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Abstract: Measurements of ocean color from Geostationary Ocean Color. Imager (GOCI) with ...... Research Tower (32.1230°N, 125.1824°E) [15]. Because of the ...
Vicarious calibration of the Geostationary Ocean Color Imager Jae-Hyun Ahn,1,2 Young-Je Park,1,* Wonkook Kim,1 Boram Lee,1,3 and Im Sang Oh,4 2

1 Korea Institute of Ocean Science and Technology, Korea Ocean Satellite Center, Ansan, South Korea Ocean Science & Technology School, Department of Convergence Study on the Ocean Science and Technology, Busan, South Korea 3 Sejong University, Geoinformation Engineering, Seoul, South Korea 4 Seoul National University, Institute of Ocean Research, Seoul, South Korea * [email protected]

Abstract: Measurements of ocean color from Geostationary Ocean Color Imager (GOCI) with a moderate spatial resolution and a high temporal frequency demonstrate high value for a number of oceanographic applications. This study aims to propose and evaluate the calibration of GOCI as needed to achieve the level of radiometric accuracy desired for ocean color studies. Previous studies reported that the GOCI retrievals of normalized water-leaving radiances (nLw) are biased high for all visible bands due to the lack of vicarious calibration. The vicarious calibration approach described here relies on the assumed constant aerosol characteristics over the open-ocean sites to accurately estimate atmospheric radiances for the two near-infrared (NIR) bands. The vicarious calibration of visible bands is performed using in situ nLw measurements and the satellite-estimated atmospheric radiance using two NIR bands over the case-1 waters. Prior to this analysis, the in situ nLw spectra in the NIR are corrected by the spectrum optimization technique based on the NIR similarity spectrum assumption. The vicarious calibration gain factors derived for all GOCI bands (except 865nm) significantly improve agreement in retrieved remote-sensing reflectance (Rrs) relative to in situ measurements. These gain factors are independent of angular geometry and possible temporal variability. To further increase the confidence in the calibration gain factors, a large data set from shipboard measurements and AERONET-OC is used in the validation process. It is shown that the absolute percentage difference of the atmospheric correction results from the vicariously calibrated GOCI system is reduced by ~6.8%. ©2015 Optical Society of America OCIS codes: (010.0010) Atmospheric and oceanic optics; (010.1285) Atmospheric correction; (010.4450) Oceanic optics; (010.0280) Remote sensing and sensors.

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1. Introduction Space-borne ocean color sensors record the total radiance exiting the top-of-atmosphere (TOA) at several wavelengths within the visible (VIS) and near-infrared (NIR) spectral domain. The physical interpretation of these ocean color data needs an additional vicarious calibration other than instrument calibration and characterization in order to achieve the desired accuracy on the normalized water-leaving radiance (nLw) product retrieved by an atmospheric correction algorithm. Vicarious calibration of ocean color sensors is generally achieved through the application of gain factors to TOA-radiances (LTOA), which update the prelaunch and onboard instrument calibration to account for characterization errors or undetermined post-launch changes in sensor response, as well as any systematic bias associated with the atmospheric correction algorithm [1–9]. The atmospheric correction is required to retrieve the surface radiance from remotely sensed TOA-radiances by removing the atmospheric effects. In a typical open-ocean region of oligotrophic waters, the upwelling radiance emerging out of the water surface contributes ~10% to the radiance at the TOA [1– 4]. Therefore, it is crucial to retrieve this small portion of the water-leaving radiance by removing the major portion of atmospheric (molecules and aerosols) contributions and specular reflection at the sea surface. For retrieving water-leaving radiances with the desired accuracy for all channels, the atmospheric path radiances resulting from scattering by air molecules and aerosols must be computed precisely, and this is often achieved through simulation of TOA radiance with a radiative transfer code. In general, the TOA radiances atmospherically corrected within an accuracy of less than 1% error [3] secure high-quality level-2 ocean color products. However,

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23238

this is seldom achieved by the atmospheric correction process because it often results in systematic errors in retrieved water-leaving radiance. Thus, the vicarious calibration gain factors are applied in combination with the atmospheric correction algorithm to force the instrument response to retrieve the expected values of nLw(λ) [1]. This procedure has been adopted for many ocean color sensors, e.g., Moderate Resolution Imaging Spectroradiometer (MODIS), Sea-Viewing Wide Field-of-View Sensor (SeaWiFS), Global Imager (GLI), MEdium Resolution Imaging Spectrometer (MERIS), and Visible Infrared Imaging Radiometer Suite (VIIRS) [1–9]. Vicarious calibration is the process used to compute vicarious gains (gvc) for the indirect calibration of space-borne sensors through simulation of TOA data. These gain factors are determined by the mean ratio of the simulated TOA radiance ( LVC TOA ) to the TOA radiance at-sensor observation (LTOA):

N   g vc (λ ) =   LVC TOA (λ ) / LTOA (λ )   / N ,  n =1 

(1)

where λ denotes the wavelength and N is the number of samples used for deriving the vicarious calibration gain factors. The vicarious calibration gain factors aim to minimize the combined effects of uncertainties due to the pre-launch radiometric calibration and characterization of the satellite sensor corrected for temporal changes in radiometric sensitivity and inaccuracy of the atmospheric correction algorithm. Hence, this adjustment of the system (sensor + algorithm) response allows the determination of nLw with the least uncertainty. Since June 2010, Geostationary Ocean Color Imager (GOCI) has been providing the regional synoptic perspectives of coastal and open ocean phenomena around northeast Asia. It is the first space-borne geostationary ocean color sensor which acquires diurnally resolved satellite ocean measurements at six visible bands (centered at 412, 443, 490, 555, 660, and 680nm) and two NIR bands (centered at 745 and 865nm) with an unprecedented temporal resolution (8 times during a day, from 9:30 to 16: 30, local time GMT + 9) and a moderate spatial resolution (~500m at nadir) [10,11]. Having collected a large set of ocean color data from GOCI, first in situ validation of GOCI products was performed in 2012 [12,13]. This validation exercise demonstrated that water-leaving radiance retrievals from GOCI were consistently higher than the in situ measurements at an open-ocean site away from the coast of the Korean peninsula. Earlier studies reported that the GOCI nLw(555 nm) were overestimated by ~40% compared to the theoretical values in an oligotrophic ocean area (chlorophyll-a concentration < 0.25 mg m−3) [14]. In view of improving the accuracy in GOCI-derived nLw retrievals, it is therefore necessary to devise a vicarious calibration method that adjusts the integrated instrument and atmospheric correction system to produce the expected values of nLw required for quantitative oceanographic applications. In this paper, a vicarious calibration approach for the GOCI mission is described in detail. The vicarious calibration process adopted here is almost identical to that previously employed to calibrate polar-orbiting ocean color sensors [1–7,9]. In a traditional way, the vicarious gain factors are derived for each band on the GOCI through simulations of the satellite signal along with in situ radiometric measurements. Initially, the calibration of GOCI NIR (nearinfrared) band is achieved over a pre-defined open-ocean site based on knowledge of the assumed aerosol type. Subsequently, the atmospheric path radiances (both Rayleigh and aerosol) are computed over arbitrary locations of the ocean using the calibrated NIR bands. To derive the calibration gain factors, the theoretical TOA radiances ( LVC TOA ) in the visible bands (412, 443, 490, 555, 660, and 680 nm) are generated through simulations for certain locations where in situ radiometric measurements (nLw) are available. The vicarious calibration of GOCI is evaluated to ensure that a relative radiometric calibration to GOCI minimizes uncertainties in the water-leaving radiance products (or remote-sensing reflectance) derived from the top-of-atmosphere. These products retrieved by an atmospheric correction algorithm with and without the vicarious calibration gain factors

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are compared to in situ radiometric measurements. In addition, the vicarious calibration results are also independently validated using the AErosol RObotic NETwork (AERONETOC) data collected at the Ieodo station [15]. The vicarious calibration gain factors derived from this study are used in the GOCI Data Processing System (GDPS) version 1.3, which was released into the public domain (http://kosc.kiost.ac/) in September, 2014. 2. Approach

2.1 Framework of the vicarious calibration process In view of describing the vicarious calibration process in detail, the simulated TOA radiance LVC TOA (λ ) representing the radiance contributions associated with air molecules (Rayleigh scattering), aerosols (including Rayleigh-aerosol interactions), sunglint, white-caps, and the water itself can be described by the following simplified model [16–18]:

VC TOA

L

 Lr (λ ) + La (λ ) + Lra (λ )   v  v VC (λ ) = +td r (λ ) td a (λ )  Lw (λ ) + Lwc (λ )   tozv (λ ) tozs (λ ) ,   +Tg (λ ) Lg (λ ) 

(2)

where Lr(λ) is the Rayleigh radiance (arising due to single- and multiple-scattering) in the absence of aerosols, La(λ) + Lra(λ) is the radiance due to multiple-interactions between aerosols and air molecules, Lwc (λ ) is the radiance arising from light reflection on the whitecaps at the sea surface [19], Lg(λ) is the sunglint radiance generated by the specular reflection of direct sunglint [20], and LVC w (λ ) is the desired Lw that varies depending on the viewing angle of the sensor. The terms td rv (λ ) and td av (λ ) represent the upward Rayleigh diffuse transmittance and upward aerosol diffuse transmittance, respectively. The quantities tozs (λ ) , and tozv (λ ) are the ozone absorptive transmittance between the sun and sea surface, and between the sea surface and sensor, respectively, which are decoupled from the scattering. Tg(λ) is the direct atmospheric transmittance. In this study, the sunglint radiance Tg(λ)Lg(λ) was omitted for brevity, because it is negligible when considering the viewing geometry for the locations of GOCI vicarious calibration. In the operational atmospheric correction model, the Rayleigh radiance Lr(λ) can be reliably estimated given the radiant-path geometries and lookup Tables [21–24]. However, estimation of the radiance La(λ) + Lra(λ) is difficult due to the variation of aerosols in space and time, which constitutes a substantial limitation in the estimation of LVC TOA (λ ) . Our approach to the vicarious calibration follows a two-step strategy, i.e., we first calibrate the GOCI NIR bands, and then utilize the retrieved aerosol properties (aerosol type and concentration) for these bands to subsequently predict aerosol radiances for all visible bands. The aerosol radiance at two NIR bands can be reliably estimated over typical case-1 waters where the NIR water-leaving radiances approach to zero, thus validating the black pixel assumption (i.e., water-leaving radiance is negligible in the NIR bands) [16,17]. A similar approach was adopted in other studies (e.g., Eplee et al. [3], Wang and Gordon [4], and Franz et al. [1]). In the vicarious calibration, assuming the longest NIR band (865nm) is correct, the vicarious calibration gain factor for the shorter NIR band (745 nm) is determined based on the known aerosol type. To achieve the NIR calibration, we chose an open-ocean site far away from land wherein the aerosol type is maritime that is of oceanic origin and generally stable. The calibration of these two NIR bands is the basis for deriving the aerosol properties in any arbitrary locations of non-turbid water, eventually allowing the estimation of the aerosol radiance La(λ) + Lra(λ) for all VIS bands.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23240

2.2 In situ radiometric data acquisition and quality assurance The Korea Ocean Satellite Research Center (KOSC), KIOST, has conducted a large number of field campaigns in coastal and open ocean waters around Korea and obtained 421 in situ above-water radiometric measurements since 2010 (Fig. 1). The normalized water-leaving radiance nLw(λ) or the remote-sensing reflectance Rrs (λ) was measured by the ASD-FieldSpec and TriOS-RAMSES hyperspectral radiometers. Of the 421 samples, 337 spectra were discarded by the strict quality-control process recommended by Moon et al. [12], which left only 84 samples for the match-up process and analysis. Of those 84 samples, most of the shipboard data were collected from highly to moderately turbid waters in which the Rrs(660 nm) is greater than 0.0013. After eliminating these turbid water measurements, a relatively small number of the potential match-ups from non-turbid water areas (i.e. 12 Rrs measurements) are eventually utilized in the VIS bands vicarious calibration process.

Fig. 1. Locations of in situ radiometric measurements in coastal and open-ocean waters around Korea. A total of 421 samples were collected, and subsequently reduced to 84 (blue diamonds) through strict quality control of both the in situ measurements and GOCI observations. Of these data, only 12 spectra were used in the vicarious calibration process (green squares).

In the above-water measurement system, three radiometric measurements are required for determination of the Lw or Rrs; i.e., the total radiance leaving the water surface L0sea+ (λ ) , sky radiance Lsky(λ), and downwelling irradiance Ed(λ) [25,26]. The Lw and the remote sensing reflectance before the bidirectional effect correction (Rrsm) can be determined as follows: Lw (λ ) = L0sea+ (λ ) − f surf Lsky (λ ) − Lb (λ ), Rrs m (λ ) =

L0sea+ (λ ) − f surf Lsky (λ ) Ed ( λ )

− Rb ,

(3) (4)

where F0(λ) is the mean extraterrestrial solar irradiance, fsurf is the air-sea Fresnel reflectance ratio, which is spectrally constant and can be estimated as a function of wind speed (0.0256 +

#242932 © 2015 OSA

Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23241

0.00039W + 0.000034W2, where W is the wind speed in ms−1). The unknown term Lb(λ) is the residual radiance from light reflected by the ship’s superstructure, microfoam, or fluctuated fsurf Lsky(λ). The term Rb (i.e., Lb/Ed) is assumed to have no spectral dependency and thus is constant across the visible wavelengths. To derive Rb, a remote-sensing reflectance model (linking Rrs to the inherent optical properties, IOP) is employed to fit the in situ Rrs measurements to the model Rrs (Rrsmodel). The general expression of this model takes the form [27]: 2

rrs

model

 bb (λ )   bb (λ )  (λ ) = 0.089   + 0.125   ,  a (λ ) + bb (λ )   a (λ ) + bb (λ ) 

Rrs model (λ ) =

(5)

0.52rrs model (λ ) 1 − 1.7 rrs model (λ )

(6)

where rrsmodel is the remote-sensing reflectance just below the surface, bb(λ) is the total backscattering coefficient, and a(λ) is the total absorption coefficient. In the NIR region, the water absorption (aw) is dominant and thus determines the spectral shape of the bb(NIR)/{a(NIR) + bb(NIR)} term in Eq. (5) [28]. Here a spectral fitting technique [12] with measurements from Ruddick et al. [28] is used to estimate the Rb over the wavelength range of 770-870 nm when Rrs(660) > 0.0025. The wavelength range is shifted to 700-745nm for relatively clear waters, where Rrs(660) ≤ 0.0025, to avoid a low signal-to-noise ratio (SNR) in this red-NIR spectral region where L0sea+ (λ ) is weak due to strong absorption. Figure 2 shows examples of the Rb correction for both clear and turbid waters.

Fig. 2. Rb correction applied to Rrsm (λ) from clear (a) and turbid (b) waters. Red solid lines represent the corrected Rrs, and black dotted lines indicate uncorrected data directly derived from Eq. (4) with Rb = 0. Grey dashed lines show the results obtained by subtracting the Rrs(755 nm) value from each wavelengths [25].

Then, in situ Rrsm is converted into Rrs and nLw that normalized to both the sun and viewing angles as: Rrs ( λ ) = Rrs m ( λ ) × ×

ℜ s ( λ , θ s =0, W )

×

ℜv ( λ , θ v =0, W )

f ( λ , θ s =0, chla )

f ( λ ,θ s =θ sm , chla )

×

Q ( λ ,θ s =θ sm , θ v =θ vm , φs − v =φsm− v , chla ) Q ( λ , θ s =0, θ v =0, φs − v =0, chla )

nLw (λ ) = Rrs (λ ) F0 (λ ),

#242932 © 2015 OSA

(7)

ℜ s ( λ , θ s =θ , W ) ℜv ( λ ,θ v =θ vm , W ) m s

,

(8)

Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23242

where θs, θv, and φs-v are the solar zenith angle, sensor zenith angle, and relative azimuth angle of sun and sensor, respectively. Terms θ sm , θ vm , and φsm− v are values of θs, θv, and φs-v associated with the time and location of each measurement. The terms ℜ s and ℜv are the downward and upward air-sea transmittance, respectively. The term f/Q represents the inwater bidirectional function. ℜ s for the GOCI bands is estimated using the function introduced in Wang (2006) [29] (Appendix A). ℜv is estimated by a simple Fresnel’s equation with the assumed wind speed (i.e., W = 0). Under the assumption that the living and non-living biogenic particles in the water column are the major factor in f/Q variations, we corrected for the f/Q variation using a look-up table provided by Morel et al. [30]. The theoretical basis of their work was described in Morel et al. [31]. For the vicarious calibration usage, the nLw is finally converted to LVC w using: m m m t s s s   LVC w ( λ , θ s , θ v , φs − v ) =  nLw ( λ ) σ ( d y ) cos(θ s =θ s ) td r (λ ) td a (λ ) toz (λ ) 

× ×

ℜ s ( λ , θ s =θ st , W ) ℜv ( λ , θ v =θ vt , W ) × ℜ s ( λ , θ s =0, W ) ℜv ( λ , θ v =0, W ) f ( λ , θ s =θ st , chla ) f ( λ , θ s = 0, chla )

×

Q ( λ , θ s =0, θ v =0, φs − v =0, chla )

Q ( λ , θ s =θ st , θ v =θ vt , φs − v =φst − v , chla )

(9) ,

where θ st and θ vt are the desired-zenith angles for the sun and the sensor of each GOCI observations, respectively. The term σ(dy) is the sun-earth distance factor which is dependent on the day of the year dy. 2.3 Vicarious calibration of GOCI NIR bands Because of the lack of reliable, coincident, and co-located aerosol properties and waterleaving radiances from in situ measurements, our calibration approach used several assumptions to determine aerosol contribution and estimate LVC TOA (745 nm) . To calibrate the shorter NIR band (745 nm), the LVC TOA (745 nm) can be estimated from the observed aerosol radiance at 865 nm. For the open ocean, it can be assumed that the aerosol type of the site is the maritime aerosol model [1,3]. We assumed constant aerosol characteristics that is an average of maritime aerosol models with relative humidity (RH) 50% and 99%. We accept that the constant characteristics represent the mean of relative humidity (RH) 50% and 99% of maritime aerosol model (denoted as M50 and M99, respectively [32]). To avoid, as far as possible, aerosols originating from continents and the effects of inter-slotradiometric-discrepancy (ISRD) [33], we select the NIR vicarious calibration site as a boxed area of 24.8-29.0°N and 132-142°E as shown in Fig. 3. To perform the NIR calibration, the spatial and temporal (2011-2012) averages of GOCI observations of cloud-glint-free LTOA(NIR) on a 10 x10 pixel area are computed to minimize the effects of spurious outliers.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23243

Fig. 3. Map of the calibration site of the GOCI NIR bands. Region within the box of 24.829.0°N and 132-142°E (red rectangle) in the GOCI coverage is established for the NIR vicarious calibration. The region is selected so as to avoid continental aerosols and slot boundary stray-light effects.

To estimate the aerosol contribution at the shorter NIR band (745nm), the aerosol radiance estimated for the longer NIR band (865nm) (see section 2.1) was conveniently converted to reflectance, ρa(865 nm) + ρra(865 nm). Subsequently, the ρa(745 nm) + ρra(745 nm) was derived using the look-up table generated through radiative transfer simulations and the single-scattering reflectance model. For the radiative transfer simulation, the Second Simulation of a Satellite Signal in the Solar Spectrum, Vector, version 1 (6SV1) [34] was used. Since the NIR calibration site is characteristic of typical case-1 waters, LVC w (NIR) in Eq. (2) is negligible because of the strong water absorption and weak reflectance. Then it is straightforward to estimate the NIR aerosol multiple-scattering reflectance in the presence of air molecules ρa(NIR) + ρra(NIR) using LTOA (NIR) − Lr (NIR) − td rv (λ ) Lwc (NIR). tozs (λ ) tozv (λ ) The aerosol radiance can be converted to reflectance using: La (NIR) + Lra (NIR) =

ρ a (NIR) + ρ ra (NIR) = π

La (NIR) + Lra (NIR) . F0 (λ ) σ (d y ) cos(θ s )

(10)

(11)

From the derived ρa(865 nm) + ρra(865 nm) and an assumed maritime aerosol type at 50% and 99% relative humidity (M50 and M99), aerosol reflectance for the GOCI NIR band at 745nm is first estimated using an analytical single-scattering aerosol reflectance model. The aerosol multiple-scattering reflectance at 865 nm can be converted to single-scattering reflectance ρ asM (865 nm) (for each aerosol model M, i.e., M50 and M99) from the relationship function CMforward derived by the radiative transfer model:

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ρ asM (865 nm) = CMforward [ ρ a (865 nm) + ρ ra (865 nm) ] ,

(12)

ρ asM (745 nm) = ε M (745 nm,865 nm) ρ asM (865 nm),

(13)

Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23244

where ε M (λ1 , λ2 ) is the ratio of single-scattering aerosol reflectance between λ1 and λ2 for the given aerosol model M which can be derived from the analytical single-scattering model.

Fig. 4. Flowchart describing the scheme for estimating the TOA radiance at 745 nm.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23245

Thus, the average of the M50 and M99 aerosol multiple-scattering reflectance at 745 nm ρ raVC (745 nm) + ρ aVC (745 nm) is computed by the single-scattering to multiple-scattering conversion function CMbackward derived through the radiative transfer simulations:  ρ asM 50 (745 nm)  ρ aVC (745 nm) + ρ raVC (745 nm) = 0.5 × CMbackward 50  ρ asM 99 (745 nm)  . + 0.5 × CMbackward 99

(14)

Finally, we calculate the theoretical TOA radiance at 745 nm ( LVC TOA (745 nm) ) using an analytic model incorporated into the atmospheric correction process [13] (Fig. 4): VC VC  VC  LVC a (745 nm) + Lra (745 nm) =  ρ a (745 nm) + ρ ra (745 nm) 

× F0 (745 nm) σ (d y ) cos(θ s ) / π ,

(15)

VC VC s   v LVC TOA (745 nm) =  Lr (745 nm) + La (745 nm) + Lra (745 nm)  toz (745 nm) toz (745 nm)

(16) + Lwc (745 nm) tozv (745 nm) td rv (745 nm) td av (745 nm). In the above equations, the term Lr(λ) can be reliably estimated a priori to less than 1% error [21–23]. To reduce uncertainties in ρa(λ) + ρra(λ), we follow strict accept criteria; i.e., the wind speed is below 4 m s −1, ρa(865 nm) + ρra(865 nm) is lower than 0.006, and scene observation times are only for period 3:16~4:16 (UTC). 2.4 Calibration of the visible bands The calibration process of the visible bands depends on a set of high-quality satellite-to-in situ match-up pairs that were sampled at individual in situ locations and screened through quality control. Our approach to the vicarious calibration of the visible bands is based on the GOCI standard atmospheric correction algorithm [13] which estimates the aerosol reflectance in the two NIR bands. Since the NIR bands are already inter-calibrated as described in section 2.3, the atmospheric correction process can be operated to determine aerosol multiple-scattered reflectance for all VIS bands ( ρ ra (VIS) + ρ a (VIS) ). For each in situ LVC w (λ ) location, the theoretically estimated LVC TOA (VIS) values can be derived from the atmospheric path radiance, transmittance and whitecap radiance from the atmospheric correction process, and the LVC w (λ ) subsequently retrieved through Eq. (2) and Fig. 5 [1,4,13]: To avoid uncertainties that arise in case-2 waters during the atmospheric correction and f/Q correction processes, our extensive quality control of the in situ and GOCI observations VC s s allows only the clear-water LVC w (λ ) such that Lw (660 nm) / toz (660 nm) / tr (660 nm) is less than 2.0 w·m−2·μm−1·sr−1. To further assure the quality of these data, any of the pixels at each VIS bands calibration site flagged by the atmospheric correction process as being contaminated by bright pixel adjacency effects and ISRD effects (slot distance ~150 km) is excluded from further consideration. In addition, both the sensor and solar zenith angle are restricted to less than 40 degrees to minimize errors from the large total air-mass.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23246

Fig. 5. A flowchart describing the scheme for estimating the TOA radiance in the visible bands

2.5. Statistical indices for verification of calibration In view of supporting a discussion on the uncertainties associated with the determination of the gain and verification process, statistical indices such as the absolute percentage difference (APD) and root mean square error (RMSE) are used. These indices are defined as follows: APD =

n n 100 K  VT − VE   K n =1  VTn 

K

RMSE =

 (V n =1

n T

− VEn )

K

 ,  

(17)

,

(18)

2

where K is the total number of match-up pairs, and VTn and VEn are the true and estimated values of the nth match-up entry, respectively. The APD and RMSE are more relevant in the present context since they capture any systematic or random variability between the retrieved (satellite) and true (in situ) values. 3. Results

Using the method described in the section 2.3, the mean vicarious calibration gain factor is first derived for the GOCI 745 nm band based on the calibration samples from open ocean waters. Vicarious calibration gains for the GOCI at 412, 443, 490, 555, 660, and 680 nm are then determined by using method described in the section 2.4 based on in situ nLw measurements. The relative uncertainties associated with both the gain determination and the validation process using radiometric match-up statistics for the GOCI retrieved Rrs and the in situ observations are estimated and the sensitivity of those results to the various assumptions used in our approach are discussed below.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23247

3.1 Verification of vicarious calibration gain factors This section presents the results to serve as the baseline for the analysis of the uncertainties in the gain factors derived for the GOCI bands. Figure 6 shows results for the vicarious calibration of the GOCI NIR band at 745 nm derived using the open-ocean site (Fig. 3) with the assumed maritime aerosol type at 50% and 99% RH. The mean vicarious calibration gain factors derived for the NIR band and VIS bands (calibrated to in situ measurement data from individual locations) are provided in Table 1 and Fig. 7.

VC

Fig. 6. Vicarious calibration of the NIR band. LTOA (745 nm) / LTOA (745 nm) values are obtained based on calibration samples spanning 2-year period from 2011 to 2012. The mean vicarious calibration gain factor derived for the GOCI NIR band at 745 nm is 0.9613. Table 1. Vicarious calibration gain factors for GOCI wavelength (nm)

412

443

490

555

660

680

745

865

Gain factor

1.0105

0.9891

0.9611

0.9186

0.9567

0.9659

0.9613

1.0

N RMSE

10 0.0073

12 0.0147

12 0.0141

12 0.0197

12 0.0147

12 0.0189

723 0.0149

N/A N/A

Fig. 7. The spectral plot of vicarious gains. Error bars indicate the standard deviation.

The percentage difference in the derived gain factors ranges from −8.14 to 1.05% which makes a substantial change in the spectral values of remote-sensing reflectance between the in situ observations and the GOCI retrievals (Fig. 8; Table 2). The uncertainty in the retrieval of Rrs from the uncalibrated GOCI bands varies from an APD of 36.5% in the blue to an APD of 73.7% in the red bands. As previously reported by Hu et al. [14], the Rrs values retrieved from the GOCI in the oligotrophic ocean are biased high relative to in situ measurements eventually causing the manifestation of observed uncertainty. However, the vicarious

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23248

calibration significantly improves agreement between the retrieved Rrs values and in situ measurements (the APDs of 15.2-30.7% indicate an improvement in the GOCI retrievals of the spectral distribution of Rrs). Because the vicarious calibration adjusts for errors in both the instrument pre-launch calibration and the atmospheric correction, the Rrs retrievals that are highly biased without vicarious calibration are significantly improved relative to the fully calibrated GOCI bands.

Fig. 8. Verification of the vicarious calibration gain factors. Red circles and blue squares represent the GOCI and in situ Rrs match-up pairs derived with- and without vicarious calibration, respectively. Table 2. Statistics from verification of the VIS bands calibration in situ Rrs (Uncalibrated)

in situ Rrs (Calibrated)

wavelength (nm)

APD

RMSE

R2

N

APD

RMSE

R2

N

412

36.5%

0.00144

0.748

10

15.2%

0.00075

0.831

10

443

22.2%

0.00088

0.211

12

21.1%

0.00078

0.304

12

490

27.2%

0.00118

0.670

12

13.3%

0.00056

0.803

12

555

57.3%

0.00186

0.808

12

10.2%

0.00050

0.878

12

660

78.8%

0.00068

0.568

12

35.5%

0.00029

0.434

12

680

73.7%

0.00074

0.535

12

30.7%

0.00028

0.511

12

3.2 Improvement in the atmospheric correction To increase confidence in the mean vicarious calibration gain factors further, a similar analysis of a more general validation of the calibration and atmospheric correction system is performed using the large number of quality-controlled GOCI match-ups independent of those used for the NIR and VIS band calibrations. For this analysis, both the calibrated and uncalibrated GOCI data are fed into the latest GOCI standard atmospheric correction algorithm [Appendix B]. In situ observations of Rrs are subjected to the following qualityrejection criteria to ensure high-quality match-ups as required by the GOCI to achieve similar quality in the ocean color retrievals: (i) the ρa(865 nm) + ρra(865 nm) value at the match-up locations is above the given threshold of 0.03, (ii) the location is under the influence of the ISRD,

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23249

(iii) the location is near a bright target such as cloud or land (within distance of 2.5 km). Finally, the number of satellite to in situ match-ups of Rrs is reduced to 71 for this validation process. As shown in Fig. 9, the GOCI retrieved Rrs compare well with in situ observations, over the range of sun and viewing geometries associated with GOCI observations of the validation (sampling) sites. Consistent with the earlier validation, the APD values are relatively high for the GOCI retrievals without calibration (34.8, 28.2, 20.0, 21.8, 36.8, and 40.2% for the GOCI bands from 412 to 680 nm), but considerably lower with vicarious calibration (32.1, 25.0, 16.5, 13.5, 28.8, and 29.7%) as the quality of Rrs retrievals relative to in situ observations is significantly improved. Although the validation of the GOCI retrieved Rrs with and without calibration is performed relative to the same atmospheric correction algorithm, there is marked variability in the difference between the GOCI and in situ Rrs in the blue bands (especially 412 nm), likely due to bias and spectral skew associated with amplified errors due to a longer spectral distance from the NIR.

Fig. 9. Validation of the GOCI retrieved Rrs and in situ Rrs. Blue diamonds represent Rrs retrievals without vicarious calibration (implemented in GDPS ver.1.1 and 1.2), and red circles represent Rrs retrievals with vicarious calibration (implemented in GDPS ver.1.3). Rrs spectra used in the vicarious calibration are also included in this validation (cal + val).

To assure stability in the calibration gain factors, further validation is performed using nLw measurements obtained from AERONET-OC data [35,36] obtained at the Ieodo Ocean Research Tower (32.1230°N, 125.1824°E) [15]. Because of the absence of level 2.0 data to assess the quality of these measurements, we used level 1.0 data after applying a qualitycontrol procedure [Appendix C]. To match the GOCI Rrs with the AERONET-OC nLw, the AERONET-OC nLw values obtained after applying the f/Q correction were converted to the GOCI. The AERONET-OC Rrs were then linearly interpolated into the GOCI blue and green bands (i.e., 412-555 nm). For the red bands (i.e., 660 and 680 nm), the AERONET-OC Rrs were converted to the GOCI Rrs using the model developed by Ruddick et al. [28]. The total number of Rrs spectra used for this validation is 42 as shown in Fig. 10. These plots show that the GOCI gain factors remain relatively stable and consistent as a function of time and over the range of sun and sensor geometries, improving agreement between the retrieved Rrs and in situ observations. As previously discussed, the Rrs retrievals without calibration are noticeably degraded for all visible bands, which serves to emphasize the importance of the vicarious calibration for GOCI and its validation agreement in those bands.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23250

Total validation results of the atmospheric correction associated with ship-measured Rrs and AERONET-OC Rrs are summarized in Table 3.

Fig. 10. Validation of the GOCI retrieved Rrs and in situ Rrs from the AERONET-OC. Blue diamonds represent Rrs retrieved using the atmospheric correction without vicarious calibration (implemented in GDPS ver.1.1 and 1.2). Red circles represent Rrs retrievals with vicarious calibration (implemented in GDPS ver.1.3). Table 3. Statistics of atmospheric correction validation with/without the calibration in situ Rrs (Uncalibrated)

in situ Rrs (Calibrated)

wavelength (nm)

APD

RMSE

R2

N

APD

RMSE

412

34.8%

0.00430

0.144

69

32.1%

443

28.2%

0.00353

0.528

70

25.0%

490

20.0%

0.00233

0.840

71

555

21.8%

0.00209

0.912

660

36.8%

0.00195

0.883

680

40.2%

0.00190

0.864

R2

N

0.00305

0.465

65

0.00353

0.794

66

16.5%

0.00213

0.911

66

71

13.5%

0.00163

0.949

66

71

28.8%

0.00147

0.936

66

71

29.7%

0.00146

0.924

66

AERONET-OC Rrs (Uncalibrated)

AERONET-OC Rrs (Calibrated)

wavelength (nm)

APD

RMSE

R2

N

APD

RMSE

412

32.0%

0.00335

0.210

40

22.3%

443

22.0%

0.00311

0.308

40

490

21.4%

0.00367

0.437

40

555

15.3%

0.00409

0.434

660

42.8%

0.00219

680

55.2%

0.00191

R2

N

0.00155

0.787

42

22.0%

0.00132

0.894

42

12.7%

0.00138

0.930

42

40

10.4%

0.00154

0.942

42

0.414

40

34.7%

0.00086

0.874

41

0.411

40

38.4%

0.00081

0.858

41

4. Summary & conclusion

In this paper, an operational vicarious calibration method was presented for the GOCI sensor that aims to maximize agreement between remotely sensed water-leaving radiance retrievals

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23251

and the expected nLw (or Rrs). This is achieved through the application of gain factors to instrument absolute radiometric calibration coefficients for the GOCI. The calibration process is divided into two steps as normally used in the traditional vicarious calibration methods, i.e., calibration of the NIR bands with an assumed aerosol type, and calibration of the VIS bands using nLw measurements. For calibration of the NIR bands, the longest NIR band at 865 nm was assumed to be absolutely calibrated, which formed the basis for calibration of the shorter NIR band at 745 nm. The vicarious calibration of the NIR bands was performed relative to the same atmosphere and the assumed maritime aerosol type at RHs 50% and 99%. To achieve this, an open-ocean site in the southeast region in the GOCI observation area far from the continent was selected that satisfied the assumption of all aerosols being maritime. Finally, the TOA radiance ( LVC TOA ) at 745 nm was estimated using a radiative transfer model with the given aerosol type to obtain the statistical mean of the ratio LVC TOA (745 nm) to LTOA(745 nm), which determines the vicarious gain at 745 nm. For the VIS band vicarious calibration, the nLws measured during several campaigns in open ocean waters around Korea and the atmospheric loads estimated from the NIR bands after calibration were used. With this approach, the vicarious calibration gain factors were determined for all VIS bands, and their stability and consistency were verified using a series of match-up pairs obtained through the standard GOCI atmospheric correction algorithm. As expected, the vicarious calibration significantly improved the agreement between the retrieved Rrs and in situ observations for the data used in the calibration itself by ~45% in the green and red bands. When a match-up analysis was performed using shipboard observations and AERONET-OC data, the APD was reduced by 6.8% after the vicarious calibration. There remains an issue concerning fixing the aerosol model in the NIR-band calibration. We considered the dominant aerosols at the calibration sites are produced mainly maritime processes and the RH that determines the aerosol optical properties (from the National Centres for Environmental Prediction, NCEP) varied from 55 to 95%. For each cloud-glintfree observation, we assumed the aerosol type to be an average of the M50 and M99 models for the expectation that the spectral slope in NIR would approximately fall between those RH range. A small calibration error at the 745 nm band induced by approximate aerosol type could be expected that it would not introduce significant errors in the Rrs retrievals, because the vicarious calibration of the VIS bands would tend to compensate for the bias and spectral skew associated with the aerosol radiance. However, the previous studies showed that the 745 nm band inter-calibration is important to correctly estimate nLw or Rrs [1,2,4,37]. Moreover, the unrealistic NIR vicarious calibration gain would erroneously retrieve aerosol optical properties (e.g., aerosol optical thickness, phase function or size distribution) that have a high dependency on the NIR band ratio. In addition, it would also lead to an erroneous relationship of water reflectance in the NIR bands used in the turbid water atmospheric correction [13], and this relationship is highly dependent on the gvc. Therefore, future improvements to our calibration would likely use maritime aerosol models with the varying RH values. Also further studies on the aerosol model assumption in the NIR calibration site should be done. In this study, the visible band calibration used in situ nLw measurements recorded by an above-water radiometer system. Although these measurements are quality controlled, uncertainties can be still significant, because the nLw is relatively weak compared with the sky radiance reflected at the air-sea surface. In particular, the uncertainty is more prominent as the wavelength increases from red and NIR where water absorption is strong, and reflectance is weak. As shown in Fig. 8, APD values at 660 and 680 nm are higher than those in other bands despite low RMSE values at 660 and 680 nm and high RMSE values in other bands. For these reasons, the next calibration campaign will include more reliable radiometry and correction techniques. To strengthen this process, we plan to use in-water radiometric measurements including an underwater profiler and optical buoy data. Finally, our correction scheme for the bidirectional effect (f/Q) which accounts for radiant-path geometry dependencies in the nLw and the Rrs due to the anisotropy of the nearsurface light field [1] is based on a biogenic optical model that does not fully consider case-2

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23252

waters. Since the near-surface light field depends on the absorption and scattering properties of the water column and its constituents, it is essential to consider a more appropriate model [38, 39] for case-2 waters. We expect to include these improvements in our future studies. Acknowledgments

This work was supported by the Korea Ministry of Oceans and Fisheries (MOF) through the project titled “Application research for Geostationary Ocean Color Imager (PM58870)” and Korea Institute of Ocean Science & Technology through the project titled “Professional Education & Training Program in Ocean Science and Technology (PO01140)” This study was supported in part by Korea Hydro and Nuclear Power Co. We are also thanks to Prof. Hajime Fukushima, Prof. Palanisamy Shanmugam, and staffs of STAR/NOAA especially Menghua Wang, for their advice and help in this work. Appendix A: Adjustment of air-sea transmittance correction model for high sun angles

When the solar zenith angle approaches near critical angles, Fresnel transmittance at air-sea interface is considerably decreased. For this correction, Wang (2006) [29] suggested a sunangle and wind-speed dependent ℜ s correction model as Eq. 19, ℜ s ( λ , θ s = 0,W = 0 )

4

= 1 +  ci (λ , W )  ln ( cos θ s )  . i

(19) ℜs ( λ ,θ s ,W ) i =1 In this study, ci values were derived from the successive-order-of-scattering simulation including polarization for SeaWiFS VIS bands (i.e., 412, 443, 490, 510, 555, and 670 nm). These coefficients were readjusted according to GOCI bands characteristics. Here a three-step strategy was employed wherein we first solved the model for all simulation cases with given coefficients, then generated hyper-spectral ℜ s ( λ , θ s = 0, W = 0 ) / ℜ s ( λ , θ s , W ) values for each case by the spectral linear interpolation, and finally updated the correlation coefficients for GOCI bands by the least mean square error method as provided in Table 4. Table 4. Adjusted coefficients (Eq. (19)) for GOCI bands.

λ (nm) 412

443

490

#242932 © 2015 OSA

W (m/s) 0.0

c1 (λ, W)

c2 (λ, W)

c3 (λ, W)

c4 (λ, W)

−8.70 × 10−3

6.38 × 10−2

−3.79 × 10−2

−3.11 × 10−2

1.9

−1.10 × 10−3

9.26 × 10−2

−5.30 × 10−4

−2.05 × 10−2

7.5

6.80 × 10−5

1.15 × 10−1

6.49 × 10−2

6.50 × 10−3

16.9

−8.80 × 10−3

6.97 × 10−2

4.24 × 10−2

4.70 × 10−3

30.0

−8.10 × 10−3

4.82 × 10−2

2.90 × 10−2

2.90 × 10−3

0.0

−1.22 × 10−2

4.15 × 10−2

−7.80 × 10−2

−4.27 × 10−2

1.9

−3.70 × 10−3

7.46 × 10−2

−3.71 × 10−2

−3.25 × 10−2

7.5

−1.80 × 10−3

1.12 × 10−1

3.79 × 10−2

−3.90 × 10−3

16.9

−9.70 × 10−3

6.78 × 10−2

3.28 × 10−2

1.30 × 10−3

30.0

−8.90 × 10−3

4.66 × 10−2

2.20 × 10−2

4.00 × 10−4

0.0

−1.56 × 10−2

1.88 × 10−2

−1.16 × 10−1

−5.11 × 10−2

1.9

−6.80 × 10−3

5.34 × 10−2

−7.62 × 10−2

−4.38 × 10−2

7.5

−1.10 × 10−3

1.08 × 10−1

3.42 × 10−2

−3.60 × 10−3

16.9

−1.04 × 10−2

6.57 × 10−2

2.33 × 10−2

−1.60 × 10−3

Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23253

555

660

680

30.0

−9.60 × 10−3

4.50 × 10−2

1.50 × 10−2

−1.70 × 10−3

0.0

−1.72 × 10−2

4.80 × 10−3

−1.37 × 10−1

−5.26 × 10−2

1.9

−9.00 × 10−3

3.68 × 10−2

−1.05 × 10−1

−5.06 × 10−2

7.5

−1.50 × 10−3

1.04 × 10−1

2.32 × 10−2

−6.20 × 10−3

16.9

−1.10 × 10−2

6.40 × 10−2

1.66 × 10−2

−3.10 × 10−3

30.0

−1.01 × 10−2

4.39 × 10−2

1.03 × 10−2

−2.90 × 10−3

0.0

−1.72 × 10−2

4.30 × 10−5

−1.43 × 10−1

−4.82 × 10−2

1.9

−1.05 × 10−2

2.47 × 10−2

−1.24 × 10−1

−5.39 × 10−2

7.5

−1.31 × 10−3

1.03 × 10−1

1.64 × 10−2

−7.14 × 10−3

16.9

−1.11 × 10−2

6.37 × 10−2

1.29 × 10−2

−3.57 × 10−3

30.0

−1.04 × 10−2

4.34 × 10−2

7.25 × 10−3

−3.28 × 10−3

0.0

−1.72 × 10−2

−6.20 × 10−4

−1.43 × 10−1

−4.74 × 10−2

1.9

−1.07 × 10−2

2.28 × 10−2

−1.28 × 10−1

−5.43 × 10−2

7.5

−1.29 × 10−3

1.03 × 10−1

1.52 × 10−2

−7.24 × 10−3

16.9

−1.11 × 10−2

6.37 × 10−2

1.21 × 10−2

−3.63 × 10−3

30.0

−1.04 × 10−2

4.34 × 10−2

6.79 × 10−3

−3.32 × 10−3

Appendix B: Latest GOCI standard atmospheric correction

This appendix describes the previous GOCI standard atmospheric correction [13] and its updates that are included in the GDPS ver.1.3. This method is theoretically based on the previous work by Wang and Gordon [16] and Gordon and Wang [17]. It starts with TOA reflectance ρTOA(λ) and different contributions to this quantity,

ρTOA (λ ) = ρ r (λ ) + ρ a (λ ) + ρ ra (λ ) + td rv (λ ) td av (λ ) ρ w (λ ),

(20)

where ρr(λ) is the single- and multiple-scattering Rayleigh reflectance in the absence of aerosols that can be accurately estimated by the radiative transfer model. ρw(λ) is the desired water-leaving reflectance retrieved by the atmospheric correction process. It estimates multiple-scattering reflectance of aerosols for all visible bands from the two NIR bands (i.e., ρa(745 nm) + ρra(745 nm) and ρa(865 nm) + ρra(865 nm)). For the majority of the open ocean, the general atmospheric correction method [13,16,17] estimates ρa(NIR)+ρra(NIR) on the basis of the black pixel assumption (i.e., ρw(NIR) = 0). In more turbid coastal waters, the black pixel assumption is invalidated by the enhanced contributions due to suspended particles in the water [40–46]. This demands an exact separation between ρw(NIR) and ρa(NIR)+ρra(NIR) in the process of atmospheric correction. As shown in Figure 11, the GOCI standard atmospheric correction algorithm iteratively subtracts water reflectance ρw(NIR) estimated by the model from the ρTOA(NIR)-ρr(NIR). To estimate ρw(NIR), Ahn et al. [13] suggested an empirical relationship of water reflectance between the red and two NIR bands (Eqs. 21 and 22) [28]:

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23254

Fig. 11. Flow chart showing the turbid water ρw(NIR) correction scheme for the GOCI standard atmospheric correction. The tdv(λ) term represents the total diffuse transmittance v

v

between the sea surface and sensor which can be expressed as td r (λ ) × td a ( λ ) . 4

ρ wn (745 nm) =  jn ρ wn (660 nm) n ,

(21)

ρ wn (865 nm) = 1.936 ρ wn (745 nm),

(22)

n =1

where ρwn(λ) is the normalized water reflectance that is defined as:

ρ w (λ ) . (23) td (λ ) td as (λ ) The relationship between ρwn(745 nm) and ρwn(680 nm) instead of ρwn(660 nm) can also be used. However, we do not consider ρwn(680 nm) in this study, since the effect of GOCI’s inter-slot-radiometric-discrepancy (ISRD) is more prominent at 680 nm than at 660 nm [33]. In order to enhance the correlation between ρwn(660 nm) and ρwn(745 nm), the current GOCI standard atmospheric correction method that is included in GDPS ver.1.3 is updated with the spectral relationship model (Eq. 24 rather than Eq. 21). In addition, to better describe the non-linear relationship of extremely turbid-water reflectance values between these two NIR bands [45–48], we update the relationship as Eq. 25. ρ wn (λ ) =

s r

5

ρ wn (660 nm) =  jn ρ wn (745 nm) n ,

(24)

n =1

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23255

2

ρ wn (865 nm) =  kn ρ wn (745 nm) n .

(25)

n =1

This model has a dependency on the vicarious calibration because it is built with the satellite-collected water reflectance spectra [13] through the nearest non-turbid water pixel atmospheric correction [40]. Hence, coefficients of this model are adjusted after application of the vicarious gain factors. To obtain a new set of empirical data, turbid water reflectance spectra were collected from the Mokpo coastal region and East China Sea (denoted as MP and ECS, respectively) for several seasons. To minimize any fluctuations of the water spectral relationship induced by the variation of aerosols, the nearest non-turbid pixel is accepted only when the ρTOA(865 nm)-ρr(865 nm) is less than 0.006. In addition, cases of high wind speed (W < 6 m/s) and pixels affected by the ISRD and adjacency effects are also excluded from further consideration. Finally, new statistical relationships are derived (Fig. 12). In these models, coefficients j1, j2, j3, j4, j5, k1 and k2 of Eqs. 24 and 25 are −0.00148, 0.4865, −22.93, 615.8, −6760.0, 30210.0, 0.5012, and 4.0878, respectively.

Fig. 12. Relationships between ρwn(660 nm) and ρwn(745 nm) and ρwn(865 nm). The dashed line represents the linear relationship from the model of Ruddick et al. [34] that the ratio of ρwn(745 nm) to ρwn(865 nm) is 1.936.

The updated GOCI standard atmospheric correction considers the remote-sensing reflectance (Rrs) variations (due to radiant-path geometry), which was omitted in Ahn et al. [13]. Similar to Eq. (9), ρwn(λ) is converted to the bidirectional-effect-corrected Rrs using: Rrs ( λ ) =

ρ wn ( λ ) ℜ s ( λ , θ s =0, W ) ℜv ( λ , θ v =0, W ) × π ℜ s ( λ , θ s , W ) ℜv ( λ , θ v , W ) ×

f ( λ , θ s =0, chla ) Q ( λ , θ s , θ v , φs − v , chla )

Q ( λ , θ s =0,θ v =0, φs − v , chla ) f ( λ , θ s , chla )

(26) .

Appendix C: Quality control of AERONET-OC acquired water-leaving reflectance

At the Ieodo station [14], there is no level 2.0 AERONET-OC data that the quality is fully assured [35]. Moreover, Moon et al. [12] requires IOP pairs to build Rrs optical closure, however, AERONET-OC does not measure them. Therefore, we additionally apply a new data screening approach that uses a different method from Moon et al. (2012) [12]. To set optical boundaries, a series of empirical relationships of Rrs spectra are simulated by HYDROLIGHT [49]. In this study, various Rrs spectra are computed using the following input parameters: • Pure water IOPs are taken from Smith and Baker (1981) [50], Pope and Fry (1997) [51], and Kou et al.(1993) [52].

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23256

• We set chla concentration range as 0.1~30.0 mg/m3. Then, its IOP are taken from Morel (1988) [53], and Loisel and Morel (1998) [54]. Specific absorption of chla in 740~880 nm is assumed to be zero. • CDOM absroption range at 440 nm considered is 0.1~0.3 m−1. • Suspended sediment concentration range is 0.1~1000.0 g/m3. From Ahn (1990) [55], IOP of 4 mineral types, namely red clay (RC), yellow clay (YC), calcareous sand (CS), and brown earth (BE), were considered. Each absorption and backscattering coefficient spectra were extrapolated over the NIR range [49]. • Inelastic scattering effects (chlorophyll fluorescence, CDOM fluorescence, and Ramman scattering) are considered. • Wavelength range of the simulation considered is 400~880 nm per 5 nm bandwidth. Then convert into AERONET-OC bands. Finally, we develop the following spectral relationships; between Rrs(443 nm)/Rrs(555 nm) and Rrs(668 nm) [Fig. 13(a)], between Rrs(412 nm)/Rrs(443 nm) and Rrs(668 nm) [Fig. 13(b)], between Rrs(443 nm)/Rrs(490 nm) and Rrs(668 nm) [Fig. 13(c)], between Rrs(668 nm)/Rrs(555 nm) and Rrs(668 nm) [Fig. 13(d)], and between Rrs(869 nm)/Rrs(668 nm) and Rrs(668 nm) [Fig. 13(e)]. Then we excluded data which exhibited spectral relationships out of boundary conditions (blue-dashed closures) [Fig. 13]. Except the relationship between Rrs(869 nm)/Rrs(668 nm) and Rrs(668 nm) [Fig. 13(e)], those boundaries do not consider Rrs(668) less than 0.0045 because these relationships showed high variations in this reflectance range. It should be noted that the verification of IOP models is beyond the scope of this study. Moreover, those IOP models have not been developed for the GOCI area, hence they would not be consistent with the underwater optical environments of the calibration sites. Moreover, the extrapolated IOPs in the NIR may lead to unrealistic relationships between Rrs(869 nm)/Rrs(668 nm) and Rrs(668 nm). For these reasons, further investigations regarding IOPs at the study sites are needed for future improvement. Because of a lack of IOP verifications, the method excluded 60 unrealistic spectra as shown in Figure 14.

Fig. 13. Rrs spectral relationships obtained through HYDROLIGHT simulations. For this simulation, the range of chla concentration varied from 0.1~30 mg m−3, CDOM absorption at 440 nm from 0.1~0.3 m−1, and suspended sediment concentration from 0.1~1000 g m−3.

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Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23257

Fig. 14. Quality control adopted for the AERONET-OC data. (a) Rrs spectra accepted by the quality-control criteria, and (b) Rrs spectra rejected by the scheme because of spurious outliers.

#242932 © 2015 OSA

Received 12 Jun 2015; revised 12 Aug 2015; accepted 13 Aug 2015; published 26 Aug 2015 7 Sep 2015 | Vol. 23, No. 18 | DOI:10.1364/OE.23.023236 | OPTICS EXPRESS 23258