1. Introduction

The radiometric objective of satellite observations is to achieve normalized water-leaving radiance (nL_w(λ), wavelength dependence suppressed hereafter) or remote sensing reflectance R_rs under 5% uncertainty at the blue band in open oceans [1–3]. Toward this radiometric goal, the satellite sensors must have an on-orbit vicarious calibration (gains) applied which are derived from pristine/non-contaminated in situ and satellite matchups [4–7]. This process requires that the ground-truth nL_w and R_rs be measured with uncertainty on the order of 1–2%, or what is referred to more generally as “1% radiometry” [8].

The ocean radiometric products in field measurements are usually obtained with two sampling strategies: above- and in-water radiometry. Each approach is characteristic of a unique way of determining L_w, which is the fundamental quantity in ocean color remote sensing. The above-water approach measures the total radiance originating from the sea surface along sensor-zenith angle (θ_v) and sensor-azimuth angle (φ_v), L_t(θ_v,φ_v), and the incoming sky radiance, L_sky(180°−θ_v,φ_v). L_w can then be determined with the following measurement equation

The on-water radiometry is an addition to the collection of satellite ocean optical calibration and validation protocols [21,22] and has recently received more attention [23]. Different from the above- and in-water methods, the on-water approach determines L_w by employing a provision to prevent the skylight and sunlight from interfering with the measurements [22,24] while eliminating additional corrections and uncertainty for this contamination. The on-water L_w product can be derived with the following measurement equation

A growing body of literature on analyses of in situ radiance and reflectance uncertainties has developed based on the in- and above-water measurements. Measurements with the smallest uncertainties were reported in the ocean subtropical waters. At the MOBY site, for instance, where the chlorophyll-a (CHL) concentration is about 0.07 mg m⁻³, the spectrally averaged (400–600 nm) difference between independent in-water L_w measurements and MOBY data is about 3.1% [30]. In turbid coastal waters, the radiometric uncertainties can increase to a more noticeable level. In this regard, Zibordi et al. [31] conducted multiple optical experiments in the Adriatic Sea (CHL = 0.6–1.5 mg m⁻³) and found that the spectrally averaged differences of L_w measurements from multiple platforms are generally within ∼5–7%, while differences for R_rs vary between ∼6% and 9%. Multiple factors may have contributed to these uncertainty results, including calibration, processing, instrument difference, and environmental disturbance, etc. In fact, the uncertainties of the satellite R_rs product also vary with water types [32], with smaller values for the open ocean and much higher values in coastal waters. Estimation of the field measurement uncertainties demands characterization of not only the measurement accuracy but also measurement precision, and ideally, their potential dependence on water types. Currently, there is a lack of uncertainty estimates of on-water radiance and reflectance measurements.

In this study, we evaluate one aspect of the measurement uncertainty of L_w and R_rs, i.e., measurement precision. We focus on the on-water hyperspectral radiometric measurements. Specifically, this contribution is composed of two major efforts: i) assessment of the measurement precision of L_w and R_rs in different types of waters, and ii) quantification of the consistency of in situ radiometric measurements determined by collocated on-water instruments. We report that the water-leaving radiance and remote sensing reflectance spectra can be obtained from the on-water observations with high precision from 360 nm to 700 nm.

2. Classification of optical water types

We first describe the classification scheme used to sort the radiometric data into different optical water types (OWTs). The method was developed earlier by Wei et al. [33], which divides the global waters into about two dozen OWTs (see Fig.  1(a)). Each OWT is characteristic of a normalized remote sensing reflectance, defined as

 

Fig. 1. (a) Normalized remote sensing reflectance spectra at five nominal bands of 412, 443, 488, 551, and 670 nm for classification of optical water types (replotted after Wei et al. [33] and Wei et al. [34]) and (b) example distribution of the optical water types in the global ocean derived from the climatology of VIIRS R_rs data.

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Taking the above spectra as references, one can sort any given R_rs spectrum into a specific water type with the following steps. First, we calculate the cosine distances between the test R_rs spectrum and each of the reference spectra as

Figure  1(b) gives an example of the optical water types derived for the global ocean. This map is based on climatology (2003–2018) of R_rs data from the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP) satellite. It is clear that the vast open oceans involve a handful of water types (approximately varying from OWTs 1 to 6). In particular, OWT 1 is coincident with the five subtropical gyres. From OWTs 1 to 6, the ratios of R_rs(443)/R_rs(551) gradually decrease, implicating increase of CHL and a_ph. The OWTs 7–23 are present in coastal and inland waters.

3. Radiometric data and analyses

3.1 Description of field measurements

We conducted the on-water radiometric measurements during multiple cruises along the U.S. coastal ocean (Fig.  2). The sampling areas included MOBY (Lanai, Hawaii), the northern Gulf of Mexico, the South-Atlantic Bight, the Mid-Atlantic Bight, and Massachusetts Bay to the southwest of the Gulf of Maine. Successful deployments were retrieved at 232 stations, representative of multiple optical water types, ranging from OWTs 1 to 22. Table  1 summarizes the water bio-optical properties and atmospheric conditions for all experiments. Among all measurements, the MOBY data represent clear subtropical gyre waters. The IOPs, including the sum of the absorption coefficient of particles and colored dissolved organic matter (CDOM), a_pg(443), and the particle backscattering coefficient, b_bp(443), are small with their median values equal to 0.016 m⁻¹ and 0.0014 m⁻¹, respectively. The most turbid waters were sampled in the northern Gulf of Mexico, where the median values of a_pg(443), b_bp(443), and CHL are approximately 0.50 m⁻¹, 0.028 m⁻¹, and 4.9 mg m⁻³, respectively. The atmospheric conditions involved clear, overcast, and mixed sky with scattered clouds. The solar-zenith angles are moderate, varying between 30°–55°. The seas ranged from very calm situations to waves of ∼1 m high.

 

Fig. 2. Station map of in situ radiometric measurements in the U.S. coastal ocean. The insert shows the location of MOBY next to Lanai, Hawaii. The open circles (“○”) and triangles (“Δ”) refer to stations used for estimation of the relative uncertainty and for intercomparison analysis, respectively. The OWTs in background are derived from the climatology of NOAA VIIRS R_rs product (9 km).

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Table 1. A summary of the on-water radiometric measurements and corresponding environmental conditions. The light absorption of particles, CDOM, and particulate backscattering coefficients were estimated using the inversion algorithm of Lee, et al. [37]. CHL concentrations of surface waters were determined with the high-performance liquid chromatography (HPLC) approach.

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An on-water radiometric system was deployed at each station to obtain L_w and the above-water downwelling irradiance (E_s) data. Briefly, the on-water instrument was built on an in situ free-fall profiling unit, known as the hyperspectral profiler or HyperPro (s/n: MPR-184; University of Massachusetts Boston (UMB)) from Satlantic. It has a floating collar (40 cm in diameter) installed around the electronic hub, onto which two fins with extended arms are attached. Two hyperspectral radiometers (HyperOCR, 350–800 nm, spectral increment of 3.3 nm) for L_w and E_s are placed vertically at each end of the two extension arms. The irradiance sensor faces upward, while the radiance sensor looks downward. Further, a customized black cone (with a diameter of the bottom opening of 10.5 cm; known as the skylight-blocking apparatus) is connected to the end of the radiance sensor. The whole system is balanced with payloads such that the bottom edge of the cone is only slightly (by a few centimeters) immersed in the water. The skylight-blocking apparatus (i.e., cone) effectively blocks skylight and sunlight contamination reflected from above the sea surface from entering the fore optics of the sensor. As such, the signals recorded by the radiance sensor represent the actual radiance emerging from underneath the water surface.

During field experiments, the instrument package was released from the stern and was kept over ∼30 m away from the ship before sampling. During sampling, the radiance sensor was always operating at the side facing the Sun, thereby minimizing the potential shadowing effect from the float [35]. At each station, we continuously logged the radiance and irradiance data for about 5–10 minutes. As a result, thousands of radiance and irradiance spectra were recovered from each deployment and were available for post-processing for subsequent uncertainty analysis. Details on the instrumental configuration and deployment can be found in the previous reports [12,22,23,26].

All radiometers used in this study were frequently calibrated following the standard ocean color protocols [36]. No significant radiometric drift or bias was observed.

3.2 Estimation of uncertainties

We estimated the measurement precision for L_w and R_rs from continuously recorded telemetry data, with the following steps:

In this context, the measurement precision is defined as the ratio of the standard deviation (STD) of the mean of repeated measurement results to the mean of these measurements. We first calculated STD of these ${\bar{L}_{w,i}}$ spectra as,

Similarly, the measurement precision of R_rs was retrieved as the following

3.3 Intercomparison of collocated measurements

For insight into the repeatability of on-water observations, we conducted an intercomparison analysis of collocated measurements from two identical instruments. These measurements were acquired in the Mid-Atlantic Bight in September 2019 (Fig.  2 and Table  1). The first radiometric system (s/n: MPR-184) was operated by the UMB team, while the second one (s/n: MPR-179) was deployed at the same time by the team from the NOAA Center for Satellite Applications and Research (STAR). The two packages shared the same configuration and the same types of radiometers, and were calibrated with the same sources at STAR before the cruise. They were deployed side-by-side in the field and collected the radiance and irradiance data almost simultaneously.

For data processing, we adopted largely the same procedures as detailed in Section 3.2, specifically including: (i) pre-processing; (ii) quality control of L_w^′(t) measurements; (iii) median spectra; (iv) correction for self-shading error; and (v) constraining the variability of incident irradiance. Note that, for Step (iii), only one median spectrum was determined for each deployment as the data segmentation is not necessary for the purpose of intercomparison. A total of 17 collocated measurements were obtained which span the optical water types from OWTs 1 to 15. CHL concentrations and bio-optical properties are moderate, with mean CHL of about 0.27 mg m⁻³, and mean a_pg(443) and b_bp(443) equal to ∼0.072 m⁻¹ and ∼0.0021 m⁻¹, respectively. All of these measurements were completed under mostly sunny skies, with the solar-zenith angle varying between 34° and 69°. The sea status was relatively calm during the field experiment.

Three metrics were used to quantify the differences between collocated radiometric data: the absolute unbiased percentage difference (UPD), bias, and root-mean-square difference (RMSD). They are specifically defined as below

4. Results

4.1 Measurement precision of in situ radiance and reflectance

We first characterize the variability of in situ L_w and R_rs data. In Fig.  3, L_w and R_rs spectra are depicted in color in accordance with their OWTs. The values of R_rs and L_w vary over three orders of magnitude between 360–800 nm. No negative reflectance or radiance values are obtained at the ultraviolet (UV), blue, red, or near-infrared (NIR) bands. The non-zero observations can be partially ascribed to the virtue of direct sampling of radiance from the on-water approach (e.g., Eq.  (3)). Still, L_w shares some important features with R_rs, particularly for the occurrences and locations of the spectral maxima and minima. The spectral variability and similarity of L_w and R_rs warrants the use of the optical classification scheme for a detailed quantification of their uncertainties.

 

Fig. 3. Hyperspectral measurements in the coastal ocean for (a) water-leaving radiance L_w and (b) remote sensing reflectance R_rs. Note that only 17 labels are marked for the color bar in (b) to highlight the water types covered by this dataset. The complete classification scheme is described in Fig.  1(a).

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In the following, we characterize the estimated precision for L_w in Fig.  4(a) and for R_rs data in Fig.  4(b). The uncertainties in Table  2 refer to spectrally averaged values of measurement precision for ${L}_{w}$ and R_rs.

 

Fig. 4. Measurement precision for the on-water hyperspectral radiometric measurements of (a) radiance and (b) reflectance. The results are depicted with regard to the optical water types [33]; a total of 17 types are covered in our data.

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Table 2. Measurement precision of in situ radiance and reflectance with respect to optical water types. The values given here represent spectrally averaged values. Note that fewer measurements were used for the quantification of U_Lw because of the data filtering for which the CV of the corresponding E_sdata was less than 10%.

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First, the values of U_Lw and U_Rrs at the UV and visible bands are conspicuously small, and they appear to be independent of the optical water types. An anomaly exists in OWT 22, in which L_w and R_rs are subjective to increased uncertainties. We found that the in situ data clustered in these types of waters represent those from turbid and highly absorptive waters. According to the estimation of the spectral absorption coefficient and CDOM and detritus absorption coefficient (a_dg), the a_pg values are 2.2, 1.4, 0.76, 0.31, 0.25 m⁻¹ at 410, 443, 486, 551, and 671 nm, respectively, and the corresponding mean a_dg values are 1.7, 1.0, 0.47, 0.16, and 0.02 m⁻¹, respectively. Due to extremely high absorption coefficient, the resulting spectral R_rs values are very small. For example, the minimum and maximum spectral R_rs values, R_rs(410) and R_rs(551), are approximately 0.0017 and 0.0046 sr⁻¹, respectively. In addition, half of these measurements falling into OWT 22 were measured under cloudy to overcast skies, where their E_s(410) values are only 1.5–50 µW cm⁻² nm⁻¹. This represents an exceptional condition, under which the ocean color satellites often cannot have ocean color measurements.

Second, it is interesting to observe that U_Rrs is overall smaller than U_Lw, which is somewhat counterintuitive. From OWTs 1 to 21, specifically, U_Lw varies between ∼1.5% and ∼4.6%; U_Rrs varies between ∼0.9% and ∼4.4%. Such an observation is nevertheless possible, considering the following facts. On the one hand, these uncertainties are quantified based on the in situ measurements of L_w and E_s. As shown in Table  2, the CV’s of E_s(551) are around 6%, a value generally greater than reported E_s measurement uncertainties [30,31]. As such, these CV’s may be ascribed to both the E_s measurement uncertainties and the variance of possibly non-stable incident irradiance itself. The latter can eventually propagate to L_w estimates, which would increase the values of U_Lw. On the other hand, R_rs is the ratio of L_w to E_s, which covary, and therefore is largely insensitive to the change of instantaneous E_s. Therefore, U_Rrs is determined by the uncertainties from both L_w and E_s measurements. As a result, we may conclude that the values of U_Lw in Fig.  4(a) and Table  2 have likely been overestimated as some of the variation can be attributed to variation in ambient light field, rather to the ability to measure L_w.

Third, both U_Lw and U_Rrs show much larger values at the NIR bands than those at the UV and visible bands. Such a different performance is related to the small values of L_w and R_rs at the NIR bands. Besides, unlike the results at the UV-visible domain, U_Lw(NIR) and U_Rrs(NIR) demonstrate a dependency on OWTs. As shown in Table  2, they tend to decrease from the clearest waters (OWT 1 in this case) towards more turbid waters (OWT 22). Yet, the U_Lw(NIR) and U_Rrs(NIR) values of > 10% are mostly found for OWTs from 1–9, where the magnitudes of L_w and R_rs are often much smaller than other types of waters.

Summarizing the uncertainty analyses, U_Lw is about 2.7% on average between 360 and 600 nm and 3.7% over 600–700 nm. U_Rrs is 1.9% over 360–600 nm and 2.8% for 600–700 nm. In the NIR bands, U_Lw and U_Rrs increase to significantly higher levels of 36% and 21%, respectively. We also note that the self-shading errors for each segmented data sequences of ${\bar{L}_{w,i}}$ and ${\bar{R}_{rs,i}}^{\prime}$ could be infinitesimally close to each other. Ignoring the shading correction, we find that the derived uncertainties will reduce to ∼1.9–2.3% for L_w and to ∼1.5–1.8% for R_rs in the UV-visible domain.

4.2 Intercomparison of collocated measurements

For a clear presentation, we introduce notations of “STAR” and “UMB” to differentiate the collocated radiometric measurements.

Figure  5 first compares two sets of radiance data, denoted as ${L}_{w}^{{STAR}}$ and ${L}_{w}^{{UMB}}$. For the purpose of simplicity, the comparisons only considered a few selected wavelengths. The error bars represent STD of the radiance measurements from each deployment, which are primarily a result of the variability of incident irradiance and sea surface waves. According to the comparisons, it is obvious that the two sets of L_w measurements agree with each other very well in the UV-visible domain. The spectrally averaged UPD is 3.4% with a near-zero bias and small RMSD of 0.0054 µW cm⁻² sr⁻¹ nm⁻¹ (Fig.  5(a)). These small differences echo the high precision of radiance measurements identified in the previous section. In the NIR domain, much elevated differences are observable between ${L}_{w}^{{STAR}}$ and ${L}_{w}^{{UMB}}$, where UPD = 26%, bias = 5.3%, and RMSD = 0.00096 µW cm⁻² sr⁻¹ nm⁻¹ (Fig.  5(b)). The relatively larger differences can be explained partly by the small values of radiance at the NIR domain, which vary between ∼0.001–0.01 µW cm⁻² sr⁻¹ nm⁻¹. Overall, the UPDs between ${L}_{w}^{{STAR}}$ and ${L}_{w}^{{UMB}}$ are comparable to the uncertainties of L_w measured with a single instrument given in Table  2 and Fig.  4.

 

Fig. 5. Comparison of in situ water-leaving radiance from the collocated on-water radiometric measurements (differentiated with superscripts of “STAR” and “UMB”) for (a) the UV-visible bands and (b) NIR bands. The spectrally averaged UPD, bias, and RMSD are given in each plot, with the solid line representing 1:1. The colors are indicative of different wavelengths (see legend for details). The error bar refers to STD of each measurement.

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We further compare the collocated R_rs data in Fig.  6. It is found that the two sets of R_rs measurements, ${R}_{{rs}}^{{STAR}}$ and ${R}_{{rs}}^{{UMB}}$, are subjected to larger differences than those of L_w, where UPD = 8.6% at the UV-visible domain and UPD = 30% at the NIR bands. In addition, ${R}_{{rs}}^{{STAR}}$ is generally higher by ∼6.6% than ${R}_{{rs}}^{{UMB}}$ at the UV-visible domain and by ∼15% at the NIR bands. The differences between collocated R_rs products are expectedly greater than the radiances, partly because the R_rs data have involved irradiance measurements from two independent instruments. Indeed, we found that these elevated differences and biases at least partially can be traced back to the irradiance measurements. As shown in Fig.  7, the two sets of irradiance measurements, ${E}_{s}^{{STAR}}$ and ${E}_{s}^{{UMB}}$, suffer larger differences, where UPD = 7.3% at the UV-visible domain and UPD = 9.2% at the NIR bands. In particular, ${E}_{s}^{{STAR}}$ is generally lower compared to ${E}_{s}^{{UMB}}$ by 5.8% at the UV-visible domain and by 6.5% at the NIR bands. Underestimation (or overestimation) of E_s can cause overestimation (or underestimation) of R_rs.

 

Fig. 6. Comparison of remote sensing reflectance derived from the collocated on-water radiometric measurements (differentiated with superscripts of “STAR” and “UMB”) for (a) the UV-visible bands and (b) NIR bands.

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Fig. 7. Comparison of above-water downwelling irradiance from the collocated on-water radiometric measurements (differentiated with superscripts of “STAR” and “UMB”) for (a) the UV-visible bands and (b) NIR bands.

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In Fig.  8(a), we sorted the collocated radiance measurements into OWTs and then derived the UPD’s for radiances within each of the OWTs. The classified UPD’s show no dependency on OWTs at the UV and visible domain (also see Table  3 for the spectrally averaged UPD’s). For wavelengths shorter than 600 nm, the UPD’s of ${L}_{w}^{{STAR}}$ and ${L}_{w}^{{UMB}}$ are largely within ∼3% (varying between 0.7% and 4.5%). This independence of OWTs agrees with the uncertainty results in Fig.  4(a). For the NIR bands, the UPD’s are much larger, which in part is related to the small radiance values in this spectral range. Besides, the UPD’s tend to decrease from OWT 1 toward OWT 8. An exception is with the radiance measurements in OWT 5, where the differences slightly increased but are still within ∼10% for 600–700 nm. This increase of differences in OWT 5 is found related to one measurement obtained off of the east New Jersey coast; it is not clear yet of the underlying cause.

 

Fig. 8. Unbiased percentage difference of collocated on-water hyperspectral radiometric measurements for (a) radiance and (b) reflectance. The y-axis depicts the optical water types corresponding to the in situ measurements. White blanks represent no data available.

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Table 3. Difference between the collocated measurement pairs with respect to optical water types. The values given here represent spectrally averaged values. The measurements are only considered for uncertainty analysis when E_sdata are subject to variation with CV less than 10%.

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The OWT-specific comparison results for R_rs are given in Fig.  8(b) and Table  3. Most of the R_rs determinations show differences of well above 5%, partly due to differences in irradiance measurements. No persuasive dependencies are observed for the visible bands. Yet, the differences at the NIR bands decrease from OWTs 1 to 8.

It is worthwhile to discuss further the large differences between two irradiance measurements. We calibrated the radiometers before the field experiments following the standard ocean optics protocol. The overall differences between the lab-measured quantities and the light references are within ∼0.5%. The sea state was relatively calm for these observations; so potential contamination of E_s measurements, for example, by possible sea sprays, cannot explain the rather systematic differences. One noticeable factor exists, however, that all of these field observations for intercomparison analysis were conducted under very large solar-zenith angles, with θ_s varying between 33° and 68° (the median solar-zenith angle is 57°) (Table  1). If there are differences in the cosine response between the two irradiance sensors, large differences (up to ∼15%) may be possible for E_s measurements under such large θ_s values [16,39]. More effort is certainly needed for a continued investigation into the potential errors associated with these irradiance sensors or irradiance sensors in general.

5. Discussion

5.1 Uncertainty components of the measurement results

The measurement precision of water-leaving radiance from the on-water approach is composed of two contributors: the uncorrected radiance L_w^′ and the self-shading error ɛ. From the measurement equation of Eq.  (3), U_Lw can be expressed as

The shadowing correction was performed with a model specifically designed for the systems equipped with the skylight-blocking apparatus [35]. The model requires the intermediate reflectance spectrum, i.e., ${\bar{R}_{rs,i}}^{\prime}$, which is the median spectrum for each individual segment of data sequence in Section 3.2. Uncertainties associated with ${\bar{R}_{rs,i}}^{\prime}$ will transfer to ɛ_i during the spectral estimation, which further propagate to the final products of L_w and R_rs. To understand the roles of the shading correction, we estimated U_ɛ by following the same procedures described in Section 3.2. In Table  4, the spectrally averaged U_ɛ values are given for each of their OWTs. First, the results clearly show that U_ɛ is dependent on the water types. Specifically, as suggested in Table  4, U_ɛ increases from OWTs 1 to 22. In other words, it decreases with the blue-green R_rs ratios, R_rs(443)/R_rs(551), or equivalently, increases with CHL. Still, the maximum values of U_ɛ are shown to be within 3.4%, 1.21%, and 0.31% for the spectral ranges of 360–600 nm, 600–700 nm, and 700–800 nm, respectively. Such dependencies reflect the sensitivity of shading errors to the estimation of absorption and backscattering coefficients in Eq.  (8) [35]. Second, it is evident that U_ɛ is spectrally dependent; it decreases from the UV bands toward longer wavelengths. On average, U_ɛ is ∼2% over 360–600 nm, ∼0.3% for 600–700 nm, and only ∼0.05% at the NIR bands for the waters in this study. Such a dependency, at least partially, is related to the fact that the pure seawater absorption and scattering coefficients play a relatively bigger role in determining the estimation of ɛ at the NIR bands.

The L_w^′ measurements obtained as such are liable to the influence of the sea surface waves. The sea waves induce the in-water light field fluctuations [40], which then propagate to the upwelling radiance L_u [41]. With the above-estimated U_ɛ, we derived U_Lw′ from Eq.  (16) by assuming negligible contribution of Δ. Note that, because of this assumption, the values given in Table  4 best describe the upper limits of U_Lw′. According to the tabulated results, U_Lw′ is spectrally dependent, increasing towards longer wavelengths, which is opposite to U_ɛ. On average, U_Lw′ is ∼2.2% over 360–600 nm, ∼3.5% for 600–700 nm, and ∼29% for 700–800 nm. Such spectral variation could primarily be a result of the spectral dependence of the light field [40]. In addition, results in Table  4 exhibit weak covariation of U_Lw′ with the OWTs, where the surface waves might have complicated this dependency.

Table 4. Comparison of the uncertainty for estimated self-shading error and measured radiance (U_ɛ and U_Lw′) in different water types.

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To sum up, U_Lw′ is generally greater than U_ɛ over the full spectral domain between 360 and 800 nm. As ∂L_w/∂L_w^′ is usually greater than ∂L_w/∂ɛ, it can be deduced that U_Lw′ will play a larger role in determining the measurement precision of L_w.

5.2 Quality control of the uncorrected radiance L_w^′

The quality control of the uncorrected radiance measurements L_w^′ is essentially to use a filter to remove potentially contaminated data. We developed this data filtering procedure in accordance with the pattern of movement of the instrument. Sitting at the surface, for example, the instrument will likely move up and down with the passage of big waves. Consequently, the skylight-blocking cone may completely rise above the water surface, such that the unwanted ambient light (skylight and sunlight) can instantly reach the fore optics of the radiance sensor. As a result, such contaminated radiance will be greater than L_w. On the other hand, it is also possible for the cone to submerge such that the entrance window of the radiance sensor is completely immersed in water. The radiance measured by a submerged radiometer can be described as L_w^′ = L_u^′·exp[z·K_L], where L_u^′ is an “apparent” upwelling radiance at depth z. L_u^′ is different from L_u because the radiance sensor is calibrated for “in-air” observation, and hence, assumes no immersion effect. In fact, L_u^′ is equal to the true in-water radiance L_u at this specific depth divided by the immersion coefficient for seawater, i.e., L_u^′ = L_u/I_f, where I_f is the immersion factor. We know that the commercial radiance sensors such as the Satlantic radiometers usually have an immersion factor of around 1.7 [42]. In addition, the exponential term exp[z·K_L] is only slightly above 1. For example, it is about 1.03 with an assumption of z = 0.03 m and K_L = 1 m⁻¹. It can be deduced that L_u^′ exp[z·K_L] is about half of the upwelling radiance right below the water surface, L_u(0⁻). That is to say, the radiance measured by a submerged sensor is smaller than L_w. The above discussion regarding the wave-induced over- and under-estimation of L_w corroborates the use of step (ii) in Section 3.2 for the filtering of the instantaneously recorded radiance L_w^′. The filtering process, the residual errors, and roughened sea surface together have contributed to U_Lw′.

From an experimentalist’s point of view, under the most unfavorable wavy conditions, at least 1/3 of the continuous measurements are valid data. The current analysis assumed a moderate threshold (±15%) for data filtering. Constraining the threshold will not significantly affect the radiometric products. In Table  5, we provide comparisons of the water-leaving radiance products after applying different thresholds: ±30% and ±15%. As expected, the UPD’s among L_w are generally within ∼0.3% except for red and NIR bands where L_w have very small values. The biases and RMSD are negligibly small as well. To increase or relax the threshold will not significantly affect final products of L_w and R_rs.

Table 5. Differences between water-leaving radiance L_w derived with thresholds of ±30% and ±15% ^a

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5.3 Dependency on the water types

Previous studies often referred to the water types as either Case 1 or Case 2, which is a classification scheme proposed by Morel and Prieur [43]. We did not use this binary scheme in that the Case 1–Case 2 classification is an oversimplification of the optical properties, in particular, of the coastal ocean. This is obvious in view of the variable spectral shapes and magnitudes of reflectance spectra as indicated in Fig.  1(a). Instead, the optical water types in this study result from a hard classification [33], which can assign a specific OWT to given R_rs spectra.

The uncertainty results quantified for L_w and R_rs at the UV-visible domain show no sign of dependency on the OWTs. This observation underlines the reliability of the on-water radiometric measurements. Such results can be attributed to the distinctiveness of the on-water radiometry — it largely bypasses the surface correction in Eq.  (1) and the extrapolation and transmission in Eq.  (2). Similar to an in-water approach, the on-water measurements have to be corrected for the shading errors, which play a secondary role in the total precision of L_w (Table  4).

6. Conclusions

The calibration of in-orbit satellite ocean color sensors requires that the ground-truth data should be achieved within ∼1–2% uncertainties. Toward this goal, great efforts were invested to assess ground-truth measurement uncertainties, particularly from the in- and above-water approaches. In this study, we have focused on a relatively less studied method — the on-water radiometry. We specifically addressed the measurement precision problems associated with the water-leaving radiance measurements from this approach.

Our examination reveals that the measurement precision of L_w (for the data precision) from the on-water approach can reach satisfactorily high levels, with the upper limits at 2.7–3.7% on average, over the UV-visible spectral domain. In addition, we find that such low uncertainties are achievable across different optical water types. The low levels of radiance uncertainties and the independence of the optical water types are an important attribute to this new method. We also assessed the measurement precision of R_rs products, which is about 1.9% over 360–600 nm and 2.8% for 600–700 nm.

The intercomparison of the collocated measurements allow for further evaluation of the consistency in the field measurement of water-leaving radiance. In general, our analyses show that the collocated radiometric data are highly consistent with each other. The L_w data are only subjected to a difference of less than ∼3.4% over 360–600 nm. The corresponding R_rs data pairs suffer increased differences of up to ∼8.6% due to a difference originating from variable irradiance measurements.

According to these analyses and earlier results, precise measurements of water-leaving radiance are attainable from the on-water approach for a wide range of waters, including stratified or shallow bottom waters. These features are important for supporting satellite calibration as well as validation exercises.