Robust approach to directly measuring water-leaving radiance in the field

doi:10.1364/AO.52.001693

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Robust approach to directly measuring water-leaving radiance in the field

ZhongPing Lee, Nima Pahlevan, Yu-Hwan Ahn, Steven Greb, and David O’Donnell »View Author Affiliations

Applied Optics, Vol. 52, Issue 8, pp. 1693-1701 (2013)
http://dx.doi.org/10.1364/AO.52.001693

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Abstract

It has been a long-standing goal to precisely measure water-leaving radiance ( $L_{w}$ , or its equivalent property, remote-sensing reflectance) in the field, but reaching this goal is quite a challenge. This is because conventional approaches do not provide a direct measurement of $L_{w}$ , but rather measure various related components and subsequently derive this core property from these components. Due to many uncontrollable factors in the measurement procedure and imprecise post-measurement processing routines, the resulting $L_{w}$ is inherently associated with various levels of uncertainties. Here we present a methodology called the skylight-blocked approach (SBA) to measure $L_{w}$ directly in the field, along with results obtained recently in the Laurentian Great Lakes. These results indicate that SBA can measure $L_{w}$ in high precision. In particular, there is no limitation of water types for the deployment of SBA, and the requirement of post-measurement processing is minimum; thus high-quality $L_{w}$ for a wide range of aquatic environments can be acquired.

1. Introduction

Spectral water-leaving radiance (

L_{w}

μW / {cm}^{2} / nm / sr

), or its equivalent, spectral remote-sensing reflectance (

R_{rs}

{sr}^{- 1}

, which is defined as the ratio of

L_{w}

to downwelling irradiance just above the surface (

E_{d} (0^{+})

μW / {cm}^{2} / nm

), is a core property for optical oceanography. Subsurface properties, such as inherent optical properties or chlorophyll concentration, as well as bottom properties of optically shallow waters, are all derived by inverting the

R_{rs}

spectrum [1

IOCCG, “Remote sensing of ocean colour in coastal, and other optically-complex, waters,” in Reports of the International Ocean-Colour Coordinating Group , No. 3, S. Sathyendranath, ed. (IOCCG, 2000).

IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications,” in Reports of the International Ocean-Colour Coordinating Group , No. 5, Z.-P. Lee, ed. (IOCCG, 2006), p. 126.

]. Separately, properties of

L_{w}

are key in validating those that are derived from airborne or spaceborne sensors and systems [3

H. Gordon, “In-orbit calibration strategy for ocean color sensors,” Remote Sens. Environ. 63, 265–278 (1998). [CrossRef]

D. K. Clark, M. A. Yarbrough, M. Feinholz, S. Flora, W. Broenkow, Y. S. Kim, B. C. Johnson, S. W. Brown, M. Yuen, and J. L. Mueller, “MOBY, a radiometric buoy for performance monitoring and vicarious calibration of satellite ocean color sensors: measurement and data analysis protocols ,” NASA Tech. Memo. 2004-211621 (NASA, 2003).

K. J. Voss, S. McLean, M. Lewis, C. Johnson, S. Flora, M. Feinholz, M. Yarbrough, C. Trees, M. Twardowski, and D. Clark, “An example crossover experiment for testing new vicarious calibration techniques for satellite ocean color radiometry,” J. Atmos. Ocean. Technol. 27, 1747–1759 (2010). [CrossRef]

P. J. Werdell, S. W. Bailey, B. A. Franz, A. Morel, and C. R. McClain, “On-orbit vicarious calibration of ocean color sensors using an ocean surface reflectance model,” Appl. Opt. 46, 5649–5666 (2007). [CrossRef]

G. Zibordi, J.-F. Berthon, F. Mélin, D. D’Alimonte, and S. Kaitala, “Validation of satellite ocean color primary products at optically complex coastal sites: Northern Adriatic Sea, Northern Baltic Proper and Gulf of Finland,” Remote Sens. Environ. 113, 2574–2591 (2009). [CrossRef]

–8

C. R. McClain, W. E. Esaias, W. Barnes, B. Guenther, D. Endres, S. B. Hooker, G. Mitchell, and R. Barnes, “Calibration and validation plan for SeaWiFS ,” NASA Tech. Memo. 104566, Vol. 3, S. B. Hooker and E. R. Firestone, eds. (NASA, 1992), p. 41.

]. Furthermore,

L_{w}

values within the red/near-infrared (800–1000 nm) and shortwave infrared (1000–2500 nm) bands, progressively assumed to be zero for different loads of suspended materials, are used in the atmospheric correction process [9

H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978). [CrossRef]

H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]

M. Wang, “Remote sensing of the ocean contributions from ultraviolet to near-infrared using the shortwave infrared bands: simulations,” Appl. Opt. 46, 1535–1547 (2007). [CrossRef]

–12

K. G. Ruddick, F. Ovidio, and M. Rijkeboer, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Appl. Opt. 39, 897–912 (2000). [CrossRef]

]. Because of such critical importance, measurement of spectral

L_{w}

in the field has been carried out for more than five decades, and generally three approaches have been developed and implemented [13

D. A. Toole, D. A. Siegel, D. W. Menzies, M. J. Neumann, and R. C. Smith, “Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability,” Appl. Opt. 39, 456–469 (2000). [CrossRef]

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, and S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004 , J. L. Mueller and G. S. Fargion, eds. (NASA, 2002), pp. 171–182.

–15

J. L. Mueller, G. S. Fargion, and C. R. McClain, Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4 (NASA, 2003).

]. Table 1 summarizes the advantages and drawbacks of these schemes, while the following provides a brief description of each approach.

Scheme 1 (S1): Measure all relevant properties from an above-surface platform, and then calculate $L_{w}$ by removing surface-reflected light.
Scheme 2 (S2): Measure the vertical profiles of upwelling radiance ( $L_{u} (z)$ ) within the water column, mathematically propagate these measurements upward toward the sea surface, and then across the surface to get $L_{w}$ .
Scheme 3 (S3): Measure $L_{u} (z)$ a few centimeters below the surface, and then mathematically propagate $L_{u} (z)$ across the surface to obtain $L_{w}$ .

Table 1. Summary of the Conventional Schemes in Obtaining

L_{w}

in the Field

	Advantages	Limitations
S1: Above-surface method	Can be used in any environment; no self-shading	Measures $L_{T}$ in the air, not $L_{w}$ ; includes surface-reflected light, requires sophisticated postprocessing to correct surface-reflected light.
S2: In-water profiling method	Avoids surface-reflected light	Measures $L_{u}$ , not $L_{w}$ ; slight self-shading; requires sophisticated postprocessing to derive $L_{w}$ ; difficult to extrapolate upwelling radiance at a depth to surface for waters that are stratified or with a shallow bottom (e.g., kelp fields)
S3: Surface floating method	Avoids surface-reflected light	Measures $L_{u}$ , not $L_{w}$ ; slight self-shading; requires careful postprocessing to $L_{w}$

All of these schemes are easily implementable in the field, but they never measure

L_{w}

directly, which leads to nonnegligible uncertainties associated with

L_{w}

produced by these schemes [13

,16

S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Ocean. Technol. 17, 811–830 (2000). [CrossRef]

]. As discussed in numerous studies, when estimating

L_{w}

using method S1, it is quite a challenge to accurately remove the surface-reflected light when the sea surface is roughened by waves, where the reflected light includes both sky and sun glint [13

,17

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt. 38, 7442–7455 (1999). [CrossRef]

,18

G. Zibordi, F. Mélin, S. B. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42, 401–415 (2004). [CrossRef]

]. The effective reflectance of the sea surface is highly wavelength- and data-collection-dependent [13

,19

Z.-P. Lee, Y.-H. Ahn, C. Mobley, and R. Arnone, “Removal of surface-reflected light for the measurement of remote-sensing reflectance from an above-surface platform,” Opt. Express 18, 26313–26342 (2010). [CrossRef]

,20

D. Doxaran, R. C. N. Cherukuru, and S. J. Lavender, “Estimation of surface reflection effects on upwelling radiance field measurements in turbid waters,” J. Opt. Pure Appl. Opt. 6, 690–697 (2004). [CrossRef]

]. The S2 method involves delicate data processing to derive the appropriate attenuation coefficient in order to propagate

L_{u} (z)

to the surface [21

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic bio-optical profiling system,” Appl. Opt. 23, 2791–2797 (1984). [CrossRef]

]. More importantly, for highly turbid waters or vertically stratified waters, it is very difficult to achieve an accurate estimation of the attenuation coefficient for this propagation [22

G. Zibordi, D. D’Alimonte, and J. F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. Atmos. Ocean. Technol. 21, 1059–1073 (2004). [CrossRef]

]. For S3, because the measurement is

L_{u} (z)

, it requires propagating

L_{u} (z)

(where

z

is typically 10–50 cm) to

L_{u} (0 -)

. Further, for both S2 and S3,

L_{u} (0 -)

has to be subjectively propagated to

L_{w}

by assuming values about the refractive index of water and the cross-surface reflectance [23

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

]. Consequently, various levels of uncertainties are associated with the calculated

L_{w}

even if each component is measured perfectly. In this study, we demonstrate a hybrid approach that measures

L_{w}

directly, and show that the approach can achieve high-precision measurement of

L_{w}

in the field.

2. Approach to Directly Measuring $L_{w}$

To maximize the advantages while avoiding the drawbacks associated with the traditional measurement schemes (S1–S3), a hybrid scheme was first utilized by Ahn [24

Y.-H. Ahn, “Development of redtide & water turbidity algorithms using ocean color satellite,” 1999, KORDI Seoul, Korea, p. 287.

]. This method, which collects upwelling radiance from a position above the sea surface while effectively blocking surface-reflected light with an apparatus, measures

L_{w}

directly in the field. The concept and strategy of this skylight-blocked approach (SBA) is presented in Fig. 1. The whole system includes a radiometer and a black cone (see Fig. 2, left panel). The cone is attached to the sensor with its open end inserted just below the surface, while the radiometer maintains a position in the air (see Fig. 2, right panel); thus the measured property by the radiometer is

L_{w}

. In such a setup, the below-surface

L_{u} (0 -)

propagates to

L_{w}

naturally and surface-reflected light is blocked mechanically, thus removing two post-measurement processing steps that introduce uncertainties in the traditional schemes.

Fig. 1. Schematic draw to show the concept of measuring

L_{w}

directly in the field. The cone is integrated with a radiometer to block surface-reflected light, with its open end inserted just below (

\sim 5 cm

) the surface when measuring

L_{w}

Fig. 2. (Left) Cone and radiometer. (Right) The system is deployed in the field.

The cone used in our system, which was custom manufactured to fit the HyperOCR radiometer (Satlantic, Inc.), has a diameter 9.8 cm and a height 10.1 cm, optimized not to interfere with the field of view of HyperOCR (11.5°) while minimizing the effect of self-shading [25

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanog 37, 491–500 (1992). [CrossRef]

]. Integrated with the Satlantic HyperPro Profiler, the system floats on the sea surface and can be deployed well away from the boat to avoid its interference to the light field. This SBA is especially useful for vertically stratified waters or coastal environments including kelp beds shallow bottoms, where it is difficult to obtain a viable profile of

L_{u} (z)

for the propagation. More importantly, because this SBA avoids the complicated postprocessing in deriving

L_{w}

, significantly less uncertainty is anticipated in the field-measured

L_{w}

spectrum. The second-order effects from slight self-shading can be corrected (in preparation), as shown in Gordon and Ding [25

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanog 37, 491–500 (1992). [CrossRef]

] and Leathers et al. [26

R. A. Leathers, T. V. Downes, and C. D. Mobley, “Self-shading correction for upwelling sea-surface radiance measurements made with buoyed instruments,” Opt. Express 8, 561–570 (2001). [CrossRef]

3. Field Measurements

Recently, we deployed a HyperOCR (350–800 nm,

\sim 3 nm

resolution) via the SBA to measure

L_{w}

in the zenith direction in Lake Michigan and Green Bay (June 25–28, 2012). Concurrent with the

L_{w}

measurements, another HyperOCR irradiance radiometer was used to measure downwelling irradiance just above the surface (

E_{d} (0 +)

). The right panel in Fig. 2 shows the two radiometers, with the one in the red circle for the measurements of

L_{w}

via SBA. A total of 19 stations were surveyed (see Fig. 3 for locations), with sea surface ranging from calm (

< 1^{'}

wave height) to rough (

\sim 2^{'} - 3^{'}

wave height) conditions. Sun angle varied in a range of

\sim 20 ° - 50 °

from zenith, and one-third of the stations had a sky covered with scatter clouds. The stations covered waters with a wide range of variability in biogeochemical properties, as indicated by the spectral

R_{rs}

(see Fig. 4), which were derived from

L_{w}

and

E_{d} (0 +)

spectra measured simultaneously and averaged for each station. The coefficient of variation (CV) of all measured

R_{rs}

ranges from

\sim 50 %

(at 530 nm) to

> 80 %

(for UV and red-infrared wavelengths).

Fig. 3. Stations surveyed in Lake Michigan and Green Bay, June 2012.

Fig. 4.

R_{rs}

spectra of the 19 stations measured via SBA.

Along with the measurements via SBA, concurrent measurements of

L_{u} (z)

were made following the profiling scheme (S2). For this deployment (two stations were omitted, so S2 covered 17 stations), radiometric measurements were made with a HyperPro II profiling system (Satlantic, Inc.), where one HyperOCR measures

L_{u} (z)

, another HyperOCR measures

E_{d} (z)

, and a third HyperOCR located on deck measures solar irradiance above the water surface (

E_{d} (0 +)

). The profiler freefalls through the water column with a descending rate at

\sim 25 cm / s

, and three back-to-back (triplicates) profiles were measured at each station.

Both systems were tethered from a small boat at least

\sim 20 m

away, and the two systems were

\sim 20 m

apart.

Also measured for each station were the total absorption and beam attenuation coefficients in the upper water column with the ac-s system (Wetlabs, Inc.), which was calibrated with DI-water and lowered into water by the side of the operating boat. The total absorption coefficient at 440 nm spanned a range of

0.13 - 0.7 m^{- 1}

, while the beam attenuation coefficient at 660 nm ranged

0.26 - 0.9 m^{- 1}

. The vertical profiles of these data did not show significant stratification of optical properties in the upper water column (20 m) during this experiment.

4. Data Processing

A. $L_{w}$ Measurements via SBA

In addition to applying common data-processing procedures (e.g., application of calibration coefficient, tilt-angle based filtering), the

L_{w}

data collected via SBA went through two extra quality-control processes.

First, there are two situations in which the data collected via SBA could be contaminated, and both may happen when the sea surface is under rough conditions. One situation is where the radiometer (along with the cone) is submerged below the sea surface; then the collected data represents upwelling radiance at a depth a few centimeters below the surface (

L_{u} (z)

), which may approximate the upwelling radiance just below the surface (

L_{u} (0 -)

). The other situation is where the entire cone swings above the sea surface; then the data collected represents upwelling radiance above the surface (

L_{T}

). Data collected under these two conditions do not represent

L_{w}

and should be removed.

In this step of data processing, which is aimed at removing the contaminated data mentioned above, the higher values in each set of

L_{w}

measurement were identified and filtered out. This is achieved by calculating the median (

μ

) and standard deviation (

σ

) of

L_{w}

for wavelengths (

λ

) longer than 750 nm of each

L_{w}

set, and the spectrum with a spectrally averaged value for

λ

between 750 and 800 nm greater than (

μ + 3 σ

) was considered contaminated and removed. This is based on the following general relationship:

L_{T} (λ) = L_{w} (λ) + L_{g} (λ)

(1)

and

L_{w} (λ) = \frac{t}{n^{2}} L_{u} (λ, 0 -)

(2)

with

L_{g}

the surface-reflected light (including glints from both sky and solar light).

t

is the transmittance,

n

the refractive index of seawater, and

t / n^{2} \approx 0.54

[23

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

,27

R. W. Austin, “Inherent spectral radiance signatures of the ocean surface,” in Ocean Color Analysis , S. W. Duntley, ed. (Scripps Institution of Oceanography, 1974). pp. 1–20.

From Eqs. (1) and (2), we have

L_{w} < L_{u} (0 -)

and

L_{w} < L_{T}

. Therefore, the high values in each set of

L_{w}

measurement represent

L_{u} (0 -)

L_{T}

. Also, because

L_{w}

is generally very small in the longer wavelengths for most aquatic environments [28

H. R. Gordon and D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981). [CrossRef]

], the use of information of wavelengths longer than 750 nm makes it easier to identify surface-reflected light. Figure 5 shows an example where outliers [the red (top) line] are detected and removed from further processing. For this station, there were 63 valid

L_{w}

spectra after applying tilt filtering (Satlantic, Inc.), one spectrum was further removed based on the above procedure, and the mean of the remaining 62 spectra was calculated to represent the water-leaving radiance of this station. Also showing in Fig. 5 is the spectrum of CV of this station (calculated as the ratio of standard deviation to the mean at each spectra band) from the remaining 62

L_{w}

spectra. Although we kept

> 98 %

of the original data, the CV is generally within 10% for the 400–700 nm range (more discussions regarding CV are presented in Section 5.B). In our datasets collected during June 2012, on average less than 3% of the measured spectrum at each station was discarded following the above process, indicating that nonaggressive filtering of the data was processed for results in this study.

Fig. 5. Example showing

L_{w}

spectra collected by HyperOCR through SBA. The red (top) line (1 out of 63 spectra) was considered as an outlier and excluded for further processing and calculation. Also shown is the spectrum of CV (right

Y

axis) of the remaining 62

L_{w}

spectra.

Second, as a first-order self-shading correction, the formula developed by Gordon and Ding [25

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanog 37, 491–500 (1992). [CrossRef]

] was used to account for the instrument shading effects associated with SBA. Basically, self-shading is modeled as a function of absorption coefficient and sun-zenith angle [25

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanog 37, 491–500 (1992). [CrossRef]

], and the concurrent measurement of total spectral absorption by the ac-s system (covers 405–720 nm) was used for this correction. While the instrument configuration in our study was not identical to that modeled by Gordon and Ding [25

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanog 37, 491–500 (1992). [CrossRef]

], it is expected that the analytical approach accounts for self-shading impacts at least to the first order.

B. $L_{w}$ Collection from Vertical Profiles

Processing of measurements from the profiler followed the protocol and software (ProSoft version 7.7.16_6, the most recently generally available release) provided by Satlantic, Inc. Basically, for each profile measurement, least-square regression was carried out between the logarithm-transferred

L_{u} (z)

and

z

(generally within 20 m depth) for measurements in the upper water column [13

,21

R. C. Smith, C. R. Booth, and J. L. Star, “Oceanographic bio-optical profiling system,” Appl. Opt. 23, 2791–2797 (1984). [CrossRef]

], resulting in an intercept and slope, with the former providing the logarithm of

L_{u} (0 -)

and the latter representing the diffuse attenuation coefficient of

L_{u} (z)

(

K_{L u}

). The mean and standard deviation of

L_{u} (0 -)

were calculated from the three back-to-back profiles for each station. We used 0.5 m bins with 0.1 m depth interpolation for this processing. We also explored using a smaller bin size, but found no systematic change in the resulting

L_{u} (0 -)

and its CV. The water-leaving radiance

L_{w}

is then calculated using Eq. (2). No self-shading correction was applied to profiling data since there are no known methods yet to accurately correct the vertically varying self-shading effects. This is also due to the fact that the biggest impact of applying this shading correction will be on the derived value of

L_{u} (0 -)

of each profile, not on the CV of

L_{u} (0 -)

when analyzing the three profiles. And the focus of this study is the precision in the measurement of

L_{w}

, which is measured by its CV; thus omitting the self-shading correction in the processing of

L_{u} (z)

is appropriate here.

5. Results

A. Comparison of Overall $L_{w}$ Spectrum

As an example, Fig. 6 shows spectral

L_{w}

obtained from the SBA and the profiling (S2) scheme. The comparison is limited to wavelengths in the range of 405–720 nm, as that is the range where self-shading correction was applied to SBA-measured

L_{w}

. Apparently, both schemes produced quite consistent

L_{w}

, although the

L_{w}

from SBA is roughly

\sim 11 %

lower than that from S2 for this station. For all 17 coincidental stations, on average, the mean

L_{w}

of each station obtained from the two schemes is very consistent [see Fig. 7(a)]. The coefficient of determination (

R^{2}

) is 0.98, with a slope of 1.005 (

L_{w}

from S2 is slightly larger) and close to 0 interception.

Fig. 6. Example to compare the

L_{w}

spectra measured via SBA and profiling.

Fig. 7. (a) Statistic relationship between SBA-measured and pro-measured

L_{w}

, for wavelength in the range of 405–720 nm. (b) Percentage difference (PD) between SBA-measured (

SBA_L_{w}

) and pro-measured (

Pro_L_{w}

)

L_{w}

. PD is defined as

2 (SBA_L_{w} - Pro_L_{w}) / (SBA_L_{w} + Pro_L_{w})

. AAPD stands for the average of the absolute value of PD, while ASPD stands for the average of the signed PD.

To further evaluate the two

L_{w}

datasets, the percentage difference (PD) between the SBA-measured

L_{w}

(

SBA_L_{w}

) and the profile-measured

L_{w}

(

Pro_L_{w}

) for each band of each station is calculated as

PD (λ) = \frac{2 (SBA_L_{w} (λ) - Pro_L_{w} (λ))}{(SBA_L_{w} (λ) + Pro_L_{w} (λ))} .

(3)

Figure 7(b) presents the spectra of the average of the absolute value of PD (AAPD), and of the average of the signed value of PD (ASPD), respectively, of the 17 stations. Apparently, for this experiment, larger difference or uncertainty (

\sim 20 %

) exists at both shorter (

\sim 400 nm

) and longer (

\sim 700 nm

) wavelengths, and

SBA_L_{w}

is generally lower than

Pro_L_{w}

except at the longer wavelengths. For the transparency window where

L_{w}

values are much higher than those at the two spectral ends (see Fig. 5, for example), however, the

L_{w}

values from the two systems are quite close (

< 10 %

difference), echoing the difficultly in obtaining confident measurement of

L_{w}

in the field when its value is small [18

,29

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: a field assessment experiment,” J. Atmos. Ocean. Technol. 19, 808–819 (2002). [CrossRef]

It is difficult to determine which system provided a more accurate measurement of

L_{w}

during this experiment, because the

L_{w}

values from both systems contain some levels of errors. First, radiometric calibration of the two radiometers was not completed simultaneously; some drifting in the calibration coefficient of either sensor or both could contribute to the difference. Second, the two systems had different self-shading effects, where one happens near the sea surface, while the profiling system experiences shading in the entire profiling process and no shading correction was applied to the

L_{u} (z)

data. And third, there are always uncertainties when propagating

L_{u} (z)

L_{w}

. Nevertheless, the quite consistent

L_{w}

values shown in Fig. 7(a) suggest that, on average,

L_{w}

obtained from both systems is valid.

B. Comparison of $L_{w}$ Precision

Although it is useful and necessary to check the consistency of

L_{w}

measured from different systems/schemes [13

,16

S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Ocean. Technol. 17, 811–830 (2000). [CrossRef]

,30

S. B. Hooker, G. Lazin, G. Zibordi, and S. D. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19, 486–515 (2002). [CrossRef]

], it is equally or more important to know how precise each measured

L_{w}

spectrum is. To obtain an objective characterization of this precision (or stability) of

L_{w}

measured via SBA, we calculated the CV spectrum of each station as shown in Fig. 8, and then the average and standard deviation of these CV spectra. As a preliminary contrast and comparison, the same calculations were carried out on the data obtained via the profiling system (S2). As an example, Fig. 8 compares the CV spectra resulting from SBA and from S2 to the

L_{w}

spectra presented in Fig. 6. For this station, CV from the SBA measurement is 3%–5% for wavelengths in the range of 350–600 nm (or

L_{w} > 0.06 μw / {cm}^{2} / nm / sr

), while the CV from the S2 measurement is 3%–10% for the same spectral range. For the 600–750 nm range, CV of

L_{w}

from S2 is generally 30% higher than that from SBA. This is partially because in the longer wavelengths the light attenuates significantly with the increase of depth due to the high absorption coefficient of water molecules; thus it is difficult to maintain high-precision measurement of such low light. Although higher CV is generally expected when

L_{w}

is approaching zero, this example demonstrates that for the same range of

L_{w}

, CV from the SBA is systematically smaller than that from the profiling.

Fig. 8. Example to compare the spectral CV of

L_{w}

measured via SBA and profiling. Also shown is the

L_{w}

spectrum (right

Y

axis) of this station.

To further highlight the significantly better precision of SBA-measured

L_{w}

, Figs. 9(a) and 9(b) show the mean spectral CV (along with its standard deviation) of the 17 coincidental stations from the two schemes, respectively. For

L_{w}

from SBA, the averaged CV is below 5% for wavelengths in the range of 400–650 nm [Fig. 9(a)]; however it is 10%–40% when

L_{w}

is obtained from S2 [Fig. 9(b)]. For the shorter (350–400 nm) and longer (650–750 nm) wavelengths where

L_{w}

values are quite low for these measurements, the averaged CV (350–400 nm) remains below 10% when

L_{w}

was measured via SBA, but it is greater than 30% when

L_{w}

was derived from profiles, and the CV (650–750 nm) of

L_{w}

from profiles is generally twice the CV (650–750 nm) when

L_{w}

was measured via SBA. Furthermore, for

L_{w}

measured via SBA, most (greater than 67%) of its CV values are within 5%, but only

\sim 30 %

of its CV values are within 5% when

L_{w}

was determined from profiles (see Fig. 10). All of these results indicate that SBA indeed achieved high-precision measurement of

L_{w}

in the 350–700 nm range, at least for waters and sea states in this experiment. Note that because of the repetitive measurements at each station, not only could the average value of

L_{w}

be derived and reported, but also could the associated uncertainty (e.g., Fig. 8) of the measured

L_{w}

—and the latter is an important measure of the quality of reported

L_{w}

Fig. 9. (a) Averaged spectrum of CV of all stations. Dotted green curve provides crude information of the

L_{w}

(SBA measured) encountered, as there is a wide range of variation. (b) Averaged CV spectrum of

L_{w}

measured from profiles. Also included (blue dots) is the mean CV spectrum from SBA for easier comparison.

Fig. 10. Distribution of the CV of

L_{w}

measured via SBA and profiling, respectively. Wavelength range is 350–720 nm.

This high-precision measurement of

L_{w}

via SBA is important in the determination of

R_{rs}

, as it is not a must to have radiometrically accurate

L_{w}

for its derivation. When a calibrated reference panel is used in the process [14

,30

,31

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanog. 30, 286–298 (1985). [CrossRef]

], measurements of

L_{w}

in relative units instead of absolute radiometric units is sufficiently reliable for the determination of

R_{rs}

. In such a setup, the precision rather than the accuracy of

L_{w}

measurement is more important, and the accuracy of

R_{rs}

will depend on the accuracy of the reference panel used to measure

E_{d} (0 +)

[14

,31

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanog. 30, 286–298 (1985). [CrossRef]

,32

D. Doxaran, N. C. Cherukuru, S. J. Lavender, and G. F. Moore, “Use of a Spectralon panel to measure the downwelling irradiance signal: case studies and recommendations,” Appl. Opt. 43, 5981–5986 (2004). [CrossRef]

] when all other aspects of measurements are well handled.

6. Discussion and Future Perspective

Spectral water-leaving radiance (

L_{w}

), or spectral remote-sensing reflectance (

R_{rs}

), plays a critical role in ocean optics and ocean-color remote sensing.

L_{w}

(or

R_{rs}

) is the property required for validation of ocean-color satellite systems (from sensor calibration to atmospheric correction), the input for the retrieval of subsurface properties and constituents, and a property to evaluate the closure of the relationship between inherent and apparent optical properties. All these tasks demand accurate determination of

L_{w}

in the field, and it is not surprising to see more than five decades of acquisition of

L_{w}

and continued improvement in instrumentation and data-processing methods. But the long-standing goal of achieving better than 5% accuracy of

L_{w}

[33

S. Hooker and W. E. Esaias, “An overview of the SeaWiFS project,” Eos 74, 241–246 (1993).

] is hardly achieved [13

,30

]. This is due to the following: (1)

L_{w}

is not a stable property in the field because of rough sea surface [34

J. R. V. Zaneveld, E. Boss, and P. A. Hwang, “The influence of coherent waves on the remotely sensed reflectance,” Opt. Express 9, 260–266 (2001). [CrossRef]

], unless the environmental condition is perfect (flat surface, clear sky, and stable water property); and (2) the conventional approaches do not obtain a direct measurement of

L_{w}

. Hooker and Maritorena [16

S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Ocean. Technol. 17, 811–830 (2000). [CrossRef]

] presented within 5% consistency of

L_{u} (0 -)

between in-water deployments, but were limited to measurements of oceanic waters, at local noon, and in the 412–555 nm spectral range. When comparing measurements between in-water and above-water strategies, Zibordi et al. [29

] indicated that the difference is

\sim 10 %

for 440 and 550 nm and more than 20% for 670 nm, and the difference reduced to

\sim 5 %

for the 412–555 nm range for clearer waters [18

]. Also note that these results provide a measure of consistency for two datasets, not necessarily the precision of each individual

L_{w}

spectrum.

Unlike laboratory measurements where almost all aspects of an experiment can be precisely controlled, field measurements of

L_{w}

are inherently subject to various disturbances that are out of the control of an operator. These aspects include rough sea surface, randomly distributed and moving clouds, a stratified upper water column, and wave-induced light focusing, just to name a few. As a result, even if all relevant components could be measured precisely, the spectral

L_{w}

determined via methods listed in Table 1 still contains various degrees of uncertainties, and the ground “truth” of

L_{w}

is elusive. Specifically, for

L_{w}

determined via S1, it is unavoidable that surface-reflected light will be introduced into the measured signal, which has to be removed properly before

L_{w}

can be determined [35

G. Zibordi, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, F. Melin, J.-F. Berthon, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppala, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26, 1634–1651 (2009). [CrossRef]

]. Mobley [17

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt. 38, 7442–7455 (1999). [CrossRef]

] introduced a simple formula along with a spectrally flat surface-reflectance value (varying with wind speed and viewing angle though). This is more appropriate for overcast sky conditions [13

], where the light quality from various angles is nearly the same (i.e., the spectral shape from different directions can be considered identical with negligible error), but could be troublesome for clear-sky days [19

,20

], where the light from overhead is quite bluer than the light from the horizon. To mitigate this limitation, Zibordi et al. [18

] suggested to aggressively filter out large values and focus on the lower 20% of data measured from an above-surface platform. By using a slightly different formula for this correction [14

,31

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanog. 30, 286–298 (1985). [CrossRef]

], Lee et al. [19

,36

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, and J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996). [CrossRef]

] used a more sophisticated processing method to remove the contaminations. In this process, the correction involves two terms: one uses the product of Fresnel reflectance and the reciprocally measured skylight to remove the primary portion of the surface contribution; the other uses a bias to account for the residual contribution and is derived iteratively through optical modeling. Nevertheless, these procedures cannot completely remove surface-reflected light, as the contribution is highly dependent on surface texture, sky-light distribution, as well as the instrument’s integration time, and the former two aspects are out of our control.

A significant advantage of S2 is that not only can

L_{u} (0 -)

be calculated from the vertical profiles of

L_{u} (z)

and

E_{d} (z)

, but also the vertical distribution of absorption and backscattering coefficients [37

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009). [CrossRef]

]. For the purpose of determining

L_{w}

, however, this scheme runs into difficulty if the upper water column is stratified, or the water is extremely turbid, or the bottom is quite shallow and/or with seagrass/kelp, situations that make it difficult to extrapolate measurements at a depth to below the surface. In addition,

L_{u}

in the longer wavelengths at deeper depths may include more relative contributions from inelastic scattering [38

A. Morel and B. Gentili, “Radiation transport within oceanic (case 1) water,” J. Geophys. Res. 109, C06008 (2004). [CrossRef]

,39

B. R. Marshall and R. C. Smith, “Raman scattering and in-water ocean properties,” Appl. Opt. 29, 71–84 (1990). [CrossRef]

], and thus contributes more uncertainties to the determination of

L_{u} (0 -)

. Furthermore, the calculated

L_{u} (0 -)

has to be subjectively propagated through the interface to get

L_{w}

, a step that will introduce some uncertainties.

S3 is a plausible approach for determination of

L_{w}

in the field [40

K. J. Voss and A. L. Chapin, “Upwelling radiance distribution camera system, NURADS,” Opt. Express 13, 4250–4262 (2005). [CrossRef]

,41

K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010). [CrossRef]

], as it can effectively avoid difficulties introduced by surface-reflected light and difficulties in obtaining the accurate vertical profiles required by S2. However, no matter how close the sensor is to the surface, the measured signal is not

L_{w}

, but

L_{u} (z)

, which has to be propagated via models through the air–water interface for determination of

L_{w}

. Uncertainties will be introduced in this calculation process.

The scheme to directly measure

L_{w}

via SBA, although might not be optimized at this point, clearly shows great promise and advantages for accurately measuring

L_{w}

in the field. In particular, it significantly reduces the requirement of post-measurement processing, thus making the data product “measured,” instead of “calculated.” It avoids surface-reflected light through a mechanical design, measures

L_{w}

propagating through the interface naturally, and is not limited for environments that are either stratified or with a shallow bottom. Measurement via SBA offers an opportunity to get the ground “truth” of

L_{w}

in the field, a goal hardly achieved so far.

The most likely source of uncertainty in the field measurement via SBA comes from two situations: (1) the sensor is submerged into water, and (2) the entire cone rises above the surface. Our results indicate that these contaminations can be quite effectively removed, as both situations would measure significantly higher values [see Eqs. (1) and (2)]. In our data processing here we removed less than 3% of the measured spectra, kept

\sim 97 %

of the lower values, and achieved

\sim 5 %

precision. Much higher precision is thus expected if we filter out data more aggressively (say 40%), but an objective decision on this criterion requires more modeling studies as well as experience with field data. This is also because

L_{w}

in the field is inherently not a constant value even in a short time scale. Because of wave-introduced roughness,

L_{w}

measured at different times could be slightly different due to wave focusing or variation in the observation angle [42

J. R. V. Zaneveld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001). [CrossRef]

,43

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters (2): bi-directional aspects,” Appl. Opt. 32, 6864–6879 (1993). [CrossRef]

]. This variation is highlighted in Fig. 11, where the CV spectrum of the SBA-measured

L_{w}

is separated into two groups: one CV spectrum for data collected under prime condition, i.e., when the water surface was calm (wave height

< 2^{'}

) while the sky is clear; and another CV spectrum for conditions not prime. As expected, the CV of SBA-measured

L_{w}

under prime condition is systematically smaller (in a range of 2%–5% for the 370–650 nm band) than that under nonprime condition. However, even for the SBA-measured

L_{w}

obtained under tough situations, the overall uncertainty is still in a range of 5%–10% for the 370–650 nm band, and that is under the current data-processing scheme (e.g., no screening of clouds). We expect this precision to improve after we carry out more experiments and gain more experience and understanding of the measurement scheme.

Fig. 11. Averaged CV spectrum of SBA-measured

L_{w}

; the blue curve is for data under prime measurement conditions and the green curve is for data under nonprime conditions. Prime condition is defined here as calm surface (

< 2^{'}

wave) and clear sky.

The major challenge in accurately measuring

L_{w}

via SBA is to minimize the self-shading introduced by the cone as well as by the floating structure, although such shading could be modeled to some degree based on radiative transfer [25

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanog 37, 491–500 (1992). [CrossRef]

,26

,44

J. P. Doyle and G. Zibordi, “Optical propagation within a three-dimensional shadowed atmosphere-ocean field: application to large deployment structures,” Appl. Opt. 41, 4283–4306 (2002). [CrossRef]

]. Note that self-shading of SBA is positively related to the size of the cone. Minimizing self-shading thus requires a small field of view and a small aperture for the radiometer, as these two factors dictate the size of the cone. It will also require a small floating collar and a longer arm between the sensor and the collar, in order to reduce the intrusion of the system into the light field to be measured by the radiometer.

The scheme of measuring

L_{w}

via the SBA also opens the door to taking cost-effective long-term measurement of

L_{w}

right on the surface, which is important in obtaining a large volume of data either for calibration/validation of satellite systems or for the study of biogeochemistry. A serious challenge in long-term field deployment in a marine environment is bio-fouling. One strategy to avoid bio-fouling is to establish the AERONET-OC network [35

,45

G. Zibordi, B. Holben, S. B. Hooker, F. Mélin, J.-F. Berthon, and I. Slutsker, “A network for standardized ocean color validation measurements,” Eos 87, 297 (2006).

], where all sensors are above the surface. But

L_{w}

through this system is determined via S1, where some contaminations due to surface-reflected light will not be avoidable [13

,17

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt. 38, 7442–7455 (1999). [CrossRef]

,18

]. With the SBA strategy, the sensor will remain in the air, and the bio-fouling will likely happen on the surface of the cone, which might effectively reduce the impact of bio-fouling on the sensor and then on data quality. But this requires dedicated effort to study and characterize the effects and to optimize the design and setup. When a mature and successful setup is available, it could significantly improve the quality and volume of

L_{w}

by taking measurements right on the surface. In addition, it could improve the earlier generation of optical drifters [46

M. R. Abbott and R. M. Letelier, “Decorrelation scales of chlorophyll as observed from bio-optical drifters in the California Current,” Deep-Sea Res. 45, 1639–1667 (1998). [CrossRef]

] for continuous monitoring of water masses at low cost.

7. Conclusions

It is critical to achieve precise and accurate measurement of water-leaving radiance (or remote-sensing reflectance) in the field, and numerous advances in technology have been achieved in recent decades for this goal. The SBA shown here measures water-leaving radiance directly, and achieves high-precision results in the field. This SBA is easily deployable not only in oceanic waters, but also in challenging environments such as shallow waters. Measurement via SBA provides the closest results to the ground truth of water-leaving radiance, and this will certainly aid in achieving the goal of measuring

L_{w}

in the field within 5% uncertainty under normal measurement conditions. The results shown here, however, are limited to a few water types and mild sea states. Extensive tests and experiments with SBA in various aquatic environments and sea states in the coming years will not only help the maturation of this measurement approach, but will also provide significant help in the advancement of hydro-optics and ocean (water) color remote sensing.

Acknowledgments

We thank Wesly Goode of the Naval Research Lab for helping set up the SBA system, Christopher Strait, Mike Twardowski, and Colleen Mouw for helping the field experiment, and Captain Richard C. Pagel of the R/V Gaylord Nelson for professional assistance. Financial support from NASA (Ocean Biology and Biogeochemistry, Energy and Water Cycle, and Applied Sciences programs) and the JPSS VIIRS Ocean Color Cal/Val Project is greatly appreciated. Comments and suggestions from two anonymous reviewers greatly improved this manuscript. This is contribution 309 of the Upstate Freshwater Institute.

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11.	M. Wang, “Remote sensing of the ocean contributions from ultraviolet to near-infrared using the shortwave infrared bands: simulations,” Appl. Opt. 46, 1535–1547 (2007). [CrossRef]
12.	K. G. Ruddick, F. Ovidio, and M. Rijkeboer, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Appl. Opt. 39, 897–912 (2000). [CrossRef]
13.	D. A. Toole, D. A. Siegel, D. W. Menzies, M. J. Neumann, and R. C. Smith, “Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability,” Appl. Opt. 39, 456–469 (2000). [CrossRef]
14.	J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, and S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3, NASA/TM-2002-210004 , J. L. Mueller and G. S. Fargion, eds. (NASA, 2002), pp. 171–182.
15.	J. L. Mueller, G. S. Fargion, and C. R. McClain, Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4 (NASA, 2003).
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18.	G. Zibordi, F. Mélin, S. B. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42, 401–415 (2004). [CrossRef]
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32.	D. Doxaran, N. C. Cherukuru, S. J. Lavender, and G. F. Moore, “Use of a Spectralon panel to measure the downwelling irradiance signal: case studies and recommendations,” Appl. Opt. 43, 5981–5986 (2004). [CrossRef]
33.	S. Hooker and W. E. Esaias, “An overview of the SeaWiFS project,” Eos 74, 241–246 (1993).
34.	J. R. V. Zaneveld, E. Boss, and P. A. Hwang, “The influence of coherent waves on the remotely sensed reflectance,” Opt. Express 9, 260–266 (2001). [CrossRef]
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36.	Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, and J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996). [CrossRef]
37.	H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009). [CrossRef]
38.	A. Morel and B. Gentili, “Radiation transport within oceanic (case 1) water,” J. Geophys. Res. 109, C06008 (2004). [CrossRef]
39.	B. R. Marshall and R. C. Smith, “Raman scattering and in-water ocean properties,” Appl. Opt. 29, 71–84 (1990). [CrossRef]
40.	K. J. Voss and A. L. Chapin, “Upwelling radiance distribution camera system, NURADS,” Opt. Express 13, 4250–4262 (2005). [CrossRef]
41.	K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010). [CrossRef]
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45.	G. Zibordi, B. Holben, S. B. Hooker, F. Mélin, J.-F. Berthon, and I. Slutsker, “A network for standardized ocean color validation measurements,” Eos 87, 297 (2006).
46.	M. R. Abbott and R. M. Letelier, “Decorrelation scales of chlorophyll as observed from bio-optical drifters in the California Current,” Deep-Sea Res. 45, 1639–1667 (1998). [CrossRef]

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: December 5, 2012
Revised Manuscript: February 3, 2013
Manuscript Accepted: February 6, 2013
Published: March 7, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics
March 22, 2013 Spotlight on Optics

Citation
ZhongPing Lee, Nima Pahlevan, Yu-Hwan Ahn, Steven Greb, and David O’Donnell, "Robust approach to directly measuring water-leaving radiance in the field," Appl. Opt. 52, 1693-1701 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-8-1693

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References

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OpticsInfoBase

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

Robust approach to directly measuring water-leaving radiance in the field

Article Tools

Article Navigation

Abstract

1. Introduction

2. Approach to Directly Measuring $L_{w}$

3. Field Measurements

4. Data Processing

A. $L_{w}$ Measurements via SBA

B. $L_{w}$ Collection from Vertical Profiles

5. Results

A. Comparison of Overall $L_{w}$ Spectrum

B. Comparison of $L_{w}$ Precision

6. Discussion and Future Perspective

7. Conclusions

Acknowledgments

References

References

Appl. Opt.

Deep-Sea Res.

Eos

IEEE Trans. Geosci. Remote Sens.

J. Atmos. Ocean. Technol.

J. Geophys. Res.

J. Opt. Pure Appl. Opt.

Limnol. Oceanog

Limnol. Oceanog.

Opt. Express

Remote Sens. Environ.

Other

Cited By

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OpticsInfoBase

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

Robust approach to directly measuring water-leaving radiance in the field

Article Tools

Article Navigation

Abstract

1. Introduction

2. Approach to Directly Measuring L w

3. Field Measurements

4. Data Processing

A. L w Measurements via SBA

B. L w Collection from Vertical Profiles

5. Results

A. Comparison of Overall L w Spectrum

B. Comparison of L w Precision

6. Discussion and Future Perspective

7. Conclusions

Acknowledgments

References

References

Appl. Opt.

Deep-Sea Res.

Eos

IEEE Trans. Geosci. Remote Sens.

J. Atmos. Ocean. Technol.

J. Geophys. Res.

J. Opt. Pure Appl. Opt.

Limnol. Oceanog

Limnol. Oceanog.

Opt. Express

Remote Sens. Environ.

Other

Cited By

Figures

2. Approach to Directly Measuring $L_{w}$

A. $L_{w}$ Measurements via SBA

B. $L_{w}$ Collection from Vertical Profiles

A. Comparison of Overall $L_{w}$ Spectrum

B. Comparison of $L_{w}$ Precision