An Evaluation of Above- and In-Water Methods for Determining Water-Leaving Radiances

1. Introduction and background

Spectral water-leaving radiance, L_W(λ), is the central physical quantity for bio-optical studies in the upper ocean; whether determined from above- or in-water data, L̂_W(λ) and L̃_W(λ), respectively, it must be accurately measured. The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Project, for example, requires L_W(λ) uncertainties within 5% (Hooker et al. 1993b). This was shown to be achievable for in-water measurements in Case-1 waters using primarily a single methodology (Hooker and Maritorena 2000), but the uncertainty associated with multiple methods has not been well quantified. The SeaWiFS calibration and validation plan (Hooker and McClain 2000) has emphasized in-water field work because when the plan was conceived, the above-water protocols were not as mature as the in-water protocols (Mueller and Austin 1992). Although there has been steady progress in defining the proper metrology for above-water measurements, intracomparisons within a group of accepted techniques have not occurred. More importantly, intercomparisons between above- and in-water methods have also not been thoroughly investigated, although individual comparisons are available in the literature (e.g., Pinkerton et al. 1999; Toole et al. 2000).

The main difficulty with above-water measurements is associated with correcting the observations for the effect of surface waves that introduce significant fluctuations into the glint and reflected skylight components of the surface radiance field. The problem is made more difficult by the presence of clouds, which increase the fluctuations and associated uncertainties. At present, there are several methods for surface glint correction that were developed for different environmental conditions, that is, clear or cloudy sky, and Case-1 or Case-2 water: Austin (1974); Morel (1980); Carder and Steward (1985); Bukata et al. (1988); Mueller and Austin (1995); Lee et al. (1996); Lazin (1998); and the recurring revision of the so-called SeaWiFS Ocean Optics Protocols by Mueller et al. (2000). All of the methods recognize the importance of making surface measurements free of sun glint effects, so the differences in the methods are primarily due to how sky glint contamination is removed from the surface signal.

The SeaWiFS ocean optics protocols deserve some extra comments because they were published (Mueller and Austin 1992) to publicly establish the measurement strategies to verify the SeaWiFS uncertainty goals of 5% in water-leaving radiances and 35% in chlorophyll a concentration (Hooker et al. 1992). From the very beginning, the protocols were considered an evolving prescription that would allow the research community to approach the unprecedented measurement uncertainties implied by the SeaWiFS goals (Hooker and Esaias 1993); research and development activities were acknowledged to be important elements for improving the state of the art in specific areas. It was always the intent of the SeaWiFS Project and the SeaWiFS Working Groups (Hooker et al. 1993a) that the ocean optics protocols would be periodically evaluated and revised to reflect technical advances during the SeaWiFS Project cycle (Mueller and Austin 1995).

Although the ocean optics protocols document agreed upon methods for making and analyzing optical measurements, they do not attempt to quantitatively resolve differences in accepted or newly emerging methods. Consequently, multiple techniques are discussed in the protocols for different types of measurements or platforms, but an unequivocal recommendation as to which is the most suitable over a wide range of conditions is not made—this type of quantitative experimentation is left to the individual investigator, which is one objective of this study.

The techniques considered here are as follows: Morel (1980); Carder and Steward (1985), and as further explained in Lee et al. (1996); the Mueller and Austin (1995) SeaWiFS protocol; and Lazin (1998). Hereafter, these methods are referred to as M80, C85, S95, and L98, respectively. Some clarification of the S95 method is needed because in its subsequent revision, there are three proposed, generalized classes of measurement methods, categorized by Mueller et al. (2000) as (a) calibrated radiance and irradiance measurements, (b) uncalibrated radiance and reflectance plaque measurements, and (c) calibrated surface polarized radiance measurements with modeled irradiance and sky radiance. The first method is associated with S95, the second with C85, and the third is not considered here.

The in-water techniques currently in use (Mueller 2000) are based primarily on the Smith and Baker (1984) method, hereafter referred to as S84. Variations are derived from the acquisition procedures (and platforms), and how the data are propagated to the surface. Two alternative techniques were implemented in the ProSoft¹ software for processing data collected with Satlantic, Inc. (Halifax, Canada) sensors. The ProSoft methods rely on a surface buoy to make measurements close to the sea surface and are categorized according to when the processing options were implemented, which occurred in 1994 and 1997, so the two are referred to hereafter as P94 and P97, respectively.

The Normalized Remote Sensing Reflectance (NRSR) Workshop (11–12 December 1997) established a baseline uncertainty in NRSR determined from in-water radiance profiles, combined with above-water measurements of solar irradiance, of approximately 5% for wavelengths less than 600 nm and a diffuse attenuation coefficient at 490 nm, K(490), less than 0.1 m⁻¹ (Hooker et al. 1999). The uncertainty estimate was based on results from the first SeaWiFS Data Analysis Round-Robin activity (Siegel et al. 1995), plus the third and fourth SeaWiFS Intercalibration Round-Robin Experiments (Mueller et al. 1996; Johnson et al. 1996, respectively).

Radiative transfer simulations of remote sensing reflectance measurements above a wave-roughened surface from Mobley (1999) showed the increase with wind speed (and resulting surface wave slope) of sky radiance and sun glint reflectance in total radiance viewed at the sea surface, relative to radiance from beneath the surface. At wind speeds approaching 10 m s⁻¹, the superior nadir viewing angle was 40°, rather than the 30° used by many of the participants (and the 20° given in the original publication of S95). At lower wind speeds and a 40° viewing angle, an effective (and spectrally constant) surface reflectance of ρ′ = 0.028 was recommended. There was a consensus at the workshop that comparative analyses need to be done, but with the following restrictions: λ < 600 nm, K(490) < 0.1 m⁻¹, percent cloud cover less than 20%, wind speed less than 10 m s⁻¹, and solar zenith angle 30°–60°. Data outside these ranges may be considered but should be excluded from the simpler comparison methods.

A field campaign was organized from 5 to 17 July 1998, sequential days of the year (SDY) 186–198, to evaluate above- and in-water measurements for SeaWiFS validation. The Acqua Alta oceanographic tower (AAOT), located about 15 km east of the city of Venice (12.5083°E, 45.3139°N), was chosen as the deployment site. Although the primary reason for selecting the AAOT was the ongoing use of the tower for bio-optical measurements within the framework of the Coastal Atmosphere and Sea Time Series (CoASTS) activity at the Joint Research Centre (JRC), the other reasons were its stability (towers do not pitch and roll like ships), the summer climatology was favorable for conditions in keeping with the NRSR Workshop recommendations, and its proximity to a strong coastal front. The water around the tower can be Case-1 or Case-2 depending on whether the coastal front is pushed on- or offshore. The opportunity for sampling different water types within one field campaign was very appealing.

The deployment was called the first SeaWiFS Bio-Optical Algorithm Round-Robin (SeaBOARR-98) experiment because the long-term objective is to evaluate the effect of the different measurement protocols on bio-optical algorithms from a variety of field campaigns. This study details the first goals and results in that long-term analysis.

1. Use two above-water sampling systems and four surface glint correction methods (M80, C85, S95, and L98) to intracompare L̂_W(λ) estimates.

2. Use three in-water sampling and analysis methods (S84, P94, and P97) to intracompare L̃_W(λ) estimates.

3. Use radiometers with a common calibration history to minimize intercalibration uncertainties.

4. Intercalibrate and monitor the stability of the sensors in the field with a second generation SeaWiFS Quality Monitor (SQM), the so-called SQM-II, to separate differences in methods from changes in performance.

5. Characterize the environmental conditions of the site during the field campaign, particularly the bio-optically active constituents, to establish a background environmental variability level.

6. Intercompare the water-leaving radiances estimated from the above- and in-water methods.

7. Use the comparison results to evaluate and rank the overall capabilities of the various methods.

2. Measurement and analysis methods

A detailed description of the AAOT is presented in Zibordi et al. (1999), so only a brief overview is given here. The water depth immediately below the tower is about 17 m and the composition of the nearby seafloor is primarily sand and silt. The tower is composed of four levels supported by four large pillars. The first (lowest) tower level, about 4.5 m above the water, has an open grid deck and no facilities. The second level is approximately 7 m above the water and contains the water filtering and hydrography laboratory plus a special open grid platform, 3.5 m wide, which extends 6.5 m over the sea toward the southeast. The Wire-Stabilized Profiling Environmental Radiometer (WiSPER) package is deployed from this platform. The third deck contains the main laboratory, and the fourth (uppermost) deck, at about 13 m above the water, contains a wind generator, solar panels, a variety of meteorological instruments, communications antennae, plus water storage tanks.

For SeaBOARR-98, the total number of optical in situ systems deployed on the AAOT was increased beyond the in-water WiSPER system to include the following above- and in-water instruments:

1. the SeaWiFS Surface Acquisition System (SeaSAS),

2. the Dalhousie University SeaWiFS Aircraft Simulator (DalSAS),

3. the miniature NASA Environmental Sampling System (miniNESS), and

4. the Dalhousie University Buoyant Optical Surface Sensor (DalBOSS).

d. Above-water determinations of water-leaving radiances

DalSAS was mounted 13.5 m above the water on the top-most deck, which had a number of superstructure obstacles. To ensure unperturbed viewing of the sea surface during as much of the day as possible, two sites were chosen: one on the northeast side and one on the southeast side. Depending on the time of day, DalSAS was moved from one location to the other. The two DalSAS irradiance sensors were positioned on the southeast side, and diffuse solar irradiance data, E_i(0⁺, λ), were collected by periodically occulting the appropriate irradiance sensor with a lollipop (a black 9-cm disk mounted on a 1-m rod). SeaSAS was mounted one deck below DalSAS on the southern corner 10.5 m above the water. When DalSAS was on the northeast side of the tower, SeaSAS was necessarily pointed 90° away; when it was on the southeast side, the two instruments were usually pointed in the same direction. In either case, there were times when the two instruments were pointed in the same and opposite directions with respect to one another (but perpendicular to the sun).

1) Measurement methods

The SeaSAS instruments measured the sky radiance reaching the sea surface, L_i(0⁺, λ), and the total radiance right above the sea surface, L_T(0⁺, λ). The latter is composed of three terms: the radiance leaving the sea surface from below (the so-called water-leaving radiance), the direct sunlight reflecting off the surface (the so-called sun glint), and the skylight reflecting off the surface (the so-called sky glint). A separate sensor measured E_d(0⁺, λ) which, in this case, was the same sensor used with miniNESS (the irradiance sensor data was sent to both acquisition systems). DalSAS made the same measurements as SeaSAS, L_i(0⁺, λ) and L_T(0⁺, λ), but the surface-viewing radiometer looked through a square aperture that was periodically blocked with a gray plaque, so it also measured the radiance of the plaque, L_p(0⁺, λ). Two separate sensors were used to measure E_d(0⁺, λ) and E_i(0⁺, λ).

The gray plaque used was a 25 cm (10 in.) gray Spectralon^TM plaque manufactured and calibrated by Labsphere, Inc. (North Sutton, New Hampshire), with a nominal 10% reflectance (SRT-10-100). This reflectance value permitted the radiometers with (typical) above-water saturation values to view the plaque under sunny conditions without saturating (approximately 6 μW cm⁻² nm⁻¹ sr⁻¹). Unlike the 99% reflectance of pure (white) Spectralon plaques, which are usually used for radiometric calibration, gray plaques are much less lambertian, because of the added impurities of the black doping material. Variations in viewing and illumination geometries, as are naturally found in the field, are likely to add significant variance in this measurement.

A directional/directional (i.e., 0°/45°) plaque calibration, instead of the standard directional/hemispherical calibration was used for this campaign, because this was closer to the actual field geometry. Before calibration, the homogeneity of the plaque was checked at a minimum of four spots on the plaque surface. There were no variations greater than 2% between the spots, so the plaque was recalibrated without any additional resurfacing (i.e., sanding). Although Spectralon is very hydrophobic, it readily absorbs grease and oil, which are very difficult to remove and can cause significant variance in calibrations. Special precautions were taken to avoid touching the diffusive material. To avoid long exposure to marine aerosols, the plaque was kept in a padded, airtight enclosure when not in use and only exposed during the measurement sequences. It was always wrapped in acid-free paper during transport and storage before, during, and after the field campaign.

2) Data analysis methods

Based on the consensus reached at the NRSR workshop (and Mobley 1999), all of the above-water methods in the SeaBOARR-98 field campaign used a nadir and zenith viewing angle of ϑ = 40° (this revision was incorporated into the second version of the ocean optics protocols). Although S95 explicitly states some common sense procedures, all of the methods make use of them, so they are assumed to be a part of all above-water methods. In particular, foam and floating material must be avoided during measurements, and because of temporal variability due to waves, it is important to record a number of spectra within a period of a few seconds (e.g., 30 spectra within 15 s).

Sea surface radiance data collected at high frequency in stable (sea and sky) conditions are a superposition of three contributions: (a) the steady, background water-leaving radiance; (b) the (mostly) random, sharp sun glint outliers; and (c) the variations in the sky glint from the waves. Some above-water techniques try to deal with the negative effects of glint at the point of measurement (Fougnie et al. 1999), but most deal with it explicitly by filtering it out or removing it with a correction scheme. The M80, C85, and L98 glint correction methods require the existence of a spectral band in the near infrared part of the spectrum (λ_r) for which L_W(λ_r) = 0. For the open ocean (Case-1 with C_a < 0.25 mg m⁻³), the assumption L_W(670) = 0 can be used (Gordon 1981); for all other Case-1 waters, the 765- and 865- nm wavelengths should be used (Gordon and Wang 1994). For Case-2 waters, the assumption L_W(1012) = 0 has been found to be appropriate even in waters heavily loaded with sediment (Bukata et al. 1995).

The first revision of the ocean optics protocols incorporated new methodologies in several areas, including expanded protocol descriptions for Case-2 waters (Mueller and Austin 1995). All of the methods are applied to all of the data collected, regardless of the water or algorithm type, because in many cases optical data are collected without a full bio-optical characterization of the acquisition site. The performance of the various methods across a wide range of conditions is needed, not only to understand the consequences of inadvertently using a method inappropriately, but also to make progress on what are the desirable or negative aspects of algorithms within the global ocean.

There is also the consideration that all the SeaSAS and DalSAS (as well as the WiSPER) data were contaminated by tower-shading and bottom-reflection effects, but only the in-water data are currently correctable (Zibordi et al. 1999). To keep the above- and in-water data comparable, tower-shading corrections were not applied to the WiSPER data, and neither the above- or in-water data were corrected for bottom reflection. This equalizes the comparisons between the above-water instruments and WiSPER, but it leaves a source of variance when comparing the P94 and P97 (DB) results with the above-water methods because they were not contaminated by tower perturbations.

(i) Near-infrared radiance ratio glint correction (M80)

In the M80 method, temporal sun glint from the high frequency spectra is removed before averaging, so the final mean spectrum incorporates sky glint only. The sky glint correction is based on the assumption that water-leaving radiance in a near-infrared band, λ_r, is negligible. Consequently, the above-water radiance measured at λ_r is due entirely to surface reflection. The infrared estimate of sky glint is extended over the whole spectrum by using the measured wavelength dependence of the incident sky radiance. Estimated sky glint is subtracted from the total signal to recover L̂_W(λ):

View Expanded

where ϕ′ = ϕ ± π/2 (90° away from the sun in either direction, i.e., ϕ⁺ or ϕ⁻ in Fig. 1).

(ii) Fresnel reflectance plus residual reflection correction (C85)

The C85 method uses data averaged over 10-s intervals, so each spectrum of sea surface radiance incorporates the contribution of temporal sun glint. The above-water measurements are corrected for sky glint assuming specular reflection of sky radiance at the sea surface. The residual reflection of downwelling radiation from the wave facets is computed assuming the residual signal in the near infrared domain is entirely due to surface reflection, that is, L_W(λ_r) = 0. This term is estimated with a horizontally oriented gray reflectance plaque with reflectance ρ_p(λ, ϑ):

View Expanded

where E_p(λ) = πL_p(λ, ϕ′, ϑ)/ρ_p(λ, ϑ). L̂_W(λ) is computed by accounting for both correction terms:

View Expanded

Note the use of ρ(λ, ϑ) rather than ρ′—the C85 method specifically uses the Fresnel reflectance.

For the purposes of this study, C85 is considered a Case-2 algorithm. The use of C85 in Case-2 waters requires more explanation: this method was devised for Case-1 conditions (Lee et al. 1996), but the formulation of the algorithm (which closely matches S95) and the small size of the correction term (ΔL) suggests it should be suitable for Case-2 waters without a heavy sediment load (like the Adriatic Sea). In terms of the published criteria for its use (Lee et al. 1996), it can be used confidently, cautiously, or uncertainly depending on the R_rs(440)/R_rs(550) ratio (greater than 1.0, between 1.0 and 0.5, and less than 0.5, respectively).

(iii) Modified fresnel reflectance glint correction (S95)

The S95 formulation is based on the version-1 revision of the ocean optics protocols, which requires the radiometer to be pointed at the sea surface at an angle ϑ = 20° (from nadir) and away from the solar azimuth angle (ϕ) by at least 90°, that is, ϕ′. Before calculating the final spectra, outliers are removed by computing mean (μ) and standard deviation (σ) estimates and rejecting spectral values more than 1.5 σ from the mean. L_T(λ) is corrected for sky glint using measurements of L_i(λ) in the direction appropriate for the specular reflection from the sea surface into the sensor. Here, L_i(λ) measurements are made by pointing the radiometer into the sky at a zenith angle equal to the nadir angle of the L_T(λ) observations (or as in Fig. 1, ϑ′ = π − ϑ) and with the same azimuth angle.² The sky glint is removed using the surface reflectance:

L̂_WλL_Tλ,ϕϑρλ,ϑL_iλ,ϕϑ(7)

With respect to the version-1 formulation, note the replacement of ρ(λ, ϑ) with ρ′, as per the recommendations of the NRSR Workshop, Mobley (1999), and the most recent version of the ocean optics protocols (Mueller et al. 2000), which also recommended nadir and zenith viewing angles of 40°. Also note the formulation in (7) is not the only above-water method discussed in the ocean optics protocols, and some investigators have interpreted the C85 method discussion in the protocols as the recommended method (e.g., Toole et al. 2000).

(iv) Near-infrared irradiance ratio glint correction (L98)

Sky glint correction for the L98 method is also based on the assumption that L̂_W(λ_r) = 0, so the signal in the λ_r part of the spectrum is wholly attributable to surface reflection. The L98 method uses the wavelength dependence of diffuse sky irradiance to extend the estimate of sky glint at λ_r over the whole spectrum. The advantage of this method is that it incorporates the effect of clouds. The technical advantage is that E_d(0⁺, λ) and E_i(0⁺, λ) can be measured with the same instrument: an upward-viewing radiometer where the diffuse component can be determined by periodically blocking the direct solar illumination of the radiometer, so E_d(0⁺, λ) and E_i(0⁺, λ) can be continuously monitored during remote sensing observations. Estimated sky glint is subtracted from the total signal to recover L̂_W(λ):

View Expanded

e. Comparison and statistical methods

The comparisons of the methods are organized by splitting them into two groups, above-water and in-water, and then considering the differences within and between groups. This produces three comparison possibilities, the first of which are the intracomparisons of the three in-water methods summarized in Table 2. The intracomparisons of the four above-water methods, incorporating the recommendations from the NRSR Workshop as summarized in Table 3, are presented next. The intercomparisons of all the methods are presented last.

Based on the formulations of the algorithms, the P94 and P97 methods are similar to one another, as are the M80 and L98 methods, and the C85 and S95 methods. All the techniques can be used in Case-1 conditions; S84, P94, C85, and S95 are the only methods formulated for the Case-2 environment. Because either above- or in-water measurements yield estimates of L_W(λ), and, for the purposes of this study, neither is assumed to be more correct than the other, an unbiased parameter is needed to compare the various methods.

1) Unbiased percent differences

The unbiased percent difference (UPD) between two data products X^A and X^B determined from simultaneous casts at time t was computed as

View Expanded

where the A and B codes identify the methods used, and the factor 200 occurs because the denominator is the average and the quotient is expressed as a percent. Absolute differences are used to ensure cancellation in any averages do not artificially lower the differences in the comparisons. Average UPD values over a particular set of data (e.g., data collected during one day) were computed as

View Expanded

where M is the number of measurements, that is, the average UPD between the water-leaving radiances estimated with the M80 and S84 methods is ψ^M80_S84(λ).

Spectral averages of the UPD were formed by summing and weighting (10) over the blue-green wavelengths used for ocean-color algorithms, that is, the first five spectral bands:

View Expanded

When a particular method type was compared against another, the All nomenclature is used with an overline—for example, Ψ^All_P94 is the overall spectrally averaged UPD computed in comparing all the indicated methods to the P94 method.

Although the primary interest is in spectral estimates of water-leaving radiance, the most frequently used ocean color algorithms use band ratios (e.g., the OC2 algorithm uses the ratio between the 490- and 555-nm bands; O'Reilly et al. 1998). Consequently, another important parameter is the UPD between band ratios of water-leaving radiances:

View Expanded

where L_W(λ_k / l, t) is the L_W(λ_k, t)/L_W(λ_l, t) ratio, and the k and l indices set the channel numbers being used; that is, the average UPD value for the 490- and 555-nm band ratio is Φ^A_B(λ_3/5). In most cases, the methods involved are explicitly stated, so the Φ_3/5 shorthand notation is frequently used [the same is true for Ψ^A_B(λ_1–5) for which the abbreviated notation is Ψ_1–5].

2) Comparison strategies and metrics

The comparison strategies used in this study are a reflection of the large diversity in methods and instrumentation, as well as the complexity of the near-coastal environment. The primary requirement is to ensure the comparisons reflect only the differences in the methods, and not differences arising from external factors that might change from one method or instrument to another. Consequently, the first strategy is to use the smallest number of instruments possible to implement all the methods. To then provide a common basis for the evaluation of the methods, the second strategy is to estimate, and remove where possible, any extraneous sources of variance. The latter includes environmental variability, sensor stability and intercalibration, and the use of a single glint filter method in the above-water methods. The third strategy is to only use UPD statistics as the comparison metric, because they are unbiased, and to evaluate the results in terms of the stated radiometric objectives (i.e., the minimum acceptable uncertainty is to within 5%, and the desired uncertainty is to within 3%).

The final strategy is to separate the results according to water type, Case-1 or Case-2, and to present the results using a three-step process encompassing a broad-to-focused perspective. Spectral averages in the 412–555-nm domain are used to synthesize an overview from which the details are discerned using a band-ratio analysis followed by a discrete wavelength investigation. The latter uses the best above- and in-water methods identified by the other two analyses. The advantage of this scheme is it partitions an otherwise large and complex matrix of possible products into well-defined and manageable subsets.

The band-ratio analysis is restricted to the 490- and 555-nm band ratio in water-leaving radiance. There are three reasons for considering such an option: (a) one of the dominant ocean-color algorithms, OC2, uses the 490- and 555-nm band ratio as its primary input variable; (b) differences in applied corrections (e.g., tower shading) are somewhat mitigated by the band-ratio process; and (c) spectral deviations might be persistently biased, that is, parts of the spectrum might be shifted in the same direction and magnitude, so a ratio analysis might not be as unsatisfactory as a spectral analysis. The latter is particularly relevant to the above-water methods because glint contamination elevates broad sections of the spectrum.

The spectral aspects of glint makes it important to use the same glint filter with the above-water methods if possible. The M80, S95, and L98 methods require the removal of temporal sun glint (plus anomalous values due to foam and floating material) from the high frequency L_T(λ) spectra, whereas C85 uses 10-s data averaging as part of the acquisition event, so glint contributions are convolved with the water-leaving radiance. Of the methods using glint filtering, only S95 includes a prescribed filter as part of the method. In order to study the effect of filtering in estimating L̂_W(λ), seven different filters are considered later in Table 5. The F₁ filter is the original S95 filter, F₂ is the revised S95 filter (Hooker and Lazin 2000), and the amount of filtering increases with increasing filter number (i.e., the amount of data retained decreases with increasing filter number).

3. Extraneous sources of variance

Hooker and Maritorena (2000) considered the total uncertainty arising from in-water optical data collection in the Case-1 environment as a function of a variety of deployment systems. They considered four sources of uncertainty: (a) calibration, (b) in situ sensor stability, (c) data collection method, and (d) data processing. A potential fifth uncertainty from environmental variability was assumed negligible, because all the data were collected from simultaneous casts in primarily homogeneous waters of the deep ocean. Furthermore, the data processing uncertainty was not fully expressed, because only one data processor was used, and was restricted to how the uncertainty associated with extrapolations of L_u(z, λ) to the surface, affect the comparisons of surface quantities like L_W(λ) or R_rs(λ).

The focus in this study is to establish the importance of data collection and processing to the total uncertainty within a combined above- and in-water perspective. These two sources of uncertainty express the principal differences in the above- and in-water protocols, because the other three are largely independent of either approach: the instruments are all calibrated the same way (standard lamps and plaques) and can be intercalibrated with the SQM to remove any calibration biases; one manufacturer is being used, so the in situ stability is usually within well-defined expectations; and all the sensors are exposed to the same oceanic and illumination environment. In such a framework, the latter three uncertainties are considered extraneous to the main objective. This is not to say they are insignificant—it is strictly an organizational expedient to clear away those problems that can be quantified expeditiously before the details of the primary objective are considered.

Calibration uncertainties were minimized by having the miniNESS, SeaSAS, DalSAS, and DalBOSS radiometers all calibrated at the same calibration facility (Satlantic) and at the same time. The monthly campaigns for the WiSPER radiometers did not permit them to be a part of the joint calibration exercise, so all the radiometers were intercalibrated using the SQM-II (section 3a). The SQM-II sessions were done in the field to also monitor the stability of the sensors while they were being deployed.

Environmental variability was minimized by only using data from simultaneous deployments of the instruments during the most stable solar illumination possible. The majority of the data were collected in Case-2 conditions, so the influence of the potentially increased heterogeneity of this type of environment was assessed (section 3b).

Data processing uncertainties were minimized by processing all the in-water data with one processor, and all the above-water data with one processor. The latter requires some common choices in filtering and sampling parameters; the importance of which are quantified below (section 3c) and then a single choice was made for all the above-water processing (section 4) where appropriate (the C85 method does not permit alternative processing parameters).

4. Results

This study is concerned with an extensive set of experimental comparisons determined from above- and in-water radiometric measurements. Seven methods for deriving water-leaving radiances are computed from five instrument systems (Fig. 2) with five common wavelengths (Table 1) using data from two water types (Case-1 and Case-2), two categories of water stratification and sea surface roughness (Table 4), plus two illumination conditions (clear and overcast skies). Embedded within this already complicated data matrix are additional subtleties associated with the sampling systems and their respective protocols.

Recognizing that no one organizational scheme can compactly and succinctly present all of the data relationships, the presentation plan adopted here is to split the presentation into in-water intracomparisons (section 4a), above-water intracomparisons (section 4b), and above- and in-water intercomparisons (section 4c). To provide some commonality and easy cross-referencing between comparison categories, an overall synthesis is established first using spectral averages, which are then used to determine the areas of inquiry demanding greater analytical detail using band ratios and discrete wavelengths. Consequently, each comparison category has a separate section dealing with spectral averages, band ratios, and discrete wavelengths.

The results are presented primarily in tables rather than figures, so the quantitative values are immediately accessible. The tables are organized following the smaller-scale presentation scheme: spectral averages are presented first followed by the band-ratio and discrete wavelength results. Each table contains partitions for the various comparison products. Although this does not duplicate the larger-scale organization of above- and in-water intracomparisons followed by the intercomparisons of all methods, it keeps all like data products together and makes the discerning of comparative relationships relatively simple.

Table 6 presents the spectrally averaged comparisons of all of the methods for the three sampling days. The data are the Ψ(λ_1–5) values for the matrixed methods that are formed by taking a particular method, given as one of the columns, and comparing the water-leaving radiances from that method with another, given as one of the rows. Within each day, the upper right-most (triangular) side of the table presents the in-water intracomparisons, the bottom left-most (triangular) side presents the above-water intracomparisons, and the upper left-most (rectangular) portion presents the above- and in-water intercomparisons. The separate comparisons along the bottom (middle and right) of the daily results are for the same method applied to two different instrument systems.

The evolution in the analytical results are presented from a large- to small-scale perspective in Tables 7–9. Table 7 displays average comparisons across the appropriate methods or instruments (shown in Table 6) for each day and for all days. The method averages quantify the overall performance of each method with respect to the others, while the instrument averages provide greater detail in instrument and protocol sampling issues. Table 8 gives the 490- and 555-nm band-ratio results (Φ_3/5) for the analyses presented in Table 7.

All the computations in Tables 6–8 are derived from the maximum number of simultaneous casts for each comparison. Consequently, the number of data points in the averages changes from method to method, and from day to day. Tables 6–8 also give the standard deviations associated with the averages, which are an indicator of any spectral dependence in the comparisons, but a detailed inquiry into the discrete wavelengths of the comparisons is presented in Table 9. To manage the complexity in the presentation, only the S84 (WP) data is used for the latter comparisons. This is an appropriate choice because the WiSPER data has the best sampling density of the in-water data, and the majority of the data were collected in Case-2 conditions where vertical resolution needs to be maximized. The significance of this point is well demonstrated by Hooker et al. (2001).

5. Discussion

Three types of comparisons were used to evaluate above- and in-water methods for determining water-leaving radiances: spectral averages of the first five SeaWiFS wavelengths (Tables 6 and 7), the ratio of the water-leaving radiances in the 490- and 555-nm channels (Table 8), and discrete wavelengths in the 412–555-nm range (Table 9). All were quantified using the UPD approach for analyzing data, which is just one of several possible analytical approaches. It was used here over regression techniques because (a) some of the analytical relationships, either initially or at a later stage of synthesis, involved a small amount of data; and (b) no one method was assumed initially superior, so an unbiased parameterization of the differences between the methods was needed.

Traditional regression techniques are a common alternative to UPD statistics, but they can produce exaggerated parameters (e.g., slopes), and the data at the end points can have undue influence (or bias) on the regression when the dynamic range or population size of the variables is limited. The latter is particularly important for optical observations, because they are usually the most challenging areas for data collection, that is, they frequently represent overcast conditions, Case-2 waters, etc. At the final summary stage of the analysis (Table 7d), data density is potentially very good (a maximum of 95 samples can be considered for each intersection if the data are taken as one group), and the dynamic range is large (data samples are from clear and overcast sky, Case-1 and Case-2 waters, calm and roughened sea surface, etc.). Under these conditions, the limitations of regression analysis are reduced.

Regardless of the problems with least squares analyses, they are a ubiquitous tool in data analysis, so the method comparisons are re-evaluated using one such technique. Figure 8 presents the relationship between L̂^All_W(λ) versus L̃^S84_W(λ), that is, all of the above-water methods regressed against the S84 (WP) in-water method. The large differences frequently associated with Case-2 conditions are clearly evident, as are the instances of small differences and the spectral properties of the differences. The level of agreement, as determined by the slope of the reduced major axis linear regression line (Ricker 1973; Press and Teukolsky 1992), m, and the coefficient of determination, R², is very good with a difference of approximately 6.0% (m = 0.940, R² = 0.980, and N = 76).

The Fig. 8 regression results are a little better than was obtained in Table 7d, for which the overall average difference for the above-water methods with respect to S84 was 7.7%. The difference between the two approaches is small and is probably an artifact of how the data were grouped for the UPD analyses. In Table 7d, averages were determined for each day of sampling, and the days were grouped independently for the final analysis. In Fig. 8, the data are handled as one large group, so the largest population of data (Case-1 with clear sky) contributes the most influence on the regression procedure, although, this is mitigated somewhat by the reasonably good distribution of the data (the dynamic range, in terms of radiance values, is fairly large).

The more informative relationships come from the individual regressions of the above-water methods against the S84 (WP) method (Fig. 9). Estimates of the intercomparison differences from the regression parameters are:

• (a) M80 11.5% (m = 0.885, R² = 0.975, and N = 19),

• (b) C85 3.6% (m = 0.964, R² = 0.993, and N = 19),

• (c) S95 0.3% (m = 1.003, R² = 0.994, and N = 19), and

• (d) L98 11.7% (m = 0.893, R² = 0.986, and N = 19).

The regressions of all the above-water methods versus the P94 and P97 (in-water) methods also produce distinct ranking groups that are the same as the paired rankings already discussed: S95 and C85 have similar regression parameters as do L98 and M80. The estimated uncertainties between the methods using the regression technique yield values for P94 and P97 that differ from the spectral approach by approximately 5%. A regression of all the above-water methods versus all the in-water methods yields an intercomparison uncertainty of approximately 6.2% with about 97% of the variance explained (m = 0.938 and R² = 0.969). The spectrally averaged UPD analysis produced an overall uncertainty of 9.1% (Table 7d).

6. Conclusions

This study used data from three different environmental conditions that covered much of the dynamic range of in situ optical measurements, but, nonetheless, it was based on a small dataset collected during three days of measurements in the near-coastal environment. One of the three days (SDY 194) was within the parameter range established by the NRSR Workshop; the other two were not, but they were typical of the kinds of environmental conditions that can be encountered during above- and in-water radiometric field campaigns. Three in-water methods for determining water-leaving radiances from profiling (S84) and fixed-depth (P94 and P97) sampling systems were combined with four above-water methods to quantify the performance of all the methods. The removal of glint contamination from the surface measurement distinguished the above-water methods from one another and included four correction schemes: near-infrared radiance ratio (M80), Fresnel reflectance plus residual reflection (C85), modified Fresnel reflectance (S95), and near-infrared irradiance ratio (L98).

The seven methods, three different days of environmental conditions, and five sampling platforms produced a large number of performance comparisons, which were separated according to UPD analyses based on spectral averages, band ratios, and discrete wavelengths. Although each method was usually found superior to the others at some stage in the performance evaluation process, the most suitable point for overall evaluation is at the intercomparison level summarized in Tables 6–9 and Figs. 8–9. Based on these summaries, some general capabilities concerning all the methods can be discerned.

1. In terms of the 5% calibration and validation objective, and the hoped for performance to within 3%, the spectral-average approach (Table 7d) produced larger average differences (and standard deviations) than the band-ratio approach (Table 8d), which were 9.1% (5.6%) and 3.7% (1.1%), respectively. Using band ratios, the S84, P94, C85, and S95 methods produced ranges of expected differences (average plus and minus 1 standard deviation) within the 5% level, and frequently to within 3%.

2. The best results were not restricted to Case-1 or clear-sky conditions; water type was seen to be important, although other environmental parameters agreed well with the UPD levels (considered in more detail below). Consider, for example, the difficult circumstance of overcast conditions, which can be highly variable in terms of sky radiance distribution and relative (percent) variations in illumination conditions during a deployment interval. Because of the low signal levels, small absolute differences represent large relative discrepancies, but all the methods agreed very well for overcast conditions when using the data from the same instrument.

3. Above- and in-water methods not formulated for Case-2 conditions were capable of results in keeping with those achieved in Case-1 waters (e.g., Table 6). Agreement to within 5% was achieved with in-water methods in Case-1 waters for all three analytical approaches. Agreement within 5% was achieved with above-water methods in Case-2 waters for all analytical approaches, and was achieved in both water types for the band-ratio and discrete wavelength analyses (spectral averages were elevated due to large uncertainties in the blue domain).

4. For both above- and in-water methods, the largest uncertainties were usually associated with the blue part of the spectrum (412–443 nm), with the blue-green transition (490–510 nm) a local minimum, which was followed by a small increase at 555 nm (Table 9). The above-water methods that calculated the surface reflectance by assuming λ_r = 0 (M80 and L98) were spectrally dependent during Case-2, clear-sky conditions, with very large uncertainties at 412 nm (as much as 38%) and minimum uncertainties at 555 nm (less than 5%).

For the in-water methods alone, the specific details of the capabilities of the methods are as follows.

• 5) P94 and P97 grouped together, but S84 performed the best. Consequently, an in-water method making use of vertical profiles of the water column should be considered superior than those using sensors at a fixed depth, although good results were obtained for the latter during Case-1 conditions and for band-ratio analyses.

• 6) The best-to-worst ranking of the in-water methods (using the minimal range in average differences) did not depend on the analytical approach (S84, P94, and P97), but the ranking of the above-water methods did (S95, L98, C85, and M80 for the spectrally averaged approach; and C85, S95, M80, and L98 for the band-ratio approach).

• 7) The in-water spectral averages intracompared best during Case-1 conditions and worst during Case-2 conditions (Table 7c), which is consistent with the higher variability associated with the latter; however, the opposite result was seen with the band-ratio analysis (Table 8c).

Before considering the above-water methods separately, it is important to remember proper data filtering to remove glint spikes is an essential part of above-water methods that permit it (the C85 method does not). Although many schemes were considered in this study (section 3c), the adopted filter retained only the lowest 5% of the data, based on the reddest (780-nm) band. Similarly, data averaging was shown to needlessly and significantly degrade the quality of the above-water data because it artificially elevated the L_T(λ) values by contaminating them with glint. Subsampling did not degrade the above-water data as significantly as averaging, but it showed that above-water sampling rates should be equal to, or greater than, 1 Hz (Fig. 7). The conclusion to be derived here is the glint field must be adequately discretized, so it can be removed by filtering. The other conclusions for the above-water methods alone are as follows.

• 8) S95 and C85 grouped together and outperformed L98 and M80, which also grouped together, with S95 performing the best overall (well demonstrated in the Table 9 results and confirmed by the regression analyses in section 5).

• 9) Intracomparisons of above-water methods during Case-2 conditions yielded both the best and worst agreement in terms of spectral averages (Table 7c) and band ratios (Table 8c), but this could have been due more to surface roughness and sky conditions than water type.

Relative (signed) differences were not the primary statistical tool in this study, but the Fig. 9 intercomparisons between the S85 and the above-water methods showed L98 and M80 underestimated L̂_W(λ) during clear-sky, Case-2 conditions; C85 and S95 overestimated L̂_W(λ) during clear-sky, Case-1 conditions; and M80 and C85 overestimated L̂_W(λ) during overcast, Case-2 conditions. These performance biases are largely in keeping with the design characteristics of the above-water methods (Table 3).

With respect to synthesizing the performance of the above- and in-water methods in different water types, it is important to remember the explicit caution about using the M80, L98, and P97 methods in Case-2 waters. In terms of the C85 method and its published use within different water types, that is, the value of the R_rs(440)/R_rs(550) ratio, for SDY 191, 194, and 195, the ratio has values of 0.49, 1.22, and 0.69, respectively. These ratios indicate the method can be used uncertainly (almost cautiously), confidently, and cautiously, respectively. For all of these methods, however, there is the counterbalancing evidence that they all performed well in Case-2 conditions in many instances, and in some cases, were comparable to the best methods (particularly in the case of the band-ratio results).

The efforts to categorize the method performance as a function of water type deserve extra comment. First of all, a primary discriminator of Case-2 suitability is whether or not the L̂_W(λ_r) = 0 assumption is made. It is important to remember this assumption is not restricted to Case-1 conditions as long as the sediment concentration is not significant, that is, Case-2 waters not characterized by a heavy sediment load (as is usually the case in the Adriatic Sea). Second, the scheme used for classifying water types (Loisel and Morel 1998) indicated each day was close to the boundary between Case-1 and Case-2 waters. Third, the data set considered here was sufficiently small that other variables might explain differences in the methods besides water type. For example, the S95 method is not sensitive to water type, but was formulated for a flat sea, and clear sky. The SeaSAS and DalSAS results (Table 6) agree well on SDY 191 (Case-2, flat sea surface, and clear sky), they do not agree well on SDY 194 (Case-1, rough sea surface, and clear sky), and they do not agree on SDY 195 (Case-2, calm sea surface, and overcast and more variable sky). The performance of the method does correlate with water type, but it also correlates with surface and sky conditions.

Taking the water-type classification issues into account, some additional capabilities about the methods emerge.

• 10) M80 and L98 appeared less sensitive to surface roughness (they produced the best agreement with the in-water methods on the roughest day, SDY 194) and always performed well when L̂_W(λ_r) = 0. Uncertainties in S95 and C85 introduced by surface roughness were smaller than the uncertainties in M80 and L98 introduced by L̂_W(λ_r) > 0 (Case-2 water).

• 11) S95 and C85 were sensitive to surface roughness, and C85 to some extent on water type. Both methods performed well in Case-2 conditions, but in the case of a rough sea surface, both methods tended to overestimate L̂_W(λ) values (C85 up to 14% and S95 up to 10% in comparison to S84).

• 12) For the special case of a single method applied to two instruments measuring simultaneously, the above-water techniques showed a sensitivity as to whether or not the instruments were pointed in the same (best agreement) or opposite (worst agreement) directions, while still satisfying the sampling protocols; no methodological dependencies were seen with the use of the same in-water method on two data streams.

For above-water measurements from two instruments (SeaSAS and DalSAS) and one method (S95), the difference between the two viewing possibilities associated with pointing an above-water radiometer ±90° with respect to the sun introduced (on average) an additional 3%–7% of variability. It is probably caused by surface waves (and wind), inhomogeneities in the sky radiance field, and geometrical aspects (i.e., a dependence on the direction of the ambient swell with respect to the instruments, the sun, and the wind): one instrument is viewing a reflection field that is brightened and roughened by the wave crests, and the other a reflection field that is darkened and smoothed by the wave troughs. This poses many practical problems with the proper deployment of an above-water system on a moving vessel or a fixed platform because there are always preferred pointing directions due to obstructions, platform orientation with respect to the sun and waves, etc.