Oceanographic lidar attenuation coefficients and ... - OSA Publishing

Oceanographic lidar attenuation coefficients and signal fluctuations measured from a ship in the Southern California Bight James H. Churnside, Viatcheslav V. Tatarskii, and James J. Wilson

We measured the attenuation coefficient of the National Oceanic and Atmospheric Administration lidar from a ship in the Southern California Bight in September 1995. The region from approximately 5 to 30 m in depth was covered. The laser was linearly polarized, and the receiver was operated with the same polarization and the orthogonal polarization. The measured values were between 0.08 and 0.12 m21 and were highly correlated with in situ measurements of the beam attenuation coefficient. Fluctuations of the lidar signal were found to be induced primarily by surface waves whose wavelengths are approximately three times the lidar spot size at the surface. © 1998 Optical Society of America OCIS codes: 010.3640, 010.4450, 010.0010.

1. Introduction

Because light in the mid-visible portion of the spectrum is capable of penetrating the air–sea interface and propagating through the upper layer of the ocean, airborne lidar has been proposed as a tool for making a variety of measurements in the upper ocean. Many of these applications rely on the direct reflection of laser radiation back to the receiver. Several airborne lidar bathymetry systems have been developed,1– 4 and their use is becoming fairly routine. Systems have been developed to image underwater objects, both from the air5 and from subsurface platforms.6 Successful experiments have been performed with lidar to profile optical scattering layers within the ocean7,8 and to profile schools of fish.9,10 Other types of lidar rely on processes other than inelastic scattering to obtain information. The most successful of these has been the use of laserstimulated fluorescence to infer chlorophyll concentrations.11–13 The Raman-scattered light from a laser has been suggested as a technique to measure surface oil thickness14 and to profile tem-

The authors are with the Environmental Technology Laboratory, National Oceanic and Atmospheric Administration, 325 Broadway, Boulder, Colorado 80303. Received 17 April 1997; revised manuscript received 5 January 1998. 0003-6935y98y153105-08$15.00y0 © 1998 Optical Society of America

perature in the water, although the latter has met with limited success. In all these applications, the signal decays exponentially with increasing depth because of absorption and scattering within the water. The rate of this exponential decay can be expressed as a lidar attenuation coefficient that depends on the lidar parameters and also on the inherent optical properties of the water.2,6,8,15 For a lidar with a small field of view and a small diameter at the surface, one would expect the lidar attenuation coefficient to be close to the beam attenuation coefficient c, which is the sum of the absorption coefficient a and the total scattering coefficient b. Clearly, any photon that is absorbed is lost, and for this geometry, any photon that is scattered should also be lost. If the diameter of the beam becomes larger, photons can be scattered in the forward direction and still remain in the beam, available for later scattering to the receiver. For a very large beam ~diameter at the surface .. c21!, nearly all of the forwardscattered photons remain in the beam until they are absorbed or scattered in the backward direction. The lidar attenuation coefficient in this case approaches a plus the backscatter coefficient bb, which is that part of the scattering coefficient corresponding to scattering angles between 90° and 180°. This is true even for a narrowly collimated lidar. For a small beam with a large field of view ~field of view much greater than the angular width of the forwardscattering peak of the scattering phase function!, forward-scattered photons will generally remain in 20 May 1998 y Vol. 37, No. 15 y APPLIED OPTICS

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cruise, lidar and in situ measurements were made on two parallel transects with five stations on each. The area covered was in the Southern California Bight, generally between San Diego and San Clemente Island. A map showing the locations of the ten stations is presented in Fig. 1, and their latitudes and longitudes are listed in Table 1. 2. Lidar System

Fig. 1. Map showing the locations of the ten measurement stations.

the field of view and also be available for later scattering. One would expect the attenuation coefficient in this case to be similar to that for a large-diameter beam. This limiting value for either a large diameter or a large field of view is the same as the diffuse attenuation coefficient when the Sun is at zenith. For this experiment, a small spot size on the surface was used, so reduction of the attenuation coefficient by the effects of a large spot size should be negligible. Also, relatively small laser beam divergence and receiver field of view were used. These values were comparable to the receiver field of view of the commercial instrument used to estimate the attenuation coefficient in situ. Thus the lidar attenuation coefficient was expected to be close to the measured value for beam attenuation coefficient. Actual values were significantly lower. The fluctuations of the lidar return were also measured and were found to be consistent with expected surface wave effects. The National Oceanic and Atmospheric Administration Research Vessel ~NOAA RyV!, David Starr Jordan, was operated for three weeks in September of 1995 with a lidar mounted on the flying bridge and directed down into the water. It was located at a height of 10.3 m above the water and directed outward at an angle of 15°. During a portion of this

The lidar was a simple system that had no scanning or imaging capabilities. The laser was a frequencydoubled, Q-switched Nd:YAG laser, linearly polarized parallel to the plane of incidence. A negative lens in front of the laser increased the beam divergence. The laser was mounted next to the receiver telescope, and the diverged beam was directed by one mirror to a second mirror in the center of the front of the telescope. This mirror was used to direct the beam to the water so that it was coaxial with the receiver. The receiver consisted of a lens that collected the scattered light onto a microchannel plate detector. An interference filter was placed in front of the detector to limit interference from background light. A rotatable polarizer in front of the filter was used to make measurements of the copolarized return and the cross-polarized return at each station. The detector was triggered to begin each measurement at a depth of 5 m, and useful signal was generally received to a depth of 30 – 40 m. The detector output was passed through a logarithmic amplifier, and this signal was digitized and stored in the computer. Approximately 1000 lidar pulses of each polarization were recorded at each station. The lidar parameters are presented in Table 2. In homogeneous water, the return signal from a lidar will experience an exponential decrease with propagation distance that is in addition to the geometric loss. For a nadir-pointing lidar, the signal can be represented as S~d! 5 C

exp~22ad! , ~d 1 nh!2

(1)

where S is the signal at a particular depth, C is a parameter that depends on the geometry and lidar

Table 1. Locations and Times of Measurement Stations

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Station

Latitude

Longitude

Date

Time

Solar Angle ~deg!

7 8 9 10 11 12 13 14 15 16

32.801 32.751 32.720 32.667 32.655 32.867 32.818 32.784 32.732 32.683

117.651 117.758 117.813 117.900 117.974 117.682 117.767 117.849 117.936 118.016

9y18 9y18 9y18 9y18 9y18 9y19 9y19 9y19 9y19 9y19

0658 0907 1055 1405 1645 0657 0908 1133 1324 1513

87 58 36 42 72 87 65 35 33 47

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Table 2. Lidar Transmitter and Receiver Parameters

Parameter Transmitter Wavelength Pulse length Pulse energy Pulse repetition rate Beam divergence Receiver Aperture diameter Focal length Field of view Optical bandwidth Electronic bandwidth Sample rate

Value 532 nm 15 ns 67 mJ 10 Hz 43 mrad 17 cm 36.7 cm 26 mrad 10 nm 100 MHz 1 GHz

parameters, a is the lidar attenuation coefficient, d is depth, h is the height of the lidar above the water, and n is the index of refraction of water. Equation ~1! neglects the change in the overlap function with depth. This function represents the loss in signal because the laser-illuminated area is larger than the area observed by the receiver or because the observed area is larger than the illuminated area at a particular depth. Thus it is always a factor less than unity in the equation for the lidar signal. If we consider only the geometric factors for our lidar, this factor decreases by approximately 22% when we vary from a depth of 10 m to a depth of 30 m. This would produce an error of only approximately 6% in our estimate of the attenuation coefficient. However, the geometric calculation does not take in account the fact that both the illumination and the observed area are spread out by waves on the surface and by multiple scattering. Both of these effects tend to equalize the illuminated area and the observed area in ways that are difficult to calculate. Because of the difficulty of the calculation and the small error produced in the estimate of the attenuation coefficient, we chose to neglect the effects of changes in the overlap function with depth. A typical lidar trace is presented in Fig. 2. This particular shot was for parallel polarization. The detector was triggered at a depth of 5 m. There is some ringing of the signal when the detector is first turned on, and this region was not used in the analysis. The peak at approximately 12 m is an artifact of the trigger circuit; it is consistent throughout the data and was also not used in the analysis. The smooth line is a fit of Eq. ~1! plus a background component to the data by use of three points along the curve. For this case, the amplitude parameter C was 4730 V m2, the lidar attenuation coefficient was 0.109 m21, and the background level was 3.39 mV, which corresponds to 2.6 dB in Fig. 2. The data and the curve agree fairly well. This agreement was typical and suggests that the lidar attenuation coefficient was not a strong function of depth in this region. Data were collected in 1-min segments. A portion of that time was used for data storage and a back-

Fig. 2. Typical lidar signal S as a function of depth d with detector triggered at 5 m. Peak at approximately 12 m is an artifact of the detector trigger.

ground light measurement. This left 500 lidar pulses of useful data from each segment. Two segments of each polarization were recorded at each station. For each lidar pulse, the return waveform was analyzed to obtain the three parameters discussed in the above paragraph. The background levels were small and consistent from pulse to pulse. The amplitude varied significantly from pulse to pulse because of surface losses. The average variability for all stations was 35%, with individual values ranging from 27% at station 11 to 46% at station 9. However, the mean values over 1000 pulses should be accurate to approximately 1%, assuming that the fluctuations of the surface are independent from pulse to pulse. The pulse-to-pulse fluctuations in the inferred attenuation coefficient were much smaller, with an average value of 6.8% for the 10 stations. 3. In Situ Packages

Two packages with in situ optical measurements were lowered into the water at each station. One was a NOAA package that included a SeaTech 25-cm transmissometer, a SeaTech light-scattering sensor, and a Chelsea Aquatrak fluorometer. The other was a Scripps package that included a Biospherical Instruments underwater radiometer, a second SeaTech 25-cm transmissometer, a WetLabs Wetstar fluorometer, and a second SeaTech light-scattering sensor. Each package also had standard conductivity, temperature, and pressure instruments. Figure 3 is a plot of the profiles of temperature and salinity for station 7 from the NOAA package. It shows a surface temperature of 20.9° and a surface salinity of 33.29 parts per thousand. These values are nearly constant in a surface mixed layer that extends to a depth of approximately 20 m. Below 20 m, the temperature decreases. The salinity decreases to a minimum at a depth of approximately 20 May 1998 y Vol. 37, No. 15 y APPLIED OPTICS

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Fig. 3. Depth ~d! profiles of temperature T and salinity S measured at station 7.

40 m and increases again at deeper levels. These characteristics were typical of all 10 stations. Figure 4 includes a plot of the profile of the beam attenuation coefficient at 532 nm as taken from the NOAA transmissometer at station 8. This instrument measures the transmission at a wavelength of 660 nm. To shift to an equivalent value at 532 nm, we use the results of an empirical relationship by Voss16: c~532 nm! 5 1.18c~660 nm! 2 0.419.

(2)

The beam attenuation coefficients generally show a fairly constant level in the top 20 m, increasing to a peak near 50 m. These features are present in Fig. 4, although there are differences in the details. The depths of the mixed layer inferred from the temperature profiles and those inferred from the beam attenuation coefficient profiles were generally about the same. Diffuse attenuation was measured with the

Fig. 5. Lidar signal amplitude C as a function of beam attenuation c measured at a depth of 20 m. The points are labeled by station number; stations in the first transect are denoted by filled circles connected by a solid line, and points in the second transect are denoted by filled squares connected by a short dashed line. The long dashed line is a linear regression between the two quantities.

532-nm channel of the Scripps radiometer. The rate of change of the radiance with depth was calculated with a moving window. The result was multiplied by the cosine of the solar incidence angle to estimate what the diffuse attenuation would be with the Sun at zenith. Gordon et al.17 use the quasi-singlescattering approximation to show that this corrected attenuation coefficient can be considered to be an inherent property of the medium. We use this adjusted value for the diffuse attenuation coefficient K. At stations 7, 11, and 12, the Sun incidence angle was greater than 70°; these data are not used. At the other stations, there was a problem with the slip rings on this package, and the data are somewhat sparse. The data from station 8, shown in Fig. 4, are typical. The light-scattering sensor was designed to provide a measure of particulate concentration. The output from this instrument was highly correlated with the beam attenuation coefficient ~correlation coefficient of 91%!. The correlation between the diffuse attenuation and either of the other two quantities was not as good ~66% with c and 56% with scattering sensor output!. 4. Lidar Signals

The lidar signal amplitude C is plotted as a function of the measured beam attenuation c at a depth of 20 m in Fig. 5. Here C is the total return; it is the sum of the copolarized and the cross-polarized values. We can see that the signal generally decreases with increasing beam attenuation. The notable exceptions are at stations 12 and 16, which are at opposite ends of the second transect. The long dashed line is a linear regression through the points. The equation is Fig. 4. Depth ~d! profiles of beam attenuation c and diffuse attenuation K with a solar-angle correction factor. 3108


C 5 219,800c 1 5370,

(3)

Fig. 6. Polarization P as a function of estimated scattering coefficient b. The points are labeled by station number; stations in the first transect are denoted by filled circles connected by a solid line, and points in the second transect are denoted by filled squares connected by a dashed line.

with a correlation coefficient of 55%. The negative slope of the relationship suggests that more particles in the water lead to a larger beam attenuation coefficient, which leads to a lower lidar signal amplitude. The correlation between the lidar signal at 20 m and the beam attenuation at 20 m was higher; the value was 82%. The polarization P is defined here as P5

Cco 2 Cx , Cco 1 Cx

(4)

where Cco and Cx are the copolarized and crosspolarized signal amplitudes. This is the ratio of the second Stokes parameter to the first. The values for the ten stations are plotted as a function of scattering coefficient b in Fig. 6. Because we did not have a direct measurement of the scattering coefficient, it had to be inferred from either another in situ measurement or the lidar measurement. The latter method provided the more consistent results. Specifically, we used Eq. ~3! as a calibration curve to obtain an estimate of the beam attenuation coefficient from the lidar amplitude and subtracted the absorption coefficient ~0.0517 m21 at 532 nm from Smith and Baker18! to obtain an estimate of the scattering coefficient. For higher scattering coefficients, the polarization decreases with increasing scattering as one would expect. This depolarization does not seem to occur until the scattering coefficient reaches a value of approximately 0.1 m21. At lower scattering values, the polarization seems to level off at a value between 0.9 and 0.95. A laboratory measurement of the polarization of the receiver produced a value of approximately 0.95. The most likely cause of this residual depolarization is probably multiple reflections of initially copolarized light within the receiver.

Fig. 7. Attenuation coefficient of the copolarized lidar return aco as a function of the beam attenuation coefficient c measured at a depth of 20 m. The points are labeled by station number; stations in the first transect are denoted by filled circles connected by a solid line, and points in the second transect are denoted by filled squares connected by a short dashed line. The long dashed line is a linear regression between the two quantities.

5. Lidar Attenuation

The measured attenuation coefficients for the two polarizations were about the same. One might expect that multiple scattering would remove photons from the copolarized component of the beam and add them to the cross-polarized component as the beam propagates down through the water. This mechanism would tend to make the copolarized attenuation greater than the cross-polarized attenuation. However, for many of the stations, the cross-polarized signal was probably dominated by copolarized light that was partially depolarized within the receiver. This leaves only a few stations with significant depolarization caused by scattering in the water. No significant difference in the attenuation coefficients for the two polarizations were observed at any of these stations. Figure 7 is a plot of the lidar attenuation coefficient for the copolarized signal as a function of the beam attenuation coefficient, as measured by the SeaTech transmissometer at a depth of 20 m, at the 10 stations where measurements were made. The correlation, approximately 88%, is clear from the figure. The long dashed line is the best linear fit through the points and is given by a 5 0.217c 1 0.0671.

(5)

It is interesting that, despite the good correlation between the lidar attenuation coefficient and the measured beam attenuation coefficient, the slope of the line relating them is not unity; a seems to vary much less than c. The transmissometer does not measure beam attenuation coefficient exactly, however, because of difficulties in rejecting light scattered at small angles. It actually has a field of view of approximately 31 mrad, which lies between the beam divergence angle and receiver field of view of our lidar. From this we 20 May 1998 y Vol. 37, No. 15 y APPLIED OPTICS

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Fig. 8. Correlation coefficient r of the lidar return at a depth of 20 m with the return at depth d for the data of station 7.

would expect the lidar attenuation coefficient and the beam attenuation coefficient to be closer to the same value than we observed. The correlation between the lidar attenuation coefficient and the adjusted diffuse attenuation coefficient was not as high. For the seven stations with solar angles less than 70°, the linear regression is given by a 5 0.406K 1 0.0709,

(6)

with a correlation of 68%. It is also interesting to look at the mean values of these quantities because we were able to sample only a rather limited range of water types during this cruise. The mean value for the lidar attenuation coefficient was 0.098 m21 ~0.096 m21 for the seven stations with lower Sun angles!. The mean beam attenuation coefficient was significantly higher at 0.134 m21. The mean value of the adjusted diffuse attenuation coefficient was significantly lower at 0.061 m21. It is interesting that, for our geometry, the lidar attenuation is nearly equal to the average of the beam attenuation and the adjusted diffuse attenuation. However, the variations about these mean values are much smaller for the lidar attenuation coefficient than for either the beam attenuation coefficient or the adjusted diffuse attenuation coefficient. 6. Lidar Signal Fluctuations

The primary source of fluctuations in the lidar signal seems to be surface waves. The main evidence for this conclusion is the high degree of correlation of the fluctuations at different depths for each shot. Figure 8 is a plot of the correlation r of the signal at a depth of 20 m with the signal at other depths for the data of station 7. The correlation is high ~above 90%! for depths from the shallowest signals available to approximately 30 m, except for the detector artifact at approximately 12 m. At depths below 30 m, the signal levels are lower, and the relative effects of noise are greater. This leads to a decrease in the correlation because the noise is uncorrelated. 3110


Fig. 9. Normalized lidar signal variance s2 as a function of depth d for station 7.

Despite the high correlation, the relative fluctuation level generally decreases with depth. This feature is also seen in modeled downwelling irradiance fluctuations19 and in measurements of downwelling solar irradiance.20,21 The relative fluctuation level is most conveniently characterized by the normalized variance, which we denote by s2; it is the variance of the signal level divided by the square of the mean signal level. This quantity is plotted as a function of depth for station 7 data in Fig. 9. The high variance feature just below 15 m in depth is an artifact of the receiver. Except for a peak at depths of approximately 17 and 23 m, the normalized variance generally decreases with depth until approximately 33 m, at which point the signal becomes very small and the noise effects become important. For sunlight, McLean19 suggests that the downwelling irradiance fluctuations become smaller with depth because of a decreasing population of waves with long focal lengths and because of multiple scattering. The latter probably dominates in the lidar case. The temporal autocorrelation of the signal at a depth of 20 m is presented in Fig. 10. The filled circles represent the data points at 0.1-s intervals. Following Ref. 21, we assume that the correlation function is an exponentially decaying cosine representative of a band-limited process. The solid curve in the figure is the best fit of such a functional form to the data. The equation is r 5 exp~22.23t!cos~9.13t!,

(7)

where t is the time delay. If we neglect the drift of the ship, we can convert the temporal wave number 9.13 s21 into a spatial wave number of 8.51 m21 using the deep-water dispersion relation.22 This implies that the surface wave that contributes most effectively to the fluctuations is one with a wavelength approximately three times the lidar spot size at the surface. It is interesting to compare the lidar autocorrelation with that of sunlight as reported by Fraser et

Fig. 10. Temporal autocorrelation coefficient r as a function of time delay t for the lidar return from a depth of 20 m at station 7. The filled circles represent the measured values at integer multiples of the 0.1-s pulse spacing. The solid curve is Eq. ~7!.

al.21 Based on their measurements and those of Snyder and Dera20 and of Prokopov et al.,23 they found that the peak frequency ~in hertz! of the autocorrelation function decreases with depth as 2d21y2. This decrease is because longer waves are contributing to the fluctuations at greater depths. For the lidar, the most effective surface wavelength is determined by the lidar spot size, and the measured angular frequency decreased by only 1.6% between a depth of 15 m and a depth of 30 m. Our value of 1.45 Hz corresponds to natural sunlight at a depth of approximately 1.9 m. The relaxation time constant for natural sunlight increases with depth; this increase is approximated by21 0.1d; the longer waves that are effective at greater depths have longer coherence time. The time constant for the lidar decreases slightly with increasing depth, although the decrease from 15 to 30 m is only approximately 20%. Thus the lidar value in Eq. ~7! corresponds to the relaxation time for natural sunlight at a depth of approximately 4.48 m. One might expect this to be more constant with depth because the same surface wavelength seems to be contributing to the fluctuations at all depths. McLean19 has evaluated lidar fluctuations with a Monte Carlo simulation. He concludes that the variance of the fluctuations will decrease with increasing spot size at the surface. This is consistent with our finding that the most effective surface wave is related to the spot size on the surface. It is also consistent with the results, from studies of natural sunlight fluctuations that the variance decreases with depth because the most effective surface wave in this case increases with increasing depth. McLean concludes that the standard deviation of a lidar return would be approximately 10% of the mean return for a surface spot diameter of 5 m and a wind of 8 m s21. Our results suggest a standard deviation of approximately 20% for a smaller spot size in light and variable winds. Although this does not constitute a direct comparison, these results are consistent.

Fig. 11. Copolarized lidar attenuation coefficient aco as a function of the lidar amplitude C for half of the data ~one file! of station 9. The open circles represent the data, and the solid line is Eq. ~8!.

The fluctuations of the lidar attenuation coefficient were also measured. These turned out to be highly correlated with the lidar signal amplitude, as shown in Fig. 11. This is a plot of the copolarized attenuation coefficient as a function of the copolarized lidar amplitude parameter for the data of station 9. The solid line is a logarithmic regression given by aco 5 5.25 3 1023 ln~C! 2 2.89 3 1023.

(8)

The correlation of the two quantities is 97%. This suggests that the larger lidar returns are attenuated more rapidly with depth. Thus the larger returns are probably more collimated, whereas the weaker returns are spread in angle by the surface. Note that this short-term relationship, caused by the effects of surface waves, is different from the effect of moving into waters with different properties and averaging the lidar signal. The waves cause larger returns to be more rapidly attenuated. Conversely, moving to a water mass with a greater beam attenuation coefficient produces more rapid attenuation of the lidar, but with a lower signal amplitude. 7. Conclusions

There are several conclusions to be drawn from this research. Under the conditions of these measurements, the lidar attenuation coefficient is highly correlated with in situ measurements of the optical properties of the water, especially the measured beam attenuation coefficient. However, a limited variation in the water properties was available during this cruise. Further measurements should be made to investigate the correlation under a much wider range of water types. Despite the high correlation, the lidar attenuation coefficient was not equal to the beam attenuation coefficient or to the Sunangle-corrected diffuse attenuation coefficient. Also, the attenuation coefficient did not seem to depend on the polarization of the receiver; both the copolarized and the cross-polarized signals had the same attenuation at the same location. 20 May 1998 y Vol. 37, No. 15 y APPLIED OPTICS

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The depolarization of the signal itself depends on the scattering coefficient for values larger than approximately 0.1 m21. This particular value probably depends on the laser divergence and receiver field of view, and further investigations should be performed. The fluctuations in the lidar signal are primarily because of the refractive effects of surface waves whose wavelengths are approximately three times the lidar spot diameter at the surface. This result is probably independent of the laser beam divergence. This paper was generated as part of a joint NOAA– U.S. Department of Defense Advanced Sensor Applications Program. We thank Dan Higgins for data processing software, Ken Bliss for collecting and helping to interpret the data from the NOAA in situ package, Greg Mitchell for providing diffuse attenuation data from the Scripps in situ package, and the officers and crew of the RyV David Starr Jordan for their excellent support during the cruise.

9.

10. 11.

12.

13.

14.

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