a. The field campaign

The Productivité des Systèmes Océaniques Pélagiques (PROSOPE) cruise was designed to study the productivity of pelagic oceanic systems as a contribution to the Joint Global Ocean Flux Study (JGOFS)–France Program. The campaign was on board the research vessel Thalassa (74.5 m length, 13.9 m breadth, and 6.2 m draught), and started in Agadir, Morocco, on 4 September 1999 and ended in Toulon, France, on 4 October. The cruise track began with a detailed study (3 days) in the productive upwelling zone off the northwest African coast and ended within the much less productive Mediterrranean Sea waters (Fig. 1a). The latter included 5-day studies of an ultra-oligotrophic regime in the Eastern Mediterranean (southwest of Crete) and a mesotrophic site in the Ligurian Sea (northwest of Corsica). In between the long-duration sites, nine daily stations were sampled over 4-h periods centered around noon.

In addition to the usual determinations of JGOFS core parameters and other biochemical studies, extensive optical sampling was executed, particularly around and during the overpass of the SeaWiFS instrument. A part of this program was devoted to the upward radiance measurements, to the comparison of the above- and in-water methods, and to the evaluation of the difficulties associated with attaining the desired radiometric accuracy, specifically in the vicinity of a large sampling platform. One above-water and two in-water systems were used for these inquiries (Figs. 1b–1d, respectively): (a) the Low-Cost National Aeronautics and Space Administration (NASA) Environmental Sampling System (LoCNESS), (b) the SeaWiFS Free-Falling Advanced Light Level Sensors (SeaFALLS), and (c) the SeaWiFS Surface Acquisition System (SeaSAS).

The environmental conditions during the cruise were generally good, even exceptional in terms of sky condition and cloud cover, as well as in terms of the sea state and ambient wind (Table 1). The chlorophyll a data for the upper layer (everywhere Case-1 conditions) spanned two orders of magnitude (0.032–3.75 mg m⁻³). The large range in chlorophyll a concentration, along with the diversity in optical measurements, makes the PROSOPE dataset well suited for investigating a variety of challenging bio-optical problems.

b. Objectives

The SeaBOARR-98 conclusions were based on three favorable days of useful data. From these data, four methods for correcting above-water observations intracompared at the 8% level, and they intercompared with three methods for processing the in-water data at the 9% level (Hooker et al. 2002a), although radiometric agreement at the 5% level was achieved in some circumstances. The methods selected for the PROSOPE cruise are a subset of SeaBOARR-98 and will be described later. Based on this previous experience, the optical sampling objectives for the PROSOPE cruise were as follows: (a) use two in-water profilers and one analysis method to compute L_W(λ) from in-water data, (b) use one above-water measurement system, and two surface glint correction methods to compute L_W(λ) from above-water data, and (c) use radiometers with a common calibration history to minimize intercalibration uncertainties. In addition, the PROSOPE analysis plan was designed to overcome some deficiencies acknowledged during the SeaBOARR-98 experiment and also included (i) intercomparing the above- and in-water methods in Case-1 waters and in deep ocean conditions, (ii) a correction scheme for the bidirectional effects at the sea surface, and (iii) identifying the origin, and quantifying the significance of, perturbations caused by the sampling platform and environmental conditions on the surface radiance field.

The magnitude of the perturbations in the proximity of a large structure is a recurring problem, which is made more complex according to the sun orientation with respect to the structure. These perturbations differentially influence the data obtained by the above- and in-water methods. For example, from the perspective of the in-water light field, investigations within 15–20 m of an offshore tower showed significant effects of the structure: approximately 3%–8% for clear-sky conditions, and as much as 20% under overcast conditions (Zibordi et al. 1999). Similar levels of uncertainties were estimated for in-water measurements from a ship (Voss et al. 1986).

For above-water measurements (recalling that the radiometer is never pointed into the ship's shadow), the perturbations are a combination of three possible effects: (a) the shadow cast by the vessel outside the field of view of the sensor, but within the attenuation pathlengths defined by the inherent water properties; (b) the interaction of the upward (in-water) radiant field with the submerged hull; and (c) the reflections off the sea surface from the interaction between the downward (above-water) radiant field and the exposed superstructure. The latter is expected to be the most important for above-water measurements, because the sun and sky are the light sources for the final perturbation and they are significantly more intense than the in-water radiant field (as shown later in Fig. 3).

a. Calibration and stability

Calibration stability over the course of a campaign is potentially an important source of variance in instrument comparisons involving individual channels (Hooker and Aiken 1998; Hooker and Maritorena 2000). For SeaWiFS field campaigns, the stability of the instruments is usually monitored with the SeaWiFS Quality Monitor, but it was not possible to use this instrument during PROSOPE. The above- and in-water instruments, however, were calibrated before and after the cruise without significant change (i.e., less than 2%).

In situ measures of instrument stability are possible by taking advantage of instrument redundancy. The likelihood that two independent sensor systems would change in exactly the same manner is assumed to be extremely unlikely, so a favorable comparison of the data from two independent instruments is a suitable demonstration of the intercalibration and stability of the sensors. For the in-water sensors, this opportunity is provided by the simultaneous deployments of the two in-water profiling systems which can be radiometrically compared at all wavelengths over the entire cruise period. Although duplicate above-water systems were not deployed, the spectral stability of the sea-viewing sensor, which was also used to measure a Spectralon plaque, can be compared to the incident solar irradiance measured with the solar reference. These stability analyses are presented below (section 6a).

b. Sampling coregistration

Simple geometric calculations show that the spectral coregistration, based on the manufacturer's specification of the SeaSAS field of view, is above the 98% level from a height of 16.5 m. The mismatch would become significant (less than 90% of mutual coverage) only if the target distance is less than 2.0 m, for example, if sampling were conducted from a very small boat. For the present experiments, it has been verified that the peaks and troughs for each channel are temporally coherent and in phase with one another, so the rejection procedure and the temporal masking are fully justified. An example time series confirming the coregistration of the channels is presented in Fig. 2.

a. In-water (S84) method

From the L_u(λ, z) near-surface profiles, the attenuation coefficient K_L(λ, z₀) is computed as the local (around the depth z₀) slope of ln[L_u(λ, z)]. Then K_L(λ, z₀) is used to extrapolate the upward radiance through the upper layer to determine L_u(λ, 0⁻) at null depth. The water-leaving radiance is then obtained using (3′). Because there is only one processing method, the in-water data are distinguished by the measurement systems (LN or SF as superscripts for LoCNESS and SeaFALLS, respectively).

b. Above-water (M80 and S95) methods

Above-water data processing consists of removing the contamination term, ΔL in (5), which adds to the marine signal and originates from reflections at the air–sea interface. The sky radiance reflected off the wave-roughened surface is a priori at the origin of the ΔL signal, but as shown later on, reflected radiation from the sampling platform is another source of contamination. Even if only the sky reflection is considered, its contribution to L_T is always important. For Case-1 waters in the near-infrared domain (e.g., at 780 and 865 nm), where the sea is essentially black, this contribution amounts to 100%, and then decreases toward shorter wavelengths where the diffuse ocean reflectance departs from zero (see discussion below with Fig. 3). In Case-2 waters, particularly when the sediment load is high, the water reflectance may deviate from zero in the near infrared and contribute to ΔL.

The M80 glint correction method is based on the existence of a black target in the near-infrared region. For all of the PROSOPE data, 865 nm is the reference infrared wavelength λ_r. The above-water radiance measured at λ_r is entirely due to surface reflection, and this estimate is extended over the whole spectrum by using the spectral dependence of the incident sky radiance L_sky(λ) measured in the direction appropriate for reflection from the sea surface. Estimated glint is subtracted from the total signal to recover L_W(λ), according to

View Expanded

It is important to note the following: (a) in turbid Case-2 waters, the L_W(λ_r) = 0 assumption often fails and this method is not universally applicable [see Hooker et al. (2002a) for a case example]; (b) if other contaminating reflections play a part (such as those originating from the ship), they are captured when measuring L_T(λ_r); and (c) these other contaminations have a spectral composition which may (and generally do) differ from that of the sky radiance used in (9), when the correction is extended throughout the visible spectrum.

The S95 method makes use of the same set of measurements, but they are used differently. The glint is removed through a constant interface reflectance factor ρ, which is applied to the spectral sky radiances according to

View Expanded

The reflectance factor ρ would be the Fresnel reflectance averaged over the field of view of the detector pointed in the θ direction, Ω_FOV, if the interface was level. Generally, this is not the case, so ρ depends on the capillary wave slopes, and, thus, on wind speed (Austin 1974; Mobley 1999). The wavelength dependence originates from the normal dispersion of the refractive index of water, which is weak and can be neglected. It is worth noting an extra source of reflected light (e.g., from the ship) is, by definition, assumed negligible when using the S95 method.

The original specifications for S95 recommended a pointing angle θ = 20° from nadir (Mueller and Austin 1995). Radiative transfer simulations above a wave-roughened surface from Mobley (1999) showed a superior angle was 40°, and that a preferred azimuth angle was 135°. With these viewing angles, the reflectance factor ρ amounts to 0.028 for W < 5 m s⁻¹, and increases up to about 0.04 when W = 15 m s⁻¹. The majority of the PROSOPE data were collected with an ambient wind close to 5 m s⁻¹ (the average wind speed for the SeaSAS casts used in this study was 5.3 m s⁻¹), so the S95 results were produced using ρ = 0.028. A separate analysis of the data using a variable ρ produced no appreciable changes in the results (the average variable ρ value was 0.029).

Above-water signals from two contrasting situations are shown in Fig. 3; also shown are examples of the spectral L_W(λ) values, as retrieved by applying the M80 and S95 methods. Although the L_T(λ) and ρL_sky(λ) values converge at 865 nm in these instances, this is not always the case, as discussed later on.

Another important point is the variable contribution of ρL_sky(λ) to L_T(λ). In Fig. 3a, dealing with clear sky and blue oligotrophic water, the sky contribution in the visible part of the spectrum is maximal (about 40%) at 555 nm, and then decreases (about 20%) for blue (412–443 nm) radiation. In contrast, Fig. 3b corresponds to a situation with hazy overcast (but bright) sky and low reflecting chlorophyll-rich waters, and ρL_sky(λ) represents about 75% of the total signal in the whole visible part of the spectrum. Note also that the incident solar irradiance peaks around 490 nm, so contamination from solar reflections (which can occur off the ship's superstructure, as discussed below) spectrally differs from reflected sky radiation, at least when the sky is not hazy and whitish.

c. Method revisions

All of the above-water data were collected using commonsense procedures. In particular, foam and floating material were avoided, and no data collection was initiated unless the solar disc was unobscured by clouds (and expected to remain so for several minutes) and the sky was also cloud free within a wide solid angle around the pointing angle of the sky sensor. For some days, respecting these constraints required a considerable amount of time.

Because this study is concerned with artificial perturbations from the sampling platform that affect the natural radiation field of the upper ocean, it is appropriate to consider the primary difference between how the above- and in-water methods sample the upper ocean. The effective surface area associated with an in-water estimate of L_W(λ), derived from a vertical profile of L_u(z, λ), is many times larger than the surface spot viewed by the above-water sensor. Surface wave effects are, therefore, effectively averaged within the in-water data, but are expressed primarily as discrete events in the above-water data. This is one possible source of a methodological bias between the two approaches, and it places a special burden on the above-water data collection and processing; that is, the sampling time must adequately capture surface variability effects, so they can be properly dealt with during data processing.

In reference to (5), the L_T signal actually results from the superposition of three contributions: (a) the steady water-leaving radiance L_W; (b) the sky glint, and possibly other reflections, ΔL, usually slowly varying with the period of the waves and swell; and (c) the mostly random, sharp, sun glint outliers produced by capillary waves. Note that even when the radiometer is pointed at least 90° away from the vertical solar plane, bright flashes from the latter occur (Fig. 2), but this third term is not identified in (5) because the sun glint spikes are removed from the high frequency spectra with the use of an appropriate filtering technique. The periodic variations of the sky glint are removed from the low frequency spectra.

Only the S95 method included a glint filter as part of the protocol. This filter, plus eight others, were evaluated by Hooker et al. (2002a) They concluded the most effective filter consisted of selecting the lowest 5% of the data in terms of radiance in the near-infrared bands, and then to use this selection as a temporal mask for all data at other wavelengths. This very high rejection rate (95% of the data recorded during each cast) was adopted for the processing of all PROSOPE data. This is an admittedly restrictive protocol that is probably more severe than most of those in common use, which are often based on some averaging and less selective procedures.

d. Statistical parameters

Three sources of L_W(λ) estimates are available, two from in-water instruments and one from above-water measurements. Although a large number of casts were collected for each instrument, only data collected simultaneously by the three instruments are used in the following analyses to minimize any source of extraneous variance. No single method is presumed more correct than the other, so an unbiased percent difference (UPD), ψ^A_B, between two methods (A and B) providing L_W(λ) estimates is defined as

View Expanded

for example, the UPD between the water-leaving radiances at 412 nm estimated with the M80 and S95 methods is ψ^M80_S95(412).

The relative percent difference (RPD) between two data products is computed as

View Expanded

For the RPD computations, the B method must be an appropriate reference value, and in this study, it is usually an in-water measurement.

Average percent differences, formed by binning the data over a subset of N casts are denoted by the so-called bar accent: δ^S95_LN(412) are the average RPD values between L^S95_W(412) and L^LN_W(412) for a subset of the total (simultaneous) dataset. Note that in all the percent differences, there is an implicit normalization with respect to the illumination conditions, because a ratio of radiance levels from two independent systems is always used.

a. Above- and in-water intracomparisons

The agreement between the in-water profilers during clear-sky conditions is presented in Fig. 4. The L_W values, regardless of wavelength, are well distributed with respect to the 1:1 line, and the histogram (inset panel) shows there is approximately a 2% bias between the two datasets. This agreement is very close to the sensor calibration uncertainty, estimated to be 1.5%–2.0% (Hooker et al. 2002b). Despite the absence of independent monitoring, it can be concluded that the performances of both sensor systems were very stable during the entire cruise period. Given this excellent level of agreement, and the fact that the majority of the in-water sampling during clear-sky conditions was with the LoCNESS profiler, the L^LN_W(λ) values are hereafter considered as reference, or sea-truth, values.

During clear-sky conditions on seven different occasions spanning six days, the sea-viewing (L_T) sensor was used to measure a calibrated gray Spectralon plaque. The irradiance values calculated for the plaque, E_p(λ), can be intracompared to the incident solar irradiance measured with the solar reference, E_d(0⁺, λ). Although the magnitudes of the two measures are expected to be biased (gray plaques have higher calibration uncertainties from the added doping material, and the near proximity of the sea-viewing sensor loads the plaque with reflections), the spectral shape of the plaque irradiance should agree well with the solar reference. The intracomparison is made by normalizing all wavelengths by the value at 510 nm (the nominal peak in solar illumination). The uncertainty (and standard deviation), calculated using the RPD formulation 100[E_p(λ) − E_d(0⁺, λ)]/E_d(0⁺, λ), is estimated to be 2.4% (2.0%) for the spectral range 412–555 nm.

b. Glint correction comparisons

As a consequence of the principles involved in their formulations, a comparison of the output of the M80 and S95 correction methods allows the detection of any ship contamination in the L_T signal. This is because the M80 method is sensitive to, and thus, is able to identify, a ship perturbation, whereas the S95 method, based on a theoretical value of the reflectance factor, will just ignore it. The presence of a ship perturbation can be detected with the ratio

View Expanded

where the numerator comes from M80 in (9) and the denominator from S95 in (10). Under normal circumstances, that is, in the absence of a ship perturbation, r(865) = 1, within the accepted variance (and provided that ρ is given a correct value). Any other reflected radiation added to the sky-reflected radiation will lead to r(865) > 1, and the departure from unity is an estimate of this effect.

In Fig. 5, the r(865) values are plotted as a function of α_s, that is, the pointing angle of the above-water sensors with respect to the perpendicular to the ship's centerline. Although the total SeaSAS dataset is composed of 137 casts (Table 1), 9 were excluded because of sampling problems (e.g., unanticipated cloud interference, ship movement during the cast, etc.). The remaining 128 casts provide a good distribution of data with respect to α_s, and show that when the instrument is pointed perpendicular to the side of the ship (α_s = 0), the r(865) values are a little larger than 1, which suggests a reduced contamination by the ship. As the radiometers are pointed more and more toward the bow or stern, that is when the distance from the ship to the surface spot decreases, r(865) dramatically increases, reaching values as high as 4–5 when α_s ≈ ±60°. These large ratios indicate the radiation reflected by the surface and seen by the sensor is largely dominated by that originating from the superstructure.

These high values, however, are not observed in a systematic manner. For example, when α_s = 40° or 60°, r(865) values span the interval 1–5, which deserves another kind of analysis involving γ_s, that is, the angle between the centerline of the ship and the position of the sun (Fig. 5, inset panel). According to the sign of γ_s, the port side of the ship (where the above-water radiometers were installed) is, or is not, illuminated by the sun, which makes a difference in the intensity (and spectral composition) of the light reflected from the superstructure. In Fig. 6, the r(865) values shown in Fig. 5 are plotted as a function of γ_s, and five categories of data in terms of binned |α_s| values are identified.

The first important observation from the Fig. 6 data is that r(865) is close to 1 under overcast conditions, whatever the sun orientation. Under a clear sky, r(865) remains close to 1, when the sun is to starboard and the superstructure from which SeaSAS was operated is in shadow (−120° > γ_s > −180°). The converse holds true when the sun is to port (120° < γ_s < 180°), and the side of the ship where SeaSAS was measuring is directly illuminated. When γ_s is small, and the sun is almost aligned with the bow, the r(865) values vary widely.

In conclusion, the contamination by the ship is reduced when the side from which the sensor is operated is in shadow, so that the superstructure is only illuminated by the sky radiation (or by uniform clouds); the contamination increases when the port side is sunlit, or if the bridge is sunlit (when γ_s is small). The geometrical aspect of the contamination is not surprising; more surprising is the importance of the effect and its complexity related to the superstructure shape. As with many ships, elements of the forward superstructure on Thalassa sloped to the sides of the vessel which provided reflection opportunities under a variety of sun geometries with respect to the bow.

Figure 7 is a plot of the average relative spectral differences between the M80 and S95 methods, during clear-sky and overcast conditions, and presented in a variety of |α_s| bins. Several aspects are worth noting.

1. As expected (Fig. 3), the M80 L_W(λ) values are persistently less than those derived from the S95 method.

2. The overcast data show a minimal and spectrally constant difference, because ΔL_ship(λ) is minimal, and its spectral composition and that of L_sky are similar. In these specific circumstances, the M80 results are the most accurate; by neglecting the ΔL_ship term, the S95 results are systematically overestimated by about 5%.

3. For the clear-sky data, the difference between the two methods is noticeable, even when |α_s| < 15°, and increases when α_s and, thus, ΔL_ship(λ) increases; these differences exhibit a spectral shape, which will be discussed later (section 6d).

c. Above- and in-water intercomparisons

The in-water data are free from the perturbations caused by the ship's superstructure, and can be used to determine their magnitude. The intercomparison is made with a reduced dataset composed of 49 casts (at 5 wavelengths), because (a) the two types of measurements (above- and in-water) do not always overlap, and only those that are exactly coincident in time are kept; (b) the above-water casts are restricted to clear-sky conditions and 90 ≤ ϕ ≤ 135°; and (c) the data with a pointing angle |α_s| > 45° are discarded, because there were only four simultaneous above- and in-water casts in this bin interval. Among the clear-sky data, only those corresponding to the most stable environmental conditions (and Mediterranean Sea waters) are considered. The intercomparison of L^S95_W (above-water, SeaSAS data, and the S95 method) and L^LN_W (in-water, LoCNESS data, and the S84 method), is made under these restrictions.

Because of bidirectional effects, the above- and in-water radiances are not straightforwardly comparable; L^S95_W must first be converted into a corrected water-leaving radiance using (6). Indeed, the above-water measurements, made at θ = 40° (whence θ′ = 29°), must be transformed on a case-by-case basis as if they were made vertically (θ = 0°). The transformation uses look-up tables derived from calculations for a clear sky, as discussed in Morel and Gentili (1996), which depend on θ′, λ, the chlorophyll a concentration, and ϕ, the azimuthal difference (between the viewing and solar planes).

The PROSOPE measurements were often made around midday, so the solar zenith angle (θ_s) was never very large, 33°–50° (Table 1); such values, combined with ϕ values between 90° and 135° and low chlorophyll concentrations (in the Mediterranean Sea), do not lead to a considerable bidirectional correction. The slant radiance slightly exceeds the nadir radiance by approximately 2%–4% (note that for low solar elevation, the increase is much more significant). The bidirectionally corrected data, denoted L^Q95_W, are shown in Fig. 8 along with the comparative histograms for the uncorrected and corrected data. The principal consequence of the Q-factor correction is a stronger central peak with fewer outliers.

Figure 8 also shows the L^Q95_W(λ) values not only overestimate L^LN_W(555), but the relative magnitudes of the overestimates tend to increase quasi-linearly with increasing radiance (in keeping with the postulated contamination from superstructure reflections at this wavelength). An inspection of the other wavelengths reveals this effect is only well expressed at the 555-nm wavelength (this is most easily seen in the solid symbols which are all well distributed around the 1:1 line across the entire range of radiance levels).

d. Spectral intercomparisons

Figure 9 is a plot of R^Q95_rs(λ) (the remote-sensing reflectance determined from the S95 method and corrected for bidirectional effects) as a function of α_s; the remote sensing reflectance is used to cancel out, in a simplified way, variations due to changing solar illumination. The data shown are only those for the Mediterranean Sea, with low chlorophyll a concentration (C_a < 0.05 mg m⁻³) and clear-sky conditions. Consequently, the station-to-station differences in R^Q95_rs(λ) are rather weak, so the dependency of reflectance on α_s is not obscured by local differences, and the trends in Fig. 9 are significant. This figure shows the ship perturbation is characterized by the following:

1. a good symmetry with respect to α_s = 0, which suggests rather homogeneous reflective properties of the superstructure, from the bow to the stern, when similarly lit;

2. as already noted, an increase in reflectance, actually in ΔL_ship(λ), as a function of α_s; and

3. an increase of this perturbation as a function of λ— from weak, but detectable, levels at 412 nm, to large values (a factor of 5–10) in the infrared part of the spectrum.

Table 2 and Fig. 10 present the average RPDs between the S95 and M80 estimates of water-leaving radiances corrected for bidirectional effects and the in-water estimates, δ^Q95_LN(λ) and δ^Q80_LN(λ), respectively, as a function of the |α_s| pointing angle (in 15° bins). For these blue waters, and when using the S95 method, the overall difference in water-leaving radiances at a single wavelength is usually small (to within 5%), except at 555 nm (as noted in Fig. 8), where it reaches values as high as 13%, and even 21%, as a consequence of a lower marine signal at this wavelength (Fig. 4). When using the M80 method, the differences, almost spectrally neutral, are always strongly negative, because of the overestimation of the ΔL_ship(λ) term (as previously noted).

Because band ratios are generally in use in ocean color algorithms (O'Reilly et al. 1998), and sometimes as simplified measurements for sensor validation, the average differences between ratios derived from above-water measurements and those derived from in-water measurements are also displayed in Table 2. The large contamination of the 555-nm channel with the S95 method results in poor agreement for the three ratios considered (much larger uncertainties that the spectral intracomparison uncertainty presented in section 6a). In contrast, the almost equal overestimates, inherent with the M80 method, cancels out when forming the band ratios, so that the corresponding average differences remain small. This apparent agreement cannot be generalized, because it depends on the spectral composition of the superstructure albedo.

The so-called Type B deviations in the RPD values within each |α_s| bin are presented in the bottom half of Table 2. This measure of dispersion is constructed by first computing the standard deviations with respect to the average RPD value in each bin. The standard deviations necessarily overestimate the true deviations associated with platform perturbations, because they also contain differences arising from sensor calibration, data processing, and in situ stability. A more accurate measure of the deviation caused by the presence of the ship is calculated by assuming relative standard uncertainties for the latter three effects (Hooker and Maritorena; Hooker et al. 2001, 2002a, b) which are then subtracted in quadrature from the calculated standard deviation of a particular δ^abw_LN(λ) value. This difference is interpreted as a Type B relative combined deviation.

The deviations in Table 2 support several important aspects of the average RPD values. First of all, the large RPD values are well resolved, because the corresponding deviations are much smaller. Second, there is a general trend of decreasing deviations from 412–490 nm, which then increase from 510–555 nm. This trend is well summarized by the overall deviation averages, and is in agreement with the behavior seen in Fig. 7. Third, the deviations basically increase with increasing |α_s|. Finally, the deviations in the band ratios are usually smaller.

In Case-1 waters, the M80 and S95 techniques do not usually underestimate the water-leaving radiance. As shown by Hooker et al. (2002a), the M80 and S95 techniques usually overestimate the water-leaving radiance, so the underestimation in Table 2 across all channels for the M80 method plus the 412–510-nm wavelengths for the S95 method cannot be explained by methodological biases in the above-water algorithms. Furthermore, Hooker et al. (2002a) also showed the band ratios from above-water methods in Case-1 and Case-2 waters usually agree with in-water estimates to within 5%, so the large uncertainties for the band ratios in Table 2 are not attributed to methodological biases.

e. Ship perturbation correction

The perturbation effect is detectable through the use of the r(865) ratio; its departure from unity forms a sensitive diagnostic parameter in Case-1 waters. Once detected, the next step is to examine whether a correction for this perturbation is possible with the available data. A simplified correction scheme can be constructed at every wavelength using the superstructure reflection term in the infrared. This spectrally constant model is expressed as

View Expanded

A spectrally dependent model can also be constructed, which has something in common with that developed for the residual term mentioned in Mueller (2000a,b) or in Toole et al. (2000). This scheme actually rests on the assumption of a white reflection by a ship's superstructure illuminated by the sun and the sky. Under this assumption, ΔL_ship(λ) will have the same spectral composition as E_d(λ, 0⁺), and is expressed as

View Expanded

The results of using these two correction schemes are presented in Table 3 (and are to be compared with the Q95 results presented in Table 2). Whatever the scheme, the corrections result in lower L^LN_W(λ) values, by a few percent for the 412–510-nm wavelengths, and more considerably at 555 nm, where the uncorrected values are significantly high (Fig. 10). The spectrally dependent model is more efficient than the neutral model in correcting the 555-nm channel; the corrected value (at 555 nm) still remains above the in-water value.

Admittedly, the ship perturbation correction hypotheses underlying (15) and (16) are questionable, although the latter could be more realistic, if the superstructure paint was close to that of a neutral reflector. In summary, the results of the corrections are in the right direction, without being fully satisfactory. To the extent that the 555-nm channel has not been fully corrected, the band ratios computed from the L^abw_W measurements remain inaccurate.

f. Clouds and oceanic swell

Among various environmental conditions, cloudiness has been identified as having a potential effect on the above-water determination of water-leaving radiances. If the excellent conditions in terms of cloud cover (CC in octa) with respect to the threshold CC < 3 are compared to the remaining data, no systematic effect related to varying cloudiness can be detected (apart from those described for hazy overcast conditions) and the δ^S95_LN(λ) and δ^M80_LN(λ) values are mostly unchanged. It must be emphasized, however, that the measurements were only made if a large fraction of the sky (around the viewing angle of the SeaSAS sky sensor) was cloud free, even when CC > 3.

One common feature of the oceanic environment, unaddressed in the protocols for above-water measurements, is how to point the surface-viewing radiometer with respect to the ambient wave field. The possible importance of swell on deriving L^abw_W(λ) was partially quantified by Hooker et al. (2002a), who showed two above-water systems pointed opposite to one another with respect to the surface wave field, but still in keeping with the pointing requirements with respect to the sun, can differ (on average) by an additional 3%–7% (during clear-sky conditions).

The effects of surface gravity waves on the above-water measurements can be addressed by splitting the 49 simultaneous above- and in-water casts into two groups: (a) calm casts with no discernible swell (and thus, no swell direction), and (b) casts with a clear swell presence and direction. This produces balanced datasets with 22 casts for calm conditions and 27 for swell. Values of δ^S95_LN(λ) were calculated for each group (and each |α_s| bin), and then the calm values were subtracted from the swell values to produce a net percent difference (NPD). The important conclusions regarding the NPD results as a function of |α_s| (top half of Table 4) are (a) the majority of the individual wavelengths have negative net difference values, which means the presence of swell results in lower above-water estimates of L_W(λ); and (b) the depressive effect of swell is more accentuated at the 412-nm wavelength (independent of α_s) and is almost insignificant at the other wavelengths.

Another aspect of the surface gravity wave field can be considered in relation to the angle β_s, that is, the angle between the radiometer and the swell direction (Fig. 5, inset panel). If the radiometer is pointed in the same direction the swell is moving toward, β_s = 0°; if pointed in the opposite direction, β_s = ±180°. The data can be binned as a function of β_s to categorize the data in terms of the wave field (45° bins are used here): the sensor is viewing (a) the wave crests moving away, |β_s| ≤ 45°; (b) along the wave troughs, 45 < |β_s| ≤ 135°; and (c) the oncoming wave crests, 135 < |β_s| ≤ 180°. Again, the calm data are subtracted from the swell data, and the results (bottom half of Table 4) are as follows.

1. Measurements along the wave troughs are a significant local minimum, which means they are radiometrically darker than the wave crests at all wavelengths;

2. the darkening effect is the largest at 412 and 555 nm; and

3. at 510–555 nm, a converse trend (i.e., a brightening) seems to occur.

As noted before, the relative ship perturbation is the largest at 555 nm. Inasmuch as the magnitude of ΔL_ship interacts with the wave orientation, it is not surprising that the response of this channel is more affected (enhanced or depressed) by the swell orientation. It must be remembered, however, that the glint filter has, in principle, removed any signals artificially brightened by wave passage, because only the darkest 5% of the data are used for deriving L^abw_W(λ). In summary, the swell effects are significant, spectrally dependent, and varying with the sampling geometry. The brightening–darkening alternation is related to the position of focal areas beneath the wave crest and to the horizontal inhomogeneity of the downward radiance field in the presence of waves (Zaneveld et al. 2001). The question is still open, and dedicated experiments are definitely needed to understand and properly account for these effects (which are not considered in the present above-water protocols).