMed]

24.

H. R. Gordon and A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery, a review,” in Lecture notes on coastal and estuarine studies (Springer Verlag, 1983), p. 114.

25.

H. Loisel and A. Morel, “Light scattering and chlorophyll concentration in case 1 waters: A reexamination,” Limnol. Oceanogr. 43(5), 847–858 (1998). [CrossRef]

26.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripts Institution of Oceanography, 1972).

27.

C. D. Mobley, Light and Water: Radiative transfer in natural waters (Academic, 1994), p. 592.

28.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32(36), 7484–7504 (1993). [CrossRef] [PubMed]

29.

A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002). [CrossRef] [PubMed]

30.

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009). [CrossRef] [PubMed]

31.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an AC-9,” J. Atmos. Ocean. Technol. 16(6), 691–707 (1999). [CrossRef]

32.

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “Scattering error correction of reflecting-tube absorption meters,” in Proc. SPIE 2258, Ocean Optics XII, (SPIE, 1994), 44–55.

33.

J. Sullivan, M. Twardowski, J. Ronald, V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” in Light Scattering Reviews 7 (Springer, 2013), pp. 189–224.

34.

Z.-P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: An evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005).

35.

J. M. Sullivan, M. S. Twardowski, P. L. Donaghay, and S. A. Freeman, “Use of optical scattering to discriminate particle types in coastal waters,” Appl. Opt. 44(9), 1667–1680 (2005). [CrossRef] [PubMed]

36.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parametrization,” J. Geophys. Res. 100(C7), 13321–13332 (1995). [CrossRef]

37.

J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express 16(2), 1196–1207 (2008). [CrossRef] [PubMed]

38.

J. H. Lee, J. H. Churnside, R. D. Marchbanks, P. L. Donaghay, and J. M. Sullivan, “Oceanographic lidar profiles compared with estimates from in situ optical measurements,” Appl. Opt. 52(4), 786–794 (2013). [CrossRef] [PubMed]

39.

M. A. Montes, J. Churnside, Z. Lee, R. Gould, R. Arnone, and A. Weidemann, “Relationships between water attenuation coefficients derived from active and passive remote sensing: a case study from two coastal environments,” Appl. Opt. 50(18), 2990–2999 (2011). [CrossRef] [PubMed]

40.

E. J. O’Connor, A. J. Illingworth, and R. J. Hogan, “A technique for autocalibration of cloud lidar,” J. Atmos. Ocean. Technol. 21(5), 777–786 (2004). [CrossRef]

41.

M. A. Vaughan, Z. Liu, M. J. McGill, Y. Hu, and M. D. Obland, “On the spectral dependence of backscatter from cirrus clouds: Assessing CALIOP's 1064 nm calibration assumptions using cloud physics lidar measurements,” J. Geophys. Res. Atmos. 115(D14), D14206 (2010). [CrossRef]

42.

Y. Wu, C. M. Gan, L. Cordero, B. Gross, F. Moshary, and S. Ahmed, “Calibration of the 1064 nm lidar channel using water phase and cirrus clouds,” Appl. Opt. 50(21), 3987–3999 (2011). [CrossRef] [PubMed]

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.3640) Atmospheric and oceanic optics : Lidar
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(280.3640) Remote sensing and sensors : Lidar

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: June 16, 2014
Revised Manuscript: July 19, 2014
Manuscript Accepted: July 20, 2014
Published: July 25, 2014

Virtual Issues
Vol. 9, Iss. 9 Virtual Journal for Biomedical Optics

Citation
James H. Churnside, James M. Sullivan, and Michael S. Twardowski, "Lidar extinction-to-backscatter ratio of the ocean," Opt. Express 22, 18698-18706 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18698


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References

  1. J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Engineer.53(5), 051405 (2014). [CrossRef]
  2. J. H. Churnside and J. J. Wilson, “Airborne lidar for fisheries applications,” Opt. Eng.40(3), 406–414 (2001). [CrossRef]
  3. J. H. Churnside, A. F. Sharov, and R. A. Richter, “Aerial surveys of fish in estuaries: a case study in Chesapeake Bay,” ICES J. Mar. Sci.68(1), 239–244 (2011). [CrossRef]
  4. J. H. Churnside and P. L. Donaghay, “Thin scattering layers observed by airborne lidar,” ICES J. Mar. Sci.66(4), 778–789 (2009). [CrossRef]
  5. M. A. Montes-Hugo, A. Weidemann, R. Gould, R. Arnone, J. H. Churnside, and E. Jaroz, “Ocean color patterns help to predict depth of optical layers in stratified coastal waters,” J. Appl. Remote Sens.5(1), 053548 (2011). [CrossRef]
  6. J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens.6(1), 063611 (2012). [CrossRef]
  7. J. H. Churnside and L. A. Ostrovsky, “Lidar observation of a strongly nonlinear internal wave train in the Gulf of Alaska,” Int. J. Remote Sens.26(1), 167–177 (2005). [CrossRef]
  8. O. A. Bukin, A. Y. Major, A. N. Pavlov, B. M. Shevtsov, and E. D. Kholodkevich, “Measurement of the lightscattering layers structure and detection of the dynamic processes in the upper ocean layer by shipborne lidar,” Int. J. Remote Sens.19(4), 707–715 (1998). [CrossRef]
  9. J. H. Churnside, V. V. Tatarskii, and J. J. Wilson, “Oceanographic lidar attenuation coefficients and signal fluctuations measured from a ship in the Southern California Bight,” Appl. Opt.37(15), 3105–3112 (1998). [CrossRef] [PubMed]
  10. J. Churnside, B. McCarty, and X. Lu, “Subsurface signals from ocean an orbiting polarization lidar,” Remote Sens.5(7), 3457–3475 (2013). [CrossRef]
  11. M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space‐based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett.40(16), 4355–4360 (2013). [CrossRef]
  12. Y. Hu, “Depolarization ratio-effective lidar ratio relation: Theoretical basis for space lidar cloud phase discrimination,” Geophys. Res. Lett.34(11), L11812 (2007). [CrossRef]
  13. W.-N. Chen, C.-W. Chiang, and J.-B. Nee, “Lidar ratio and depolarization ratio for cirrus clouds,” Appl. Opt.41(30), 6470–6476 (2002). [CrossRef] [PubMed]
  14. I. Mattis, A. Ansmann, D. Müller, U. Wandinger, and D. Althausen, “Dual-wavelength Raman lidar observations of the extinction-to-backscatter ratio of Saharan dust,” Geophys. Res. Lett.29, 014721 (2002).
  15. Z. Liu, N. Sugimoto, and T. Murayama, “Extinction-to-backscatter ratio of asian dust observed with high-spectral-resolution lidar and Raman lidar,” Appl. Opt.41(15), 2760–2767 (2002). [CrossRef] [PubMed]
  16. G. Pappalardo, A. Amodeo, L. Mona, M. Pandolfi, N. Pergola, and V. Cuomo, “Raman lidar observations of aerosol emitted during the 2002 Etna eruption,” Geophys. Res. Lett.31(5), L05120 (2004). [CrossRef]
  17. A. H. Omar, D. M. Winker, M. A. Vaughan, Y. Hu, C. R. Trepte, R. A. Ferrare, K.-P. Lee, C. A. Hostetler, C. Kittaka, R. R. Rogers, R. E. Kuehn, and Z. Liu, “The CALIPSO automated aerosol classification and lidar ratio selection algorithm,” J. Atmos. Ocean. Technol.26(10), 1994–2014 (2009). [CrossRef]
  18. H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt.21(16), 2996–3001 (1982). [CrossRef] [PubMed]
  19. J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosol: A numerical study,” J. Atmos. Ocean. Technol.15(4), 1043–1050 (1998). [CrossRef]
  20. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res.: Ocean.106(C4), 7163–7180 (2001). [CrossRef]
  21. A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr.26(3), 263–306 (1991). [CrossRef]
  22. L. Prieur and S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr.26(4), 671–689 (1981). [CrossRef]
  23. R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt.36(33), 8710–8723 (1997). [CrossRef] [PubMed]
  24. H. R. Gordon and A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery, a review,” in Lecture notes on coastal and estuarine studies (Springer Verlag, 1983), p. 114.
  25. H. Loisel and A. Morel, “Light scattering and chlorophyll concentration in case 1 waters: A reexamination,” Limnol. Oceanogr.43(5), 847–858 (1998). [CrossRef]
  26. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripts Institution of Oceanography, 1972).
  27. C. D. Mobley, Light and Water: Radiative transfer in natural waters (Academic, 1994), p. 592.
  28. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt.32(36), 7484–7504 (1993). [CrossRef] [PubMed]
  29. A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt.41(30), 6289–6306 (2002). [CrossRef] [PubMed]
  30. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt.48(35), 6811–6819 (2009). [CrossRef] [PubMed]
  31. M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an AC-9,” J. Atmos. Ocean. Technol.16(6), 691–707 (1999). [CrossRef]
  32. J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “Scattering error correction of reflecting-tube absorption meters,” in Proc. SPIE 2258, Ocean Optics XII, (SPIE, 1994), 44–55.
  33. J. Sullivan, M. Twardowski, J. Ronald, V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” in Light Scattering Reviews 7 (Springer, 2013), pp. 189–224.
  34. Z.-P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: An evaluation of remote sensing methods,” J. Geophys. Res.110, C02017 (2005).
  35. J. M. Sullivan, M. S. Twardowski, P. L. Donaghay, and S. A. Freeman, “Use of optical scattering to discriminate particle types in coastal waters,” Appl. Opt.44(9), 1667–1680 (2005). [CrossRef] [PubMed]
  36. A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parametrization,” J. Geophys. Res.100(C7), 13321–13332 (1995). [CrossRef]
  37. J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express16(2), 1196–1207 (2008). [CrossRef] [PubMed]
  38. J. H. Lee, J. H. Churnside, R. D. Marchbanks, P. L. Donaghay, and J. M. Sullivan, “Oceanographic lidar profiles compared with estimates from in situ optical measurements,” Appl. Opt.52(4), 786–794 (2013). [CrossRef] [PubMed]
  39. M. A. Montes, J. Churnside, Z. Lee, R. Gould, R. Arnone, and A. Weidemann, “Relationships between water attenuation coefficients derived from active and passive remote sensing: a case study from two coastal environments,” Appl. Opt.50(18), 2990–2999 (2011). [CrossRef] [PubMed]
  40. E. J. O’Connor, A. J. Illingworth, and R. J. Hogan, “A technique for autocalibration of cloud lidar,” J. Atmos. Ocean. Technol.21(5), 777–786 (2004). [CrossRef]
  41. M. A. Vaughan, Z. Liu, M. J. McGill, Y. Hu, and M. D. Obland, “On the spectral dependence of backscatter from cirrus clouds: Assessing CALIOP's 1064 nm calibration assumptions using cloud physics lidar measurements,” J. Geophys. Res. Atmos.115(D14), D14206 (2010). [CrossRef]
  42. Y. Wu, C. M. Gan, L. Cordero, B. Gross, F. Moshary, and S. Ahmed, “Calibration of the 1064 nm lidar channel using water phase and cirrus clouds,” Appl. Opt.50(21), 3987–3999 (2011). [CrossRef] [PubMed]

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