Implementation of an analytical Raman scattering correction for satellite ocean-color processing

Lachlan I.W. McKinna; P. Jeremy Werdell; Christopher W. Proctor

doi:10.1364/OE.24.0A1123

1. Introduction

Raman scattering is a trans-spectral process whereby water molecules absorb and re-emit photons at wavelengths different to, and typically longer than, the Raman excitation (absorption) wavelength [1]. Both in situ measurements and radiative transfer studies have shown that Raman scattering can contribute significantly to the sensor-observed remote-sensing reflectance signal, R_rs,S(λ), particularly in oligotrophic waters [2–5]. This is of consequence to ocean-color semi-analytical algorithms (SAAs) that derive water-column optical properties from space-borne observations of R_rs,S(λ). Most SAAs utilize a quasi-single-scattering approximation (QSSA) [6] to mathematically conceptualize R_rs,S(λ) in order to invert the sensor-observed signal in the visible range (400 – 700 nm) and derive inherent optical properties (IOPs; the absorption and backscattering coefficients) of seawater and its constituents. However, the QSSA considers only the elastically-scattered contribution to the remote-sensing reflectance, R_rs,E(λ). This can lead to biases in derived IOPs because the unaccounted for Raman-scattered contribution to the remote-sensing reflectance, R_rs,R(λ), is incorrectly interpreted as an elastic scattering effect [2, 7, 8]. Thus, the objective of a Raman scattering correction (RSC) is to quantify and remove R_rs,R(λ) from R_rs,S(λ) as below

R_{r s, E} (λ) = R_{r s, S} (λ) - R_{r s, R} (λ) .

We also note that other inelastic scattering effects such as fluorescence also contribute to R_rs,S(λ_S), however, in this paper we focus on Raman scattering only.

For ocean-color processing, empirical and analytical approaches have been proposed to account for R_rs,R(λ) [9–12]. Recently, Westberry, et al. [2] developed an analytical RSC for data collected by NASA’s Moderate Resolution Imaging Spectroradiometer aboard the Aqua spacecraft (MODISA) [2]. The method calculates R_rs,R(λ) analytically by quantifying the flux of incident irradiance absorbed at Raman excitation wavelengths, λ_ex, that are scattered (emitted) into the sensor wavelengths, λ_S. The RSC, discussed in detail elsewhere [2, 9], comprises three key quantities/components: (i) the incident downwelling irradiance, E_d(λ), (ii) the Raman scattering cross-section, and (iii) first-order estimates of the in-water upward and downward diffuse attenuation coefficients (K_u(λ) and K_d(λ)).

The Raman redistribution function for water, f(λ_{ex $\to$}λ_S), describes at which wavelengths photons are absorbed to later be re-emitted at λ_S [1]. For ocean-color science, we consider that a given sensor band is centered on λ_S. Thus, in order to apply an RSC to that sensor band, knowledge of E_d(λ_ex) is required. However, for most multiband ocean-color sensors complementary bands centered on λ_ex do not exist, making it difficult to directly quantify E_d(λ_ex). One approach to address this concern is to use coincident measurements from a separate remote-sensing instrument that includes the wavelength of interest. Indeed, Westberry et al. [2] noted that MODISA had a lack of ultraviolet (UV) bands needed for their analytical RSC and subsequently used UV radiometry collected by the Ozone Mapping Instrument (OMI) aboard NASA’s Aura mission to estimate E_d(λ_ex).

The pixel sizes of MODISA and OMI differ greatly (MODISA 1 km x 1 km; OMI: 13 km x 24 km), and as such it is not practicable to use OMI data as an ancillary data input for E_d(λ_ex). In addition, the OMI mission’s lifespan (2004 – present) does not completely overlap with other ocean-color mission such as the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS; 1997 - 2010), thereby limiting the applicability of an OMI-based RSC. Further, of the four spectral bands distributed with OMI’s level-3 surface irradiance product, only one is appropriately centered for use in the RSC (see Table 1). As an alternative, we propose the computationally efficient semi-analytical downwelling irradiance model of Gregg and Carder [13] to calculate both E_d(λ_ex) and E_d(λ_S) during pixel-by-pixel processing.

Table 1. Band centers for MODISA and the band centers for the corresponding Raman excitation band. The single OMI level-3 band suitable for use in the Raman correction is also given.

View Table | View all tables in this article

Westberry et al. [2] used bio-optical models [14] to extrapolate/interpolate IOPs in order to estimate the K_u(λ) and K_d(λ) at λ_ex. The extrapolation procedure is rather straightforward for smoothly varying IOPs and pure water IOPs. However, the spectral absorption coefficient of phytoplankton, a_ϕ(λ), can be quite variable in the UV depending on the types of phytoplankton present, incident irradiance intensity, and the presence of photoprotective pigments [15]. Thus, Westberry et al. [2] proposed that a_ϕ(λ) be extrapolated from the shortest sensor wavelength (e.g. 412 nm for MODISA) into the UV as spectrally flat. We modified the approach used to extrapolate of a_ϕ(λ) in an attempt to improve estimates of the K_u(λ) and K_d(λ).

In this paper, we present an RSC that has been implemented within the NASA Ocean Biology Processing Group’s (OBPG) L1-to-L2 processing code, L2GEN. The RSC is based on the method of Westberry et al. [2] which we have modified to be a computationally efficient, stand-alone correction scheme that does not require ancillary OMI irradiance data. We also have extended the algorithm to support a range of past and present ocean-color sensors. Once implemented, we used the Generalized Inherent Optical Properties algorithm (GIOP) [16] to derive IOPs both with and without the RSC applied. Derived IOPs were then quantitatively compared with in situ measurements. We henceforth use the suffix “-RA” to denote that the RSC was applied, and the suffix “ –NR” to denote that the RSC was not applied. The comparison of derived IOPs with in situ measurements allowed us to quantify differences between GIOP-RA and GIOP-NR. Further, to test the temporal stability of the RSC, we examined the SeaWiFS time series for the Bermuda Atlantic Time Series (BATS) region.

2. Raman scattering correction algorithm

2.1 Raman excitation spectral response functions

The Raman redistribution function, f(λ_{ex $\to$}λ_S), can be considered as a spectral response function that describes a band of excitation wavelengths, λ_ex. Across this excitation band, light is absorbed at some efficiency described by the Raman absorption coefficient, a^R(λ_ex) [17], to be later scattered (emitted) into a spectral line centered on λ_S (Fig. 1). The Raman scattering coefficient, b^R(λ_S), can thus be expressed as

Fig. 1 Left-hand side: Raman excitation spectral response function (blue) for spectral emission at 412 m (illustrated as black line). Right-hand side: Raman excitation spectral response function (blue) for emission across an 11 nm band centered on 412 nm (illustrated as a black rectangle).

Download Full Size | PDF

b^{R} (λ_{S}) = \int_{λ_{e x}} a^{R} (λ_{e x}) f (λ_{e x} \to λ_{S}) d λ_{e x} .

For ocean-color processing, we wish to calculate how much light is scattered into a sensor band, not a spectral line. In order to accomplish this, we assume that all ocean-color bands have out-of-band corrections applied [18] to make them box-shaped with the correct center and 11 nm width [19]. We then considered each band to be the sum of multiple spectral lines spaced 1 nm apart and then calculate the f(λ_{ex $\to$}λ_S) for each of these spectral lines. For example, band 1 of SeaWiFS is centered on 412 nm and after out-of-band correction has a bandwidth 11 nm, we thus calculated f(λ_{ex $\to$}λ_S) eleven times over the range 407 - 417 nm. The multiple redistribution functions were then summed together to form a new curve, which was normalized to have an under-curve area equal to one (Fig. 1).

For each band of every ocean-color sensor supported, we computed complementary Raman excitation spectral response functions (SRFs). For example, Table 1 details MODISA ocean color bands and the corresponding Raman excitation bands. Once derived, the Raman excitation SRFs were used to compute band-pass averaged parameters required for the RSC algorithm such as the pure water IOPs and atmospheric transmittance coefficients.

2.2 Remote-sensing reflectance due to Raman-scattering

The semi-analytical model we have used to estimate R_rs,R(λ_S) is described in detail elsewhere [2, 9, 20] and for a single sensor band, it has the mathematical form

\begin{array}{l} R_{r s, R} (λ_{S}) = [\frac{1}{4 π n^{2}} \frac{b^{R} (λ_{s})}{[K_{d} (λ_{e x}) + K_{U} (λ_{S})]} \frac{E_{d} (0^{-}, λ_{e x})}{E_{d} (0^{+}, λ_{S})}] \dots \\ \dots \times [1 + \frac{b_{b} (λ_{e x})}{μ_{u} [K_{d} (λ_{e x}) + K_{U} (λ_{S})]} + \frac{b_{b} (λ_{S})}{K_{U} (λ_{S})}] . \end{array}

For brevity, details of the symbols in Eq. (3) are described in Table 2. On the right-hand side of Eq. (3), the first bracketed term describes first order scattering effects, whilst the second bracketed term accounts for higher order scattering. We acknowledge that Raman scattering does have slight angular dependency described by a scattering phase function [21], however, for our purposes we assume emissions are isotropic.

Table 2. Summary of terms used to calculate the Raman scattering contribution to the remote-sensing reflectance

View Table | View all tables in this article

2.3 Diffuse attenuation coefficients

A number of mathematical approximations for K_u(λ) and K_d(λ) exist. Below, are the functions used for approximating the vertical attenuation coefficients in the RSC. The diffuse attenuation coefficient of downwelling irradiance was calculated as

K_{d} (λ) = [a (λ) + b_{b} (λ)] / \cos θ_{s o l z}

where θ_solz is the solar zenith angle and a(λ) and b_b(λ) are the total absorption and backscattering coefficients, respectively [22]. The diffuse attenuation coefficient of the upwelling radiance was calculated as

K_{U} (λ) = [a (λ) + b_{b} (λ)] / μ_{u}

where μ_u is the mean cosine of upwelling irradiance and was set to a value of 0.5 [9].

2.4 Deriving and extrapolating IOPs

To compute K_u(λ) and K_d(λ), first-order estimates of a(λ) and b_b(λ) are needed at both λ_ex and λ_S. Our approach derives a(λ_S) and b_b(λ_S) using the Quasi-Analytical Algorithm (QAA) [23] and then interpolates/extrapolates these to λ_ex and λ_S. The QAA is an ocean-color algorithm that solves for IOPs algebraically using a series of semi-empirical relationships. Because the QAA has no iterative (spectral matching) component, it is computationally inexpensive and was thus considered suitable for use in the RSC. We note, that any SAA algorithm, including GIOP, could be used in place of the QAA.

After deriving a(λ) and b_b(λ) with the QAA, bio-optical models are used to separate out the optically-active sub-components. Specifically, a(λ) and b_b(λ) can be expressed as

a (λ) = a_{w} (λ) + a_{ϕ} (λ) + a_{d g} (λ)

b_{b} (λ) = b_{b w} (λ) + b_{b p} (λ)

where a_w(λ), a_ϕ(λ) and a_dg(λ) are the spectral absorption coefficients of water, phytoplankton, and colored dissolved and detrital matter, respectively. Whereas, b_bw(λ) and b_bp(λ) are the spectral backscattering coefficients of water and particulate matter, respectively.

Values of a_w(λ) and b_bw(λ) were treated as spectral constants [24, 25] with no temperature-salinity dependence. Therefore a_w(λ_ex), a_w(λ_S), b_bw(λ_ex) and b_bw(λ_S) were determined by convolution of a_w(λ) and b_bw(λ) with sensor-specific and Raman SRFs. In addition, a_dg(λ) and b_bp(λ) were modeled using an exponential function and power law, respectively [26, 27]

a_{d g} (λ) = a_{d g} (443) \exp {- S (λ - 443)}

b_{b p} (λ) = b_{b p} (555) {[555 / λ]}^{γ}

where S is an exponential decay coefficient and γ is a power law exponent. The QAA derives a_dg(443), b_bp(555), S and γ. Thus, it is straightforward to compute a_dg(λ) and b_bp(λ) at both λ_ex and λ_S.

There are several methods for modeling the spectral shape and magnitude of a_ϕ(λ). We modeled the normalized spectral shape of the phytoplankton absorption coefficient, a*_ϕ(λ), as a function of chlorophyll-a (Chla) concentration following Bricaud, et al. [28]. To initiate this, a band-ratio algorithm [29] was used derive the required value of Chla. The resulting spectra have magnitudes at a*_ϕ(443) equal to 1.0. Once the spectral shape has been derived, a_ϕ(λ) is scaled using the QAA-derived value of a_ϕ(443). Thus, a_ϕ(λ) can be expressed as

a_{ϕ} (λ) = a_{ϕ} (443) \times a_{ϕ}^{*} (Chla; λ)

We note that a suitable and efficient technique for extrapolating a*_ϕ(λ) into the UV (< 400 nm) was required. Westberry, et al. [2] suggested extrapolating a*_ϕ(λ) as spectrally flat below the sensor’s shortest wavelength. As an alternative, we fitted a straight line between the two shortest blue bands (e.g. 412 and 443 nm for SeaWiFS/MODISA) and then use this to extrapolate a*_ϕ(λ) out to 350 nm (see Fig. 2).

Fig. 2 Normalized phytoplankton absorption coefficients at MODISA band centers. The Three lines demonstrate a*_ϕ(λ) modeled for different Chla concentrations. Solid lines represent interpolated data, dotted lines represented linear extrapolations to wavelengths shorter than 412 nm.

Download Full Size | PDF

2.5 Downwelling irradiance model

To efficiently calculate the spectral downwelling irradiance, E_d(λ), at both λ_ex and λ_S we used the semi-analytical model of Gregg and Carder [13], referred to here as GC1990. The GC1990 model calculates both the diffuse and direct atmospheric transmittance in order to derive E_d(λ). To do so, GC1990 requires information about atmospheric parameters including: the Angström coefficient, the aerosol optical depth, atmospheric pressure, ozone concentration, column water vapor, the solar zenith angle, and the aerosol single scattering albedo. Fortunately these parameters are either derived by, or provided as ancillary data to, the atmospheric correction procedure in L2GEN. We do however need to estimate the aerosol optical thickness, τ(λ), in the UV. This is done by extrapolation using the power-law function

τ (λ) = τ (490) {[490 / λ]}^{α}

where τ(490) is the derived aerosol optical thickness at 490 nm and α is the Angström coefficient in the shortwave visible domain. We acknowledge that this power law extrapolation may not always be appropriate in regions with highly absorbing aerosols.

3. Data and algorithm evaluation

3.1 Satellite data processing

The most recently reprocessed (v2014.0) SeaWiFS and MODISA data were used in this study [30, 31]. Using L2GEN, which is distributed with NASA’s SeaWiFS Data Analysis System visualization and processing software suite (SeaDAS v7.2; http://seadas.gsfc.nasa.gov), atmospheric correction was applied to top-of-atmosphere ocean-color radiometry to derive R_rs,S(λ_S). After atmospheric correction was completed, the RSC was run to calculate R_rs,R(λ_S). The default configuration of the GIOP algorithm [16] as implemented in L2GEN was then used to derive IOPs both with and without R_rs,R(λ_S) subtracted from R_rs,S(λ_S). We note that for this study we tested the RSC with the GIOP algorithm, however, it can conceivably be applied to any of the SAAs [23, 27, 32–35] currently implemented within L2GEN.

3.2 Algorithm validation

To compare the retrieval skill of GIOP-RA with GIOP-NR, a product validation (matchup) analysis was conducted. Specifically, we validated SeaWiFS and MODISA retrievals of b_bp(λ_S), a_dg(λ_S) and a_ϕ(λ_S). This was achieved by comparing derived IOPs with in situ measurements extracted from the NASA SeaWiFS Bio-optical Archive and Storage System (SeaBASS; http://seabass.gsfc.nasa.gov). To quality control data points used in the matchup analysis, we followed the approach of Bailey, et al. [36]. A 5-by-5 pixel region was drawn around each in situ measurement. To retain the highest quality matchups, we excluded any 5-by-5 pixel region that: (i) contained less 12 valid pixels (48%), (iii) had a coefficient of variation exceeding 0.15, (iii) had a difference between in situ measurement and satellite overpass time greater than +/− 3 hours, or (iv) had solar and/or sensor zenith angles exceeding 70° and 56°, respectively. We also noted some anomalous outliers associated with the “Plumes and Blooms” in situ bio-optical time-series. We infer these matchups are likely associated with optically challenging coastal conditions that were undocumented in SeaBASS’ metadata. As such we excluded all Plumes and Blooms data from this study.

Using Type-II linear regression statistics, IOPs derived using the GIOP-RA and GIOP-NR were compared with in situ values. The regression slope, standard deviation of the slope, and r-squared (r²) values were computed on log-10 transformed data using reduced major axis linear regression. As measures of bias, the median ratio (MR) and median percent error (MPE) were computed on non-transformed data as

M R = median ({\hat{X}}_{i} / X_{i})

M P E = median [100 % \times | {\hat{X}}_{i} / X_{i} - 1 |]

Where

{\hat{X}}_{i}

denotes satellite-retrieved values and X_i denotes in situ measurements. The aforementioned matchups metrics were used to quantitatively compare GIOP-RA and GIOP-NR retrievals.

3.3 Temporal evaluation

A matchup analysis provides a robust assessment of the absolute accuracy of an algorithm, however, it only represents a discrete number of observations that are sparse both in space and time. In order to understand if the RSC is temporally stable (i.e. does not contribute unwanted trends and/or artifacts into the derived IOP products), we examined a regional ocean-color time-series. Specifically, we selected a geographic box (30 - 34°N, 62 - 66°W) that encompassed the Bermuda Atlantic Time-series Study site (BATS). The BATS site is well-studied and located southeast of Bermuda in the North Atlantic Gyre. The region is considered oligotrophic, and thus makes it an ideal location to test the RSC. Specifically, we processed eleven years of the SeaWiFS time-series (1997–2009). Data were processed using L2GEN from L1-to-L2 and IOP products were derived using GIOP-RA and GIOP-NR. For our analysis we examined b_bp(443), a_dg(443) and a_ϕ(443).

4. Results

4.1 Extrapolating the phytoplankton absorption coefficient

We acknowledge that our approach for extrapolating a*_ϕ(λ) into the UV range (350 – 400 nm) may not always be appropriate, particularly at wavelengths shorter than 350 nm where a*_ϕ(λ) can become highly variable. Fortunately, the shortest Raman excitation wavelengths used in this study were centered on 362 nm. Thus, the simple linear extrapolation method was deemed suitable as a computationally efficient first-order estimate of a*_ϕ(λ) in the UV region. Nonetheless, we performed a brief analysis to compare the linear fit extrapolation method described in section 2.4 and spectrally flat extrapolation method of Westberry et al. [2].

A subset of quality-controlled near surface (0 – 10 m) a_ϕ(λ) spectra (spectral range: 350-750 nm) were extracted from the SeaBASS archive. The geographic extract region {35°N-35°S, 180°W-180°E} spanned a range of water types including the oligotrophic subtropical gyres, productive upwelling zones, and optically complex coastal waters. All absorption spectra were normalized to 1.0 at 443 nm. We then compared actual values of a*_ϕ(362) and a*_ϕ(383) with the extrapolated estimates (see scatter plots Fig. 3). The MPE values (Table 3) indicated that the spectrally flat extrapolation method overestimated a*_ϕ(362) and a*_ϕ(383) by 73 and 44 percent, respectively. Whilst the simple linear fit extrapolation underestimated a*_ϕ(362) and a*_ϕ(383) by 40 and 10 percent, respectively. In addition, the linear fit extrapolation had regression slopes for a*_ϕ(362) and a*_ϕ(383) of 0.59 and 0.90, respectively. Whereas, the spectrally flat extrapolation had regression slopes for a*_ϕ(362) and a*_ϕ(383) of 0.22 and 0.46.

Fig. 3 Left-hand side: normalized phytoplankton absorption coefficients extracted from SeaBASS. Center: scatter plot of extrapolated estimates of a*_ϕ(362) compared with actual values. Left-hand side: scatter plot of extrapolated estimates of a*_ϕ(383) compared with actual values. Blue triangles denote spectrally flat extrapolation from 412 nm. Red circles denote simple linear model extrapolation.

Download Full Size | PDF

Table 3. Regression statistics for extrapolated values of the normalized phytoplankton absorption coefficients compared with actual values

View Table | View all tables in this article

These results indicate that the simple linear fit extrapolation provides a slightly better first-order estimate of a*_ϕ(UV) than a spectrally flat extrapolation from 412 nm. We acknowledge that estimates of a*_ϕ(UV) are challenging due, in part, to variable absorption by mycosporine-like amino acids (MAAs). However, with an improved understanding of a_ϕ(λ) behavior in the UV region, we expect our simple extrapolation will be updated with a refined method.

4.2 Matchup analysis

By using the same processing software (L2GEN), inversion algorithm (GIOP), and in situ data points (SeaBASS), it was possible to directly compare the retrieval skill of GIOP-RA with GIOP-NR. Scatter plots shown in Fig. 4 compare GIOP-derived and in situ IOPs at 443 nm. From inspecting the scatter plots, differences between GIOP-NR and GIOP-RA were difficult to discern visually. However, using Type-II linear regression statistics, it was possible to elucidate more subtle differences in IOP retrievals (full statistics in Tables 4 and 5).

Fig. 4 Comparison plots of GIOP-derived IOPs and in situ observations at 443 nm for SeaWiFS and MODISA. Scatter plots on the left-hand column (blue shaded) denote IOPs derived with no Raman correction applied (GIOP-NR). Scatter plots on the right-hand columns (red shaded) denote IOPs derived with the Raman correction applied (GIOP-RA). See Tables 4 ad 5 for accompanying statistics.

Download Full Size | PDF

Table 4. Matchup statistics for IOPs retrieved using the GIOP algorithms compared with in situ (SeaBASS) observations at SeaWiFS wavelengths. The two major columns denote IOPs derived with no Raman correction applied (GIOP-NR) and IOPs derived with the Raman correction applied (GIOP-RA)

View Table | View all tables in this article

Table 5. Matchup statistics for IOPs retrieved using the GIOP algorithms compared with in situ (SeaBASS) observations at MODISA wavelengths. The two major columns denote IOPs derived with no Raman correction applied (GIOP-NR) and IOPs derived with the Raman correction applied (GIOP-RA)

View Table | View all tables in this article

For b_bp(λ_S) retrievals, r² values were similar for both GIOP-NR and GIOP-RA retrievals. Sensor-wise, r² values ranged from 0.57 – 0.62 and 0.44 – 0.50 for SeaWiFS and MODISA, respectively. We note that for the GIOP-RA retrievals, regression slopes were consistently closer to unity at all wavelengths for both SeaWiFS and MODISA. These results are encouraging and suggest that the RSC worked as expected. Specifically, b_bp(λ_S) retrievals at the lower end of the dynamic range (clearest waters) where Raman scattering is expected to cause positive bias [8] were reduced thereby ‘tilting’ the regression slope closer to unity. Both MR and MPE values indicate that GIOP-RA b_bp(λ_S) retrievals were biased slightly lower than those of GIOP-NR. However, we note that the magnitude of the biases reported here are consistent with previous studies of the GIOP algorithm [16, 37]. Further, the MPE can be a somewhat misleading metric. For example, the median value of all in situ b_bp(443) data points was 0.003 m⁻¹. Therefore a 20% relative error equates to an absolute error of 0.0006 m⁻¹ which is approaching the instrument offset uncertainties for commercial sensors such as the HOBI Labs Hydroscat-6 [8].

For retrievals of a_dg(λ_S), GIOP-RA and GIOP-NR had r² values, regression slopes, MRs, and MPEs that remained similar for both SeaWiFS and MODISA (see Tables 4 and 5). These results suggest that a_dg(λ_S) retrievals are less sensitive to the RSC. For SeaWiFS, the retrieval skill of a_dg(λ_S) (for both GIOP-RA and GIOP-NR) reduced with increasing wavelength evidenced by lower r² values and increased bias. This result is consistent with previous assessments of the GIOP algorithm [16, 37]. We note that for MODISA, the retrieval skill for a_dg(λ_S) was poor at all sensor wavelengths for both GIOP-RA and GIOP-NR evidenced by low r² values (< 0.25), regression slopes of approximately 1.5 and MPEs in excess of 50%. These results should be interpreted with caution as GIOP retrievals of a_dg(λ_S) at MODISA wavelengths have previously been reported as skillful based on high quality bio-optical algorithm development data sets [16]. It is thus likely that the reduced retrieval skill of a_dg(λ_S) for MODISA reported here is due, in part, to the dynamic range quality and of the in situ data set.

The retrieval skill of a_ϕ(λ_S) for SeaWiFS was good for both GIOP-RA and GIOP-NR as indicated by r² values ranging from 0.61 – 0.68. However, the MR metric revealed a 5 – 10% positive bias in retrievals. Nonetheless, there was little discernable difference between the GIOP-RA and GIOP-NR methods. For MODISA, retrievals of a_ϕ(λ_S) were very good with r² values ranging from 0.73 – 0.87 and regression slopes and MRs close to unity for all wavelengths. There was little difference in the skill of GIOP-RA and GIOP-NR at retrieving a_ϕ(λ_S) for MODISA. However, we do note that for GIOP-RA retrievals of a_ϕ(λ_S) had slightly larger MPEs for wavelengths 488 – 667 nm.

To directly compare differences between GIOP-NR and GIOP-RA IOP retrievals, the median ratio of the two was calculated for each IOP product at each sensor wavelength (see Table 6 and Fig. 5). For b_bp(λ_S), the comparison showed, as expected, that GIOP-RA retrievals were on average slightly less than those of GIOP-NR at all wavelengths. The magnitude of the difference was similar for both SeaWiFS and MODISA (3.5 – 4.5%) and increased slightly with wavelength. Whilst for a_dg(λ_S), the relative comparison showed there was little difference (0.0 – 0.1%) between GIOP-NR and GIOP-RA for both SeaWiFS and MODISA. For a_ϕ(λ_S), the results showed that GIOP-NR retrievals were larger than those of GIOP-RA, however the differences had no apparent spectral dependency. We note that relative differences at all SeaWiFS wavelengths were larger (2.2 - 3.4%) than those for MODISA wavelengths (0.7 – 0.9%).

Table 6. Median ratio of IOPs derived without the Raman correction applied (GIOP-NR) and IOPs derived with the Raman correction applied (GIOP-RA) at both SeaWiFS and MODISA wavelengths.

View Table | View all tables in this article

Fig. 5 Histograms of the ratio of GIOP-NR to GIOP-RA. The three columns left-to-right correspond to the IOPs: b_bp(443), a_dg(443) and a_ϕ(443), respectively. The top rows are SeaWiFS results, whilst the bottom rows are MODISA results. The vertical solid black line denotes where the ratio is equal to 1.0, and the dotted vertical black line is the median value of each distribution.

Download Full Size | PDF

Overall, the matchup analysis does not reveal large differences between GIOP-NR and GIOP-RA retrieval skill. Importantly though, the analysis revealed that the RSC did not degrade spectral IOP retrievals. Unfortunately, at the time of this study the SeaBASS in situ data set did not contain many IOP measurements from oligotrophic waters with coincident satellite observations. For example, the sub-tropical oligotrophic gyres make up approximately 40% of the world’s oceans [38] and are regions in which Raman scattering is known to bias b_bp(λ_S) retrievals [8]. The continued collection of high quality in situ IOP measurements from oligotrophic waters will enable us to extend our evaluation of the RSC and further improve our validation of GIOP-RA retrievals.

4.3 Time series case study

Using the eleven-year SeaWiFS time-series (1997-2009) for the BATS region, we compared temporal differences between IOPs derived with GIOP-RA and GIOP-NR. Plots of the time-series comparison are shown in Fig. 6. The first noticeable feature is a clear seasonal cycle that is tracked well by both a_dg(443) and a_ϕ(443). Peaks in this cycle correspond with the well documented winter bloom that occurs in the BATS region [39]. On average, a_dg(443)-RA were about 4% smaller than a_dg(443)-NR, and a_ϕ(443)-RA were about 2% smaller than a_ϕ(443)-NR. Whereas, b_bp(443)-RA were on average about 8.5% smaller than b_bp(443)-NR. These differences between RA and NR IOPs are of similar magnitude to those reported elsewhere [2, 8].

Fig. 6 SeaWiFS IOPs derived using the GIOP algorithm for BATS region. Left-hand panels show time-series plots of and b_bp(443) (top), a_dg(443) (middle) and a_ϕ(443) (bottom). The colors denote IOPs derived from remote-sensing reflectances without (red) and with (blue) the RSC applied. The right-hand panels are time-series of the relative difference between b_bp(443) (top), a_dg(443) (middle) and a_ϕ(443) (bottom) derived from Raman-corrected and Raman-uncorrected remote-sensing reflectances.

Download Full Size | PDF

The relative differences between GIOP-RA and GIOP-NR exhibited a seasonal cycle. Specifically, during February-March, the relative differences in b_bp(443), a_dg(443) and a_ϕ(443) were smallest at approximately 7%, 3%, and 1%, respectively. Whilst during July-August the relative differences in b_bp(443), a_dg(443) and a_ϕ(443) were largest at approximately 10%, 5% and 2.5%, respectively. The observed cycle in relative differences followed seasonal changes in water clarity. The smallest relative differences were observed during the winter bloom peak (February-March) when waters are most productive. Whereas, the largest relative differences occurred during the middle of the year (July-August) when waters are stratified and conditions are clearest. This temporal pattern in the relative differences demonstrates how the RSC is dependent on K_u(λ) and K_d(λ) (water clarity), coefficients that vary seasonally. Further, the seasonality in relative differences demonstrates that even for oligotrophic waters, the RSC should not be treated as a systematic bias.

Importantly, the time-series results demonstrate that the RSC did not introduce unwanted long-term trends or temporal artifacts. However, we acknowledge that there are some missing data towards the end of the time-series (2008-2009) that are associated with SeaWiFS spacecraft operating anomalies. We note that the magnitude of relative differences between GIOP-RA and GIOP-NR derived IOPs are larger for the BATS time-series than for the in situ data set. This is because the IOPs derived for the BATS region fall at the lower end of the in situ data set’s dynamic range. Thus, relative differences between the time series data differ from the median relative differences calculated over the entire dynamic range of the in situ data set.

Finally, ocean-color observations have been listed as an Essential Climate Variable (ECV) required for monitoring global climate change [40]. Indeed, a multi-mission time-series (1997 – present) of Chla is presently used as an ECV to report on changes in global phytoplankton stocks [41]. However, a number of IOP-based ocean-color algorithms have been proposed, and/or developed, to extend our understanding of ocean biogeochemistry beyond bulk estimates of phytoplankton stocks inferred from Chla. For example, from b_bp(λ) it is possible to estimate parameters such as particulate organic carbon (POC), primary productivity (PP), phytoplankton carbon, and phytoplankton community composition [42–46]. Thus, it is critical to apply a RSC in order to improve estimates of b_bp(λ), which may otherwise propagate biases through to IOP-based biogeochemical parameters.

5. Conclusions

Here we presented a RSC algorithm necessary for improving global retrievals of IOPs, particularly in oligotrophic waters. The matchup analysis results revealed that the retrieval skill of GIOP was not markedly hindered by the RSC and retrievals of b_bp(λ_S) were slightly improved, particularly for MODISA. Further, the time-series analysis demonstrated the RSC did not introduce unwanted temporal trends or artifacts. These results provide confidence that the RSC presented here is robust and suitable for standard ocean-color processing. Further, the current correction scheme as implemented in L2GEN is computationally efficient and supports the following past and present ocean-color sensors: the Ocean Color Temperature Scanner (OCTS), SeaWiFS, MODIS (Aqua and Terra), the Medium Resolution Imaging Spectroradiometer (MERIS), and the Visible Infrared Imaging Radiometer Suite (VIIRS). We plan to maintain ongoing algorithm support for planned and soon-to-be launched ocean-color missions, such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, and modify the RSC algorithm as relevant advances are made by the ocean-color research community. In particular, alternative K_u(λ) and K_d(λ) formulations as well as an improved spectral model of a_ϕ(λ) in the UV are potential avenues for improvement.

Acknowledgments

A NASA Ocean Biology and Biogeochemistry Program award for the Science of Terra and Aqua supported this work. We thank Tommy Owens for time-series data processing support. Ivona Cetinić, Amir Ibrahim and other members of the NASA OBPG are also duly acknowledged for providing valuable scientific advice. We also wish to recognize the efforts of Emmanuel Boss who kindly reviewed this paper.

References and links

1. G. E. Walrafen, “Raman spectral studies of effects of temperature on water structure,” J. Chem. Phys. 47(1), 114–126 (1967). [CrossRef]

2. T. K. Westberry, E. Boss, and Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52(22), 5552–5561 (2013). [CrossRef] [PubMed]

3. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38(15), 3166–3174 (1999). [CrossRef] [PubMed]

4. R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27(19), 4002–4011 (1988). [CrossRef] [PubMed]

5. C. Hu and K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36(27), 6962–6967 (1997). [CrossRef] [PubMed]

6. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. Atmos. 93(D9), 10909–10924 (1988). [CrossRef]

7. H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39(18), 3001–3011 (2000). [CrossRef] [PubMed]

8. Z. Lee and Y. Huot, “On the non-closure of particle backscattering coefficient in oligotrophic oceans,” Opt. Express 22(23), 29223–29233 (2014). [CrossRef] [PubMed]

9. S. Sathyendranath and T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37(12), 2216–2227 (1998). [CrossRef] [PubMed]

10. Z. Lee, C. Hu, S. Shang, K. Du, M. Lewis, R. Arnone, and R. Brewin, “Penetration of UV-visible solar radiation in the global oceans: Insights from ocean color remote sensing,” J. Geophys. Res. Oceans 118(9), 4241–4255 (2013). [CrossRef]

11. Z. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, and C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33(24), 5721–5732 (1994). [CrossRef] [PubMed]

12. B. R. Marshall and R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29(1), 71–84 (1990). [CrossRef] [PubMed]

13. W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless marine atmospheres,” Limnol. Oceanogr. 35(8), 1657–1675 (1990). [CrossRef]

14. Z.-P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: An evaluation of remote sensing methods,” J. Geophys. Res. Oceans 110, C02017 (2005).

15. A. Bricaud, M. Babin, H. Claustre, J. Ras, and F. Tièche, “Light absorption properties and absorption budget of Southeast Pacific waters,” Journal of Geophysical Research: Oceans 115(C8), C08009 (2010). [CrossRef]

16. P. J. Werdell, B. A. Franz, S. W. Bailey, G. C. Feldman, E. Boss, V. E. Brando, M. Dowell, T. Hirata, S. J. Lavender, Z. Lee, H. Loisel, S. Maritorena, F. Mélin, T. S. Moore, T. J. Smyth, D. Antoine, E. Devred, O. H. d’Andon, and A. Mangin, “Generalized ocean color inversion model for retrieving marine inherent optical properties,” Appl. Opt. 52(10), 2019–2037 (2013). [CrossRef] [PubMed]

17. J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37(15), 3324–3332 (1998). [CrossRef] [PubMed]

18. M. Wang, B. A. Franz, R. A. Barnes, and C. R. McClain, “Effects of spectral bandpass on SeaWiFS-retrieved near-surface optical properties of the ocean,” Appl. Opt. 40(3), 343–348 (2001). [CrossRef] [PubMed]

19. NASA Goddard Space Flight Center, Ocean Ecology Laboratory, “Spectral Response Functions and Bandpass Averaged Quantities,” in Ocean Color Documents (http://oceancolor.gsfc.nasa.gov/DOCS/RSR_tables.html, 2012).

20. C. D. Mobley, “Hydrolight Technical Note 10: Interpretation of Raman Scattering Computations,” (Sequoia Scientific, 2012).

21. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic Press, 1994).

22. S. Sathyendranath and T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing,” J. Geophys. Res. 93(C8), 9270–9280 (1988). [CrossRef]

23. Z. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41(27), 5755–5772 (2002). [CrossRef] [PubMed]

24. A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tièche, “Optical properties of the “clearest” natural waters,” Limnol. Oceanogr. 52(1), 217–229 (2007). [CrossRef]

25. R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). [CrossRef] [PubMed]

26. C. S. Roesler, M. J. Perry, and K. L. Carder, “Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34(8), 1510–1523 (1989). [CrossRef]

27. K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. Oceans 104(C3), 5403–5421 (1999). [CrossRef]

28. A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with the chlorophyll a concentration in oceanic (Case 1) waters: analysis and implications for bio-optical models,” J. Geophys. Res. Oceans 103, 31,033 - 031,044 (1998).

29. J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. Oceans 103(C11), 24937–24953 (1998). [CrossRef]

30. NASA Goddard Space Flight Center; Ocean Ecology Laboratory, Ocean Biology Distributed Active Archive Center, “Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua Ocean Color Data,” (http://oceancolor.gsfc.nasa.gov/, 2014).

31. NASA Goddard Space Flight Center; Ocean Ecology Laboratory, Ocean Biology Distributed Active Archive Center, “Sea Viewing Wide-Field-of-view Sensor (SeaWiFS) Ocean Color Data,” (http://oceancolor.gsfc.nasa.gov/, 2014).

32. T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semianalytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt. 45(31), 8116–8131 (2006). [CrossRef] [PubMed]

33. S. A. Garver and D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation: 1. Time series from the Sargasso Sea,” Journal of Geophysical Research: Oceans 102(C8), 18607–18625 (1997). [CrossRef]

34. L. I. W. McKinna, P. R. C. Fearns, S. J. Weeks, P. J. Werdell, M. Reichstetter, B. A. Franz, D. M. Shea, and G. C. Feldman, “A semianalytical ocean color inversion algorithm with explicit water-column depth and substrate reflectance parameterization,” Journal of Geophysical Research: Oceans 120, 1741–1770 (2015).

35. F. E. Hoge and P. E. Lyon, “Spectral parameters of inherent optical property models: method for satellite retrieval by matrix inversion of an oceanic radiance model,” Appl. Opt. 38(9), 1657–1662 (1999). [CrossRef] [PubMed]

36. S. W. Bailey, S. B. Hooker, D. Antoine, B. A. Franz, and P. J. Werdell, “Sources and assumptions for the vicarious calibration of ocean color satellite observations,” Appl. Opt. 47(12), 2035–2045 (2008). [CrossRef] [PubMed]

37. P. J. Werdell, B. A. Franz, J. T. Lefler, W. D. Robinson, and E. Boss, “Retrieving marine inherent optical properties from satellites using temperature and salinity-dependent backscattering by seawater,” Opt. Express 21(26), 32611–32622 (2013). [CrossRef] [PubMed]

38. C. R. McClain, S. R. Signorini, and J. R. Christian, “Subtropical gyre variability observed by ocean-color satellites,” Deep Sea Res. Part II Top. Stud. Oceanogr. 51(1-3), 281–301 (2004). [CrossRef]

39. D. K. Steinberg, C. A. Carlson, N. R. Bates, R. J. Johnson, A. F. Michaels, and A. H. Knap, “Overview of the US JGOFS Bermuda Atlantic Time-series Study (BATS): a decade-scale look at ocean biology and biogeochemistry,” Deep Sea Res. Part II Top. Stud. Oceanogr. 48(8-9), 1405–1447 (2001). [CrossRef]

40. GCOS, Implementation plan for the global observing system for climate in support of the UNFCCC (2010 Update) (World Meteorological Organization, Available online at http://www.wmo.int/pages/prog/gcos/Publications/gcos-138.pdf, 2010), p. 180.

41. B. A. Franz, M. J. Behrenfeld, D. A. Siegel, and P. J. Werdell, “3.k. Global Oceans: Global ocean phytoplankton,” in State of the Climate in 2014, J. Blunden and D. S. Arndt, eds. (Am. Meterol. Soc., 2015), pp. S85–S87.

42. D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Röttgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5(1), 171–201 (2008). [CrossRef]

43. I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D'Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” Journal of Geophysical Research: Oceans 117, n/a-n/a (2012). [CrossRef]

44. M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005). [CrossRef]

45. J. R. Graff, T. K. Westberry, A. J. Milligan, M. B. Brown, G. Dall’Olmo, V. Dongen-Vogels, K. M. Reifel, and M. J. Behrenfeld, “Analytical phytoplankton carbon measurements spanning diverse ecosystems,” Deep Sea Res. Part I Oceanogr. Res. Pap. 102, 16–25 (2015). [CrossRef]

46. T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosciences 7(10), 3239–3257 (2010). [CrossRef]

	Band center (FWHM^†) [nm]
MODISA ocean color bands	412 (11)	443 (11)	488 (11)	531 (11)	547 (11)	667 (11)
Corresponding Raman excitation for MODISA	362 (7)	383 (7)	419 (8)	450 (9)	467 (9)	530 (11)
OMI level-3 bands suitable for Raman correction	-	380 (0.55)	-	-	-	-

Equation term	Definition	Units
$λ_{e x}$	Raman excitation wavelength/s	nm
$λ_{S}$	Raman emission (sensor) wavelength/s	nm
$n$	Refractive index of seawater	-
$b^{R}$	The Raman scattering coefficient	m⁻¹
$b_{b}$	The total backscattering coefficient	m⁻¹
$E_{d} (0^{-}, λ_{e x})$	The downwelling irradiance just below the air-sea interface at the Raman excitation wavelengths	W m⁻²
$E_{d} (0^{+}, λ_{S})$	The downwelling irradiance just above the air-sea interface at the Raman emission (sensor) wavelength	W m⁻²
$K_{d}$	The diffuse attenuation coefficient of downwelling irradiance	m⁻¹
$K_{U}$	The attenuation coefficient of upwelling radiance	m⁻¹
$μ_{u}$	The mean cosine of the upwelling irradiance	-

Extrapolation method	UV wavelength (nm)	r²	Slope (SE)	Ratio	MPE
Spectrally flat	362	0.25	0.22 (0.02)	1.73	73.5
Spectrally flat	383	0.63	0.46 (0.02)	1.44	43.9
Simple linear model	362	0.25	0.59 (0.05)	0.61	38.6
Simple linear model	383	0.63	0.90 (0.03)	0.91	10.4

		GIOP-NR SeaWiFS						GIOP-RA SeaWiFS
		N	r²	Slope (SE)	Ratio	MPE	N	r²	Slope (SE)	Ratio	MPE
$b_{b p}$	412	85	0.60	0.76 (0.06)	0.93	21.1	85	0.60	0.79 (0.06)	0.92	24.1
	443	85	0.61	0.78 (0.06)	0.94	19.3	85	0.61	0.81 (0.06)	0.92	21.2
	490	85	0.62	0.81 (0.06)	0.93	18.6	85	0.62	0.85 (0.06)	0.88	20.2
	510	85	0.61	0.82 (0.06)	0.92	18.8	85	0.62	0.86 (0.06)	0.88	21.5
	555	85	0.61	0.84 (0.06)	0.91	20.3	85	0.61	0.88 (0.06)	0.86	20.7
	670	85	0.57	0.87 (0.07)	0.83	25.2	85	0.57	0.91 (0.07)	0.81	27.9
$a_{d g}$	412	177	0.49	1.09 (0.06)	0.82	46.7	177	0.49	1.09 (0.06)	0.82	47.2
	443	177	0.48	1.05 (0.06)	0.73	48.9	177	0.48	1.06 (0.06)	0.73	49.0
	490	177	0.44	1.00 (0.06)	0.63	54.2	177	0.44	1.00 (0.06)	0.63	54.2
	510	177	0.43	0.97 (0.06)	0.61	57.0	177	0.42	0.98 (0.06)	0.61	56.8
	555	177	0.38	0.88 (0.06)	0.52	63.8	177	0.38	0.89 (0.06)	0.52	63.6
	670	177	0.35	0.85 (0.06)	0.30	72.7	177	0.35	0.85 (0.06)	0.30	72.4
$a_{ϕ}$	412	191	0.66	1.15 (0.05)	0.69	38.5	191	0.65	1.17 (0.06)	0.67	40.2
	443	191	0.63	1.15 (0.06)	0.73	34.0	191	0.61	1.18 (0.06)	0.73	35.7
	490	191	0.62	1.12 (0.06)	0.80	30.0	191	0.61	1.15 (0.05)	0.78	31.8
	510	191	0.66	1.12 (0.05)	0.82	34.8	191	0.65	1.15 (0.06)	0.79	34.9
	555	186	0.69	1.14 (0.06)	0.93	45.5	186	0.68	1.17 (0.06)	0.91	45.8
	670	191	0.68	1.06 (0.05)	1.10	53.7	191	0.66	1.07 (0.05)	1.06	51.3

		GIOP-NR MODISA						GIOP-RA MODISA
		N	r²	Slope (SE)	Ratio	MPE	N	r²	Slope (SE)	Ratio	MPE
$b_{b p}$	412	33	0.50	0.87 (0.12)	0.98	14.7	33	0.50	0.91 (0.12)	0.94	13.4
	443	33	0.50	0.88 (0.12)	1.01	14.3	33	0.49	0.92 (0.13)	0.99	11.8
	488	33	0.48	0.90 (0.13)	1.05	13.2	33	0.47	0.95 (0.13)	0.99	12.0
	531	33	0.47	0.90 (0.13)	1.03	12.5	33	0.47	0.94 (0.13)	0.98	12.6
	547	33	0.45	0.91 (0.13)	1.00	13.9	33	0.44	0.95 (0.14)	0.95	13.9
	667	33	0.39	0.90 (0.14)	1.04	18.4	33	0.38	0.95 (0.14)	1.00	15.2
$a_{d g}$	412	31	0.14	1.52 (0.31)	0.78	56.4	32	0.15	1.52 (0.30)	0.79	55.0
	443	31	0.15	1.52 (0.31)	0.72	49.3	32	0.16	1.52 (0.30)	0.72	48.0
	488	31	0.16	1.52 (0.30)	0.64	52.8	32	0.17	1.52 (0.30)	0.64	51.5
	531	31	0.17	1.52 (0.30)	0.53	55.6	32	0.18	1.52 (0.30)	0.53	55.3
	547	31	0.17	1.53 (0.30)	0.53	55.2	32	0.18	1.53 (0.30)	0.53	54.0
	667	31	0.25	1.33 (0.25)	0.31	69.5	32	0.25	1.31 (0.24)	0.31	69.5
$a_{ϕ}$	412	35	0.80	1.03 (0.08)	0.95	35.5	36	0.78	1.01 (0.08)	0.97	34.5
	443	35	0.76	1.02 (0.09)	1.00	35.6	36	0.74	1.00 (0.09)	1.03	33.6
	488	35	0.76	1.00 (0.09)	1.12	27.0	36	0.73	0.98 (0.08)	1.12	29.7
	531	35	0.85	1.05 (0.07)	0.99	32.8	36	0.84	1.03 (0.07)	0.97	36.8
	547	35	0.87	1.02 (0.06)	1.20	30.7	36	0.85	1.00 (0.07)	1.20	31.3
	667	35	0.78	1.07 (0.09)	1.18	38.6	35	0.76	1.06 (0.09)	1.25	39.2

Implementation of an analytical Raman scattering correction for satellite ocean-color processing

Abstract

1. Introduction

2. Raman scattering correction algorithm

2.1 Raman excitation spectral response functions

2.2 Remote-sensing reflectance due to Raman-scattering

2.3 Diffuse attenuation coefficients

2.4 Deriving and extrapolating IOPs

2.5 Downwelling irradiance model

3. Data and algorithm evaluation

3.1 Satellite data processing

3.2 Algorithm validation

3.3 Temporal evaluation

4. Results

4.1 Extrapolating the phytoplankton absorption coefficient

4.2 Matchup analysis

4.3 Time series case study

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Tables (6)

Equations (13)

Optics Express

		SeaWiFS median [GIOP-NR / GIOP-RA]	MODISA median [GIOP-NR /GIOP-RA]
$b_{b p}$	412	1.035	1.038
	443	1.036	1.041
	490*	1.037	1.044
	510^	1.038	1.045
	555‡	1.038	1.046
	670†	1.043	1.045
$a_{d g}$	412	1.000	0.998
	443	1.001	0.998
	488*	1.000	0.999
	531^	1.000	0.998
	547‡	1.000	0.998
	670†	1.000	1.000
$a_{ϕ}$	412	1.034	1.008
	443	1.032	1.007
	488*	1.033	1.008
	531^	1.030	1.009
	547‡	1.022	1.007
	670†	1.030	1.007