1. Introduction

To achieve mission objectives for acquiring high quality radiometric data and derived biogeochemical products, current and heritage satellite ocean color (OC) remote sensing sensors have relied on robust in-orbit radiometric calibration and validation procedures [1–3]. In fact, the latest report of the International Ocean Colour Coordinating Group (IOCCG 14) [4] was exclusively devoted to in-orbit satellite OC sensor calibration, and thus underscores the necessity of employing proper post-launch calibration procedures in retrieving geophysical parameters from top of atmosphere (TOA) sensor measurements. Among those post-launch calibration procedures, the final adjustment made to the sensor’s TOA measurements, based on in situ surface measurements or climatology model, is known as a vicarious calibration procedure. There are two basic kinds of vicarious calibration [4]. The first one is usually referred to as the (system) vicarious calibration procedure. In that procedure, calibration coefficients are obtained by forcing satellite-derived water-leaving radiances to agree with in situ ones, and this approach is traditionally employed in the vicarious gain derivations of the current ocean color data processing [5–7]. The second procedure, which is referred to as a radiometric vicarious calibration, consists of simulating the TOA signal that the sensor should measure under certain conditions, and to compare it to the measured signal, then the derived gains can be used for the verification of the sensor radiometric accuracy as well as calibration performance.

For most heritage and current satellite OC sensors, vicarious calibrations have traditionally been carried out with the first approach (i.e., the system vicarious approach) and they are usually conducted at an open ocean location where atmospheric aerosol loads and variability are minimal. Customarily OC vicarious calibrations of visible bands are carried out based on measurements made off Lanai Hawaii by the Marine Optical BuoY (MOBY) [7, 8] whereas the near-infrared (NIR) band adjustments are based on the matching of aerosol type retrieval from South Pacific Gyre to those observed at the Tahiti AERONET site [7, 9]. The MOBY based system vicarious procedure for visible bands assumes that satellite-retrieved atmospheric properties over the site location are accurate and reapply those in gain derivations. As a result, it combines both: the calibration of the sensor and atmospheric correction algorithm. At the same time, the onboard sensor calibration process includes multiple instruments (solar diffuser, its monitor, etc.) which have a tendency to change their characteristics over time (instrument drift) and thus require their own separate monitoring and calibration [10]. In addition, any potential uncertainty in the NIR band adjustment, currently carried out separately from MOBY, will also be propagated to become uncertainties in vicarious adjustment of the visible channels through the atmospheric correction process, with an impact that can vary significantly [6, 11, 12]. As a result, although retrievals of the normalized water-leaving radiance (nLw), chlorophyll concentration and inherent optical properties (IOP) from the current OC sensors are reasonably accurate for most oceanic waters where atmospheric parameters are not significantly different from those at the MOBY calibration site, they generally become less accurate in estuarine and coastal areas due to: greater variations of atmospheric composition [13–16], algorithms issues, e.g., the black ocean assumption at the NIR bands [17–19] and possibly calibration issues as well.

In spite of these challenges, the next generation of satellite OC sensors (for instance, the planned future Ocean Color Imager (OCI) of Pre-Aerosol, Cloud, and Ocean Ecosystem (PACE) mission) are looked at to provide high quality OC observations of the inland, estuarine and coastal areas, which in the aggregate have significant implications to global biogeochemistry and are particularly relevant to living marine resources and sustainable ecosystem services [1]. In addition, more and more future and current satellite OC sensors have incorporated hyper-spectral capabilities for the better characterization of the radiometric signals of both atmosphere and water. Thus, an OC vicarious calibration approach, which is capable of making radiometric assessments: (i) both in multi- and hyper-spectral scales, (ii) over the whole spectral range and independently of the atmospheric correction process, (iii) through OC and atmospheric data provided by existing infrastructure and with little or no additional cost, would be highly desirable.

In fact, alternative methods for in-flight and vicarious calibration of satellite sensors have long been proposed. For example, Vermote et al. [20] proposed Rayleigh scattering based methods for in-flight calibration of the visible channels of the Satellite Pour l’Observation de la Terre (SPOT). Gordon and Zhang [21] also examined the accuracy one could expect in estimating the TOA reflectance of the ocean–atmosphere system with the use of RT simulations based on a measurement suite carried out at the sea surface (i.e., measurements of the normalized sky radiance and the aerosol optical thickness (τ_a)). However, most of the simulations in their study were carried out in the NIR (865 nm) where the water contribution is negligible. In addition, Martiny et al. [22] evaluated the radiometric calibration of the Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) in the NIR by the use of ground-based radiometer measurements of solar extinction and sky radiance in the Sun’s principal plane, at two Aerosol Robotic Network (AERONET) sites, one located 13 km off Venice, Italy, and the other on the west coast of Lanai Island, Hawaii. Melin and Zibordi [23] also carried out a regionally specific vicarious calibration study for the SeaWiFS and Moderate Resolution Imaging Spectroradiometer (MODIS) sensors with the use of the nLw data collected at the AERONET-OC sites in the northern Adriatic Sea and Baltic Proper. Similarly, an analysis of the MOBY like system vicarious calibration for the Visible Infrared Imaging Radiometer Suite (VIIRS) sensor has been recently carried out based on the nLw data collected at the WaveCIS AERONET-OC site of Gulf of Mexico [24].

In this study, we utilized a radiative transfer (RT) based vicarious approach for satellite OC sensors which makes use of high quality data from multiple sites of the ocean color component of the existing AERONET-OC [25] sites. And, we analyzed its capability for achieving a required uncertainty level below 0.5% for calibrations in blue–green spectral regions, which corresponds to the radiometric uncertainty lower than 5% in satellite derived nLw products in terms of absolute values for oligotrophic-mesotrophic waters [1, 4]. This RT based approach is also capable of carrying out OC sensor calibrations independently of the atmospheric correction process. And, whereas the main objective of the vicarious calibration procedure is to determine the calibration coefficients that will lead to satellite retrieved radiometric products with lower uncertainties, the potential of this RT based approach for delineating the uncertainties associated with the sensor calibration and atmospheric correction process may also offer possibilities for the developments of the improved atmospheric correction algorithms, especially for coastal locations.

In Section 2 that follows, we will present the background of the AERONET-OC network, and details of the sites from which data have been extensively used in this study. In Section 3, implementation of the radiative transfer simulations for the ocean-atmosphere coupled system is detailed along with the discussions on in situ and satellite data processing and filtering procedures. Matchup comparisons between the simulated and satellite (MODIS and VIIRS) TOA radiance data as well as procedures for the derivation of radiometric calibration gain factors will be presented in Section 4. Analysis of the derived gain factors for the evaluations of cross site discrepancy and temporal variability will be discussed in Section 4. Summary and conclusions are presented in the last Section 5.

2. AERONET-OC sites

AERONET-OC provides capabilities for measuring the radiance emerging from the sea (i.e., water-leaving radiance) through modified sun-photometers (SeaPRISM) installed on offshore platforms, in addition to the standard land-based AERONET aerosol data. In fact, the AERONET-OC network was primarily designed to support long-term satellite OC investigations through consistent and accurate cross-site measurements [15] and has been instrumental in satellite OC validation activities through standardized measurements that are: (i) performed at different sites with a single measuring system and protocol, (ii) calibrated with an identical reference source and method, and (iii) processed with the same software. SeaPRISM data from each AERONET-OC site are transferred by a satellite link directly to NASA, processed by the NASA AERONET group, and posted on the NASA AERONET website [26].

Feasibility of the proposed radiative transfer vicarious calibration approach will be demonstrated in detail for two AERONET-OC sites: specifically at the Long Island Sound Coastal Observatory (LISCO) in Long Island Sound, NY and WaveCIS in the Gulf of Mexico. The LISCO platform combines a multispectral SeaPRISM system with a collocated hyper-spectral HyperSAS system (Satlantic, Canada) [27, 28] and is located approximately 3 km off the shore of Long Island near Northport, NY. The coordinates of the site are N 40°57′16″, W 73°20′30″. Based on time-series IOPs derived from one year of LISCO’s SeaPRISM nLw data using the Quasi Analytic Algorithm (QAA) [29, 30], which retrieves spectra of absorption and backscattering coefficients, the particulate backscattering coefficient at 551 nm for the LISCO water is found to be in the range of 0.01 to 0.03 m^–1, the total absorption coefficient at 443 nm varies from 0.38 to 1.2 m^–1; the absorption due to Colored Dissolved Organic Matter (CDOM) at 442 nm is typically close to 0.4 m^–1 and in few cases can be as high as 1 m^–1. The WaveCIS site is located approximately 18 km off the shore in the Timbalier Bay area, MS. The coordinates of the site are N 28°52′00″, W 90°28′59″. Time-series IOPs of the WaveCIS water derived in a similar way as for LISCO show that the particulate backscattering coefficient at 551 nm for the WaveCIS water is usually around 0.01 m^–1. Unlike the LISCO water, the total absorption of the water body is low, with its seasonal average being equal to 0.31 m^–1 at 442 nm, of which ~0.15 m⁻¹ is attributed to CDOM. Aerosol optical properties observed at the LISCO and WaveCIS sites are quite different. For LISCO, the three-year (2011–2013) average Angstrom exponent γ (443, 870) defined between 443 & 870 nm is 1.76, whereas it is 1.23 for WaveCIS. This implies that the aerosols over WaveCIS are dominated by coarse particles whereas the LISCO site has notable contributions from fine aerosol particles. Analysis of the two-year AERONET-OC time series data set reveals that aerosol optical thickness at 443 nm are on average 0.16 and 0.13 for LISCO and WaveCIS locations respectively.

The time series and matchup comparison analysis between the satellite and in situ nLw data shown hereafter have been quality assured through the application of standard OC satellite data validation procedures [13, 14, 25]. Figure 1 displays the time series of the VIIRS, MODIS and AERONET-OC SeaPRISM nLw at 551 nm for a two-year period (2012 & 2013). The satellite data shown in Fig. 1 incorporate the latest NASA’s reprocessing (i.e., version 2013.1). The figure shows good agreement in temporal and seasonal variations between the satellite and AERONET-OC SeaPRISM retrieved water-leaving radiance data. This indicates that both satellite and in situ derived radiometric data from those sites have quality that is reasonable for OC satellite data validation use. We will demonstrate that, despite high variability of the oceanic and atmospheric conditions, these data are also appropriate for vicarious calibration purpose.

 

Fig. 1 Time series of nLw(551nm), in mW/cm²/μm/sr, derived from AERONET-OC SeaPRISM (green squares), MODIS (blue squares), and VIIRS (brown circles) for (a) WaveCIS and (b) LISCO. The period of SeaPRISM data gap for LISCO is resulted from a minor damage of the instrument sustained during hurricane Sandy and subsequent re-calibration at NASA.

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3. Radiative transfer simulations for the ocean-atmosphere coupled system

3.1 Implementation of the ocean-atmosphere coupled system

Our approach for a radiometric vicarious calibration of OC sensors is based on accurate Radiative Transfer (RT) simulations, which take into account the interactions of atmosphere-ocean dynamic systems and are carried out for the full TOA–ocean–TOA light path, using information on atmospheric and oceanic parameters available at AERONET-OC sites. The TOA signal measured by a satellite sensor observing oceanic targets is predominantly made up of scattering of the incident solar irradiance by atmospheric components, while contributions from the water-leaving signal account for only around 10% [31]. Atmospheric Rayleigh scattering is the main process contributing to the TOA signal with additional atmospheric contributions from aerosol scattering and gaseous absorption. TOA contributions from the water are from backscattering by the water body, diffuse reflection by whitecaps, and sea surface reflectance. Ideally, if optical properties of each layer of the ocean–atmosphere system (such as the single scattering albedo (SSA), scattering phase function, optical thickness), along with the environmental conditions (such as atmospheric pressure for the estimation of the Rayleigh component [32] and the wind speed for the simulation of the sun glint caused by the wind-ruffled sea surface [33]), are known, the TOA radiance for a specific sensor viewing direction under particular solar illumination geometry can be simulated through a RT code, as depicted in the flow diagram of Fig. 2.

 

Fig. 2 Flow diagram of RT simulations of the TOA radiance L_t (λ).

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High quality aerosol optical thickness data set is readily available to us through AERONET-OC measurements. In addition, the AERONET-OC inversion algorithm [34–36] provides aerosol SSA data together with scattering phase functions obtained through multiple AERONET sky radiance measurements. IOPs of water (i.e., absorption and scattering coefficients) are derived from the water-leaving radiance data of AERONET-OC using a QAA [29, 30], while the Petzold scattering phase function [37] is assumed for water. Wind speed and atmospheric pressure data for the site locations are acquired from the National Weather Service, and molecular absorption in the atmosphere is acquired from the NASA Ozone Monitoring Instrument (OMI). The RayXP RT code [38, 39] is employed for the full sunlight path through the ocean–atmosphere system and TOA radiance simulations are carried out with the AERONET-OC retrieved optical properties of the ocean and the atmosphere within the field of view of a sensor during satellite overpass time. In addition, the TOA radiance is generated for the specific viewing geometry of the sensor and thus direct comparison between the simulated and measured TOA radiance, L_t(λ), can be made to check the radiometric accuracy of the satellite sensor.

In generating simulated TOA radiance for the matchup with satellite data, all input in situ AERONET-OC data to the RT simulations are selected from the measurements made within a ± 2h time window of the satellite overpass time of the locations of the sites. This approach ensures that the in situ data set is minimally affected by the natural temporal changes in the atmosphere and water and it is also in line with the validation and vicarious exercises carried out for other OC sensors [23, 25, 40]. In addition, all input AERONET-OC data used in this study are level 1.5 data, and have been manually checked, making sure that no corrupted spectra were present in this data set. Unlike the MOBY-based system vicarious procedure that is restricted only to visible channels, the proposed approach is applicable to all parts of the spectrum, including NIR, provided that input optical properties are available for those wavelengths. Thus, L_t simulations for 862 nm VIIRS nominal center wavelength are carried out with τ_a values interpolated from the AERONET-OC SeaPRISM measurements at 870 nm using γ values defined between the 443 and 870 nm. AERONET-OC SeaPRISM does not provide measurements at the VIIRS’s 745 nm and MODIS’s 748 nm bands, and as a result, τ_a values at those wavelengths are derived from the AERONET-OC SeaPRISM measurements at 870 nm using γ values defined between the 551 and 870 nm. Input Rayleigh optical thickness, τ_R, values are also calculated for those exact VIIRS & MODIS center wavelengths. The AERONET-OC inversion algorithm derives the SSA values only at the 443, 671 and 870 nm wavelengths and, as a result, values for the VIIRS & MODIS center wavelengths are obtained through linear interpolations. In addition, water-leaving radiances at 745 and 748 nm are not negligible, especially for typical water conditions encountered at the LISCO and WaveCIS locations and need to be taken into account in the simulations. For the LISCO, time-series of hyper-spectral nLw(λ) measurements are available through the HyperSAS instrument suite and annual average nLw value at 745 nm, which is observed to be ~0.05 mW/cm²/µm/sr, is used in all the simulations carried out for LISCO site. However, for the WaveCIS site, annual average of VIIRS retrieved nLw(745nm), which is observed to be ~0.034 mW/cm²/µm/sr, is used in all simulations. We were forced to use the annual average values because water leaving radiance retrievals for the 745 nm channels are very often negative mainly due to over correction of sky and sun glint in the case of LISCO’s HyperSAS instrument, and algorithm failure in the case of VIIRS retrievals at WaveCIS. In our simulations, water-leaving radiance at 862 nm is always assumed to be negligible. This assumption is based on the AERONET-OC SeaPRISM water-leaving radiance data at 870 nm wavelength which frequently exhibits negative values and on average is almost always nearly zero at both sites.

3.2 Satellite data

Pseudo Level 1 VIIRS images of the LISCO and WaveCIS locations have been obtained for two years (January 2012 to December 2013) period from NASA Ocean Color website [41]. Calibrations on these Level 1 images are based on results from the prelaunch characterization (e.g., spectral response, polarization sensitivity, response versus scan angle, etc.), however temporal calibrations which take into account the change in radiometric response for the sensor bands are not included in this data level yet. These images are then processed with the SeaDAS software version 7.0.2 package in order to generate the fully calibrated and geo-located level 2 data (i.e., the prelaunch-calibrated radiances are multiplied by trending coefficients that track the on-orbit change of the radiometric gains). In the SeaDAS processing, vicarious calibration coefficients at all wavelengths have been set to unity gain. VIIRS TOA L_t (λ) at all wavelengths are acquired along with the solar and sensor geometries which are subsequently used in TOA simulations in order to make the direct comparisons between the simulated and satellite L_t (λ) possible. We also acquired the VIIRS Sensor Data Record (SDR) data of Interface Data Processing Segment (IDPS) processing from the NOAA's Comprehensive Large Array-data Stewardship System (CLASS) [42] for the same data period and locations. This NOAA VIIRS SDR data differs from that of NASA in significant ways, for instance, they are completely calibrated and geo-located at the SDR level, and their onboard and temporal calibration methodologies also differ from NASA’s. Comparison between the NASA and IDPS VIIRS L_t data exhibits almost perfect correlation at every wavelength but shows slight discrepancy in terms of magnitude. For consistency purpose, we used only the NASA VIIRS data for all analyses in this study. Similarly, MODIS level 1 collection 6 images of the WaveCIS location are also acquired from the NASA Level 1 and Atmosphere Distribution System (LAADS) [43] of Goddard Space Flight Center. Unlike NASA VIIRS data, these data are fully calibrated and geo-located, thus SeaDAS processing is not required in the acquisition of the TOA radiance.

For the coastal areas such as LISCO’s location, the TOA radiance measured by satellite over sea can be affected by a fraction of light reflected from the mainland, the so-called adjacency effect, thus reducing the image contrast when the atmospheric turbidity increases. A study has been carried out to investigate and quantify the adjacency effect over the LISCO area using the high resolution Level 1 MERIS data [44]. It has been found that the adjacency effect is significant up to 1.5 km from the coast that is, 2 km before the platform location, and becomes negligible in the direct vicinity of the platform and further offshore. Moreover, radiometric vicarious gain coefficients, whose derivation procedures are detailed in the next section, for the LISCO site exhibit very small (only about 0.5%) discrepancies from the ones derived for the WaveCIS. Therefore VIIRS TOA images of the LISCO locations are assumed free or negligible (if any) of adjacency effect and are used without any further correction.

The VIIRS and MODIS TOA L_t (λ) used for comparisons with the simulation results are all extracted from a small region (3 × 3 pixel box) centered at the site locations. In this processing we utilize a scheme in which average values of the L_t(λ) of all pixels, except the center of the region of interest, are evaluated against simulated TOA L_t(λ). The exclusion of the central pixel is intended to minimize the potential uncertainty resulting from the platform effects due to the high albedo (reflectivity) of the platform structure. In addition, a satellite data filtering criterion, which excludes the satellite L_t(λ) data with high spatial variability from the analysis, is also applied to ensure that the data used for the comparisons are not affected by the unexpected environmental conditions within the region of interest. In this filtering procedure, we employ a statistical parameter, the relative standard deviation (coefficient of variation), calculated as σ_rel = σ/µ where σ and µ are the standard deviation and mean, respectively, calculated from the data of the region of interest (i.e., the 3 × 3 pixel box). In other words, σ_rel is the ratio of the standard deviation to the mean of the data of individual pixels within the 3 × 3 pixel box and is, therefore, a good indicator of the spatial variability of the region of interest. σ_rel is set to 0.2 for all the L_t(λ) comparison analyses.

Level 2 quality flag conditions are acquired through the standard NASA processing scheme, and any individual pixel is excluded from the match-up comparison process if it is flagged, through the data processing, by at least one of these conditions: land, cloud, stray light, bad navigation quality, both high and moderate glint, and high sensor viewing and/or solar zenith angles. Data points with the solar-sensor relative azimuth angle less than 40° (i.e., TOA radiance measurements made close to the direct solar path) are also excluded from the analysis. In addition, at least 50% of the pixels in the region of interest must satisfy all quality flag conditions in order to qualify for the match-up comparisons with the simulated TOA L_t(λ) and to be used in the derivation of radiometric vicarious gain factors. Furthermore, it is observed that even after applications of strict data filtering procedures, few (6 out of 108 matchups) corrupted L_t spectra (i.e., spectra with very high L_t values) remain in the final VIIRS data set. Those corrupted L_t spectra exhibit radiance values as high as 45 mW/cm²/μm/sr at 412 nm and 3 mW/cm²/μm/sr at 862 nm whereas averages of the typical quality assured L_t spectra at those wavelengths are around 7.45 and 0.43 mW/cm²/μm/sr, respectively. They are therefore subsequently excluded from the analysis.

4. Match-up comparisons between satellite and simulated L_t(λ) and derivation of radiometric vicarious calibration gain factors

The match-up comparison analyses between the simulated and measured TOA radiances which will be presented here are based on linear regressions between any two data sets being compared. In this step, a statistical match-up comparison filtering procedure [40] is further applied. In the procedure, the relative percentage difference of the i^th match-up, denoted as RPD_i, is first calculated as

4.1 Match-up comparisons between VIIRS and simulated L_t(λ)

Figure 3 shows the matchup comparisons between simulated and VIIRS L_t(λ) of WaveCIS (a) and LISCO (b) sites. ∆ has been set to 2 for this match-up comparison analyses and this procedure typically filters out only very few (~3%) extreme cases. There are 66 and 35 matchup points available for WaveCIS and LISCO sites, respectively. Excellent correlations with the overall R values close to 1 are observed for both sites. Moreover, it is also observed that the spectral variation ranges of simulated and VIIRS L_t(λ) are the same. Furthermore, regression lines for the comparisons are very close to 1:1 lines. In fact, these observations prove that the simulated L_t(λ) data are spectrally and magnitude wise consistent with those of measured (i.e., VIIRS).

 

Fig. 3 Matchup comparisons between the simulated and VIIRS L_t (λ) for (a) WaveCIS and (b) LISCO sites. Regression lines are shown in red, while the thick dotted black lines are 1:1 lines.

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Detailed regression analyses of the L_t(λ) match-up comparisons at 6 individual VIIRS nominal center wavelengths are presented in Fig. 4. R values obtained for the comparisons at every wavelengths are high (R ≥ 0.97 for 410 – 551 nm channels and R ≥ 0.93 at channels with λ ≥ 671 nm) exhibiting the high consistency between the simulated and VIIRS L_t data. It can be also observed that the regression lines of the comparisons at 410 and 551 nm wavelengths are very close to the 1:1 lines. These observations underscore that the simulated data set is highly consistent with that of the VIIRS sensor in blue and green wavelengths, and therefore further strengthens the approach’s potential for application as a radiometric calibration and validation reference for OC satellite sensors.

 

Fig. 4 Match-up comparisons between the simulated and VIIRS L_t(λ) at individual wavelengths: (a) 410, (b) 443, (c) 486, (d) 551, (e) 671 and (f) 862 nm (data of both WaveCIS and LISCO are shown together).

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On the other hand, the regression lines for the comparisons at 671, 745, and 862 nm wavelengths (see Fig. 4 for 671 and 862 nm) are observed to be significantly deviating from the 1:1 lines. However, matchup points mostly concentrate along the regression lines indicating that measured TOA L_t(λ) are well characterized by the simulated values at every wavelength.

4.2 Match-up comparisons between MODIS and simulated L_t(λ)

Figure 5 exhibits the matchup comparisons between simulated and MODIS L_t(λ) of WaveCIS site. It should be noted here that, after the filtering procedures specified in section 3.2, not enough match-up points were available for the LISCO location for statistically meaningful comparison. This is mostly due to LISCO’s location, which is in close proximity to the shore and thus affected by the MODIS sensor’s relatively low (1 km) spatial resolution. Furthermore, it is observed that few (~12) matchup points with large discrepancies between the simulated and satellite data for WaveCIS site still exist in the comparison after the standard filtering procedures, which were used for VIIRS data, and because of that ∆ is set to 1 resulting in 63 matchup points. As in the comparisons with VIIRS data, simulated data exhibit good correlation and consistency with the satellite data achieving overall R value greater than 0.98.

 

Fig. 5 Matchup comparison between simulated and MODIS L_t(λ) for the WaveCIS site.

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At the same time matchup comparisons for MODIS reveal that, unlike VIIRS, the uncertainties between MODIS and simulated L_t are higher than those of VIIRS at every wavelength. Correlations for the comparisons at 412 – 486 nm wavelengths are moderately high with their R values greater than or equal to 0.9. Only modest correlation is achieved for the comparisons at 551, 667 and 869 nm (R values are 0.85, 0.78, and 0.75, respectively). This can be largely explained by the MODIS’s lower 1 km nadir nominal resolution, compared to VIIRS’s 750 m. For a 3 x 3 pixel box, MODIS data is averaged over roughly the twice of the area that VIIRS will cover with the same approach, thus comparisons are affected by the spatial variations within the region of interest. However, overall consistency between simulated and MODIS data can be readily observed through the regression line between them which is very close to the 1:1 line (Fig. 5).

4.3 Derivation of the radiometric vicarious calibration gain factors

As a demonstration of the approach’s potential as a calibration reference, we further derived the calibrations of the VIIRS and MODIS sensors based on our simulated data set. Due to the high temporal and spatial heterogeneities in both atmospheric and water conditions of the site locations, the ∆ parameter for statistical filtering procedure has been set to 1, and this further filters out ~22% of the match-up points resulting in ~80 and ~60 match-up points with VIIRS and MODIS data, respectively (see Tables 2 and 3 for details), available for the vicarious gain factor derivation procedure. In the case of the VIIRS data, we derive three separate sets of the gain factor, g_c(λ): one set derived from combined match-up points for the LISCO and WaveCIS sites, and another two derived using match-up points for each site separately. This is to verify that g_c(λ) derived for each sites are consistent with one another. For MODIS, g_c(λ) values for only the WaveCIS site were obtained. Calculations are carried out as follows:

Table 2. Vicarious Calibration Coefficients for MODIS

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Table 3. Vicarious Calibration Coefficients for Three Sensors in NIR Channels. g_c Values Shown for AAOT Site Are Taken from [23], and for WaveCIS and LISCO Are Derived Using the Proposed Method.

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In Table 1, the calibration gain factor sets derived using the proposed method are shown along with the system vicarious calibration gain set used in the NASA’s most current VIIRS reprocessing (i.e., 2013.1). Similar results for MODIS Aqua and the WaveCIS site are shown in Table 2. With each gain set thus derived, the standard deviation values (STD) are also calculated in order to quantify the dispersion of individual gain coefficients around the derived average g_c values. The g_c values derived for VIIRS sensor’s 410, 443, 486 and 551 nm channels are within 1.3% – 4.7% of the value one, and they are within 0.55%, 1.15%, 3.6%, and 2%, respectively, of the standard MOBY based gains (see Table 1 for details), which should be considered consistent taking into account the radiometric instability of the VIIRS sensor, differences in atmospheric and water properties of the study areas, and the intrinsic uncertainties associated with the MOBY based calibration. On the other hand, g_c values derived for MODIS sensor’s 412, 443, 488, 552 and 667 nm channels are 0.6%, 1.79%, 0.07%, 0.99%, and 3% from the value one, respectively, and they are within 0.7% – 3% from standard MOBY based gains.

Table 1. Vicarious Calibration Coefficients for VIIRS

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For the 671, 745 and 862 nm channels of VIIRS, the g_c values significantly deviate from the typical vicarious adjustment range (i.e., they are equal to 0.901, 0.859, and 0.701, respectively), whereas the gains used in the NASA VIIRS processing are 1.0257, 1.047, and 1.0, respectively. Such large deviations also exist for MODIS in NIR channels (see Table 2 for details). It should be noted here that, in the vicarious calibration study by Melin and Zibordi [23], which is also based on the data from the AAOT AERONET-OC site, but with a methodology different from ours, the gain values derived for the NIR wavelengths of the MODIS and SeaWiFS sensors also exhibit very similar values to ours, and significantly lower than 1.0. In their study, they considered two approaches. The first one assumes the vicarious calibration coefficients fixed at their standard (NASA) values in the NIR and computes vicarious calibration coefficients in the visible bands using the AERONET-OC retrieved water-leaving radiance data as target datum. In the second approach vicarious calibration coefficients for NIR bands are first calculated using an AERONET-OC retrieved aerosol model as well as τ_a as target datum before proceeding to vicarious gain derivation in visible. Although the gain coefficients derived for the visible channels with the first approach are consistent with the standard NASA ones, the second approach (generally similar to ours) results in significantly lower gain coefficients for red and NIR channels (see Table 3 for details).

It is observed that the average percent contribution of aerosol component to the TOA radiance, which is calculated based on the two year time series level 2 VIIRS data of NASA standard processing, at the LISCO and WaveCIS locations is around 10% at 410 nm and almost linearly increases as the function of wavelength toward longer end of the spectrum resulting in 60% at the 862 nm. Similarly, it is found that differences between the gains derived with the proposed method and those of the MOBY like approach rapidly increase with wavelength and they are well correlated with the aerosol radiance contribution to TOA radiance. This means that the differences mentioned above are mostly due to the effects related to aerosols, and they are very significant for NIR bands, smaller for the red and still can be noticeable even at the green bands. Moreover, in a radiometric calibration related study carried out by Santer and Martiny [45] based on the RT simulations as well as AERONET sky radiance measurements, it was found that with the use of aerosol phase functions derived with [34–36], the discrepancies between the simulated and measured sky radiances are higher than 6% in the backward direction and can reach 11% at a scattering angle of 135° even during a clear day. Based on this finding, they proposed a method to convert sky radiances measured in the principal plane into atmospheric phase functions [45]. The radiometric calibration of the 865 nm band of SeaWiFS is subsequently evaluated using the measurements made at two AERONET sites and it was also found that TOA radiance from the SeaWiFS for the 865 nm channel are generally lower than the corresponding simulated radiance by 7.0% [22].

Based on the above considerations, we conclude that such large discrepancies between the simulated and satellite data at red (VIIRS only) and NIR (both MODIS & VIIRS) channels cannot be entirely attributed to either our methodology or the radiometric accuracy of the sensors but these may at least partially result from the in situ AERONET-OC SeaPRISM aerosol retrievals. These discrepancies can occur because of the typically small aerosol optical thicknesses τ(440) < 0.1 over the ocean, for which the AERONET inversion algorithms for aerosols are less accurate [46] and, as suggested in [45], because of the inaccurate retrievals of the phase function for the scattering angles relevant to the sun – sensor configurations. However, if that proves to be the case, the current approaches [47] based on AERONET aerosol characteristics can be affected and probably should also be revisited. Thus, further analyses of the AERONET-OC aerosol retrievals are necessary. We conclude that, although correlations between the simulated and satellite TOA L_t at the red and NIR channels are high (R ≥ 0.93 for those channels), the quality of the AERONET retrievals can be a main factor of uncertainty, validities of the resulting g_c values are inconclusive at the moment and further separate study should be granted to resolve the issues. Furthermore, it should be noted here that all input parameters to the TOA simulations are subject to the uncertainties associated with the measurement systems and the inversion algorithms. The radiative transfer simulation code being used itself may also have uncertainties. Moreover temporal variability in the in situ measured and derived atmospheric and water parameters within the ± 2h time window will also aggregate to the final uncertainty budget of the simulated data and subsequently manifest in the matchup comparisons with the satellite measured TOA values. Whereas quantifying the uncertainties associated with each parameter used in the simulations is beyond the scope of this study, overall uncertainty budget of such RT simulated TOA radiance data is usually estimated to be around 2 ~3.6% [4, 45], and it can be observed that the discrepancies between the gain coefficients derived with the proposed method and those of standard MOBY based approach are well within this uncertainty range at least for the blue and green wavelengths.

STD in the derived gain factors for VIIRS are approximately ~0.019 in the 410 nm channel and increase to values of the order of 0.03 to 0.05 at green and red wavelengths. It should be noted here that these STD levels are also comparable to those from the vicarious calibration approach carried out by Melin and Zibordi with the AERONET-OC data from coastal sites (AAOT & GDLT (Gustaf Dalén Lighthouse Tower)) for the MODIS and SeaWiFS sensors in visible channels [23]. The STD levels for NIR channels with the proposed approach are also about the same as in [23]. Moreover, in the derivations of vicarious gains for the visible channels, the approach of [23] utilizes only water-leaving radiance data as the target datum, and gain coefficients are derived through the atmospheric correction process as in the case of MOBY, whereas our approach compares the data derived from completely different sets of measurements and the gains are derived independently of the atmospheric correction procedure. On the other hand, with the current operational MOBY based system vicarious calibration procedure used for oligotrophic waters, the STD levels in visible channels are in the range of 0.007–0.009 [7]. These lower STD levels are likely the result of very stable marine and atmospheric conditions at the MOBY site. However, if operational use of the proposed approach is envisaged, with the inclusion of the match-up data from the twelve currently operational coastal AERONET-OC sites at different geographical locations, it might be reasonable to expect the lower levels of STDs than the ones achieved in this study.

4.4 Analysis of the derived vicarious calibration gain factors

In order to verify the proposed approach’s potential as a calibration reference, we further make assessments of the cross-site discrepancies in the derived gain factors for the VIIRS sensor. It can be readily observed in Table 1 that the gains derived separately for each site are in excellent agreement. The g_c(λ) values for the two sites are close at all wavelengths despite the significant difference in water and atmospheric conditions at these sites. We calculate the cross site discrepancy, denoted as U(λ) in %, as follows:

The U(λ) values are observed to be very low across the spectrum. They are well below or around 0.5% across the spectrum, except in the 671 and 745 nm channels where the U values are close to 1% (see Table 4 for details).

Table 4. Cross-site Discrepancy and Temporal Variability in Vicarious Gain Coefficients Derived with the Approach

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Figure 6 illustrates a temporal variability analysis of the gain factors over a two-year period. The individual calibration coefficients (circles) are plotted as a function of time around the constant line (shown in blue), which represents the average vicarious gain. The filled circles are the individual calibration coefficients that passed the quality screening process; the candidates for the gain derivations are shown in black, while grey represents non-candidates. Red circles are four-month averages of the candidate calibration coefficients and error bars around them represent the one standard deviation range. It can be seen that the derived gains appear to stabilize in the first 4 months of the mission, and the successive four-month average gain coefficients are very close to the overall mean value (shown by the blue constant line). The average temporal variability in gain coefficients is calculated by averaging the absolute percent differences between the overall vicarious gain value and the individual four-month average gain coefficients and they are observed to fall within the 0.28% – 1.23% interval in the blue and green channels.

 

Fig. 6 Time series of individual calibration coefficients (g_i) for VIIRS at (a) 410, (b) 443, (c) 486 and (d) 551 nm.

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5. Summary and conclusions

We applied an RT simulation based vicarious calibration approach for the radiometric calibration of the current operational multi-spectral OC satellite sensors. This approach relies on in situ data acquired at coastal AERONET-OC sites whose data has been extensively used for satellite data validation. Matchup comparisons carried out between the simulated and VIIRS TOA radiance exhibits very high correlation (R ≥ 0.93) at every wavelength demonstrating the applicability of the approach for the radiometric calibration of the OC sensors. Observed consistency in the radiometric vicarious calibration gain factors derived for the two coastal locations with different marine and atmospheric properties further strengthen the approach’s potentials in assessing the radiometric accuracy of the satellite sensors. Cross-site discrepancy is well below or around 0.5% in blue and green part of the spectrum. The average temporal variability in the blue and green channels falls within the 0.28% – 1.23% range and the derived gains appear to stabilize in the first 4 months of the mission. In addition to the system vicarious calibration procedure, this proposed approach also offers the potential to assess the radiometric accuracies independently of the atmospheric correction procedure. Furthermore, with the future inclusion of more AERONET-OC sites as references for different geographical locations, the proposed approach may potentially be used for monitoring the sensors’ radiometric stability over time as a complement to the onboard temporal calibration procedures. Moreover, this approach is also adaptable to hyper-spectral resolution, and implementation of that can be achieved by the readily available hyper-spectral radiance measurements from LISCO, which in addition to the standard AERONET-OC SeaPRISM instrument is also equipped with a hyper-spectral HyperSAS system (Satlantic, Canada) and therefore can be employed as an OC sensor calibration reference source for current and future multi- and hyper-spectral satellite OC sensors. While the average radiometric gain coefficients derived with the proposed method are highly consistent cross site, the derivations are intended only as a demonstration of capability, and should not be regarded as final calibration results, since they may change with the progressively evolving onboard temporal calibration procedures and radiometric stability of sensors, as well as with the inclusion of the more AERONET-OC sites as reference sources if operational use of the approach proposed here is envisioned. In particular, unlike the system vicarious calibration, the gains derived from this method may not be directly implemented for current ocean color data processing. It can be expected that in an ideal case, as long as the sensor calibration improves, both the MOBY based system vicarious approach and this RT based approach should converge providing high quality atmospheric and oceanic data in open ocean and coastal areas with current or slightly adjusted atmospheric correction procedures.