# Apparent Visible Wavelength (AVW)

## 1 - Product Summary

This algorithm returns the weighted harmonic mean of the visible-range (400 – 700 nm) remote sensing reflectance ($R_{rs}$) wavelengths, outputting the Apparent Visible Wavelength (AVW) in units of nanometers. The AVW is an optical water classification index, representing a one-dimensional geophysical metric that is inherently correlated to $R_{rs}$ spectral shape (Vandermeulen et al. 2020). Since the entire visible-range spectrum is utilized in the calculation of AVW, this product ensures that any diagnostic signals present in the $R_{rs}$ signal are considered, and affords the opportunity to describe and analyze spectral trends in $R_{rs}$ in terms of a single variable.

Algorithm Point of Contact: Ryan Vandermeulen, NASA Goddard Space Flight Center.

## 2 - Algorithm Description

Inputs: $R_{rs}$ at all available wavelengths between 400 – 700 nm (rrs_vvv).

Outputs: avw, Apparent Visible Wavelength (nm)

Approach: The Apparent Visible Wavelength (AVW) is calculated as the weighted harmonic mean of all $R_{rs}$ wavelengths, weighted as a function of the relative intensity of $R_{rs}$ at each wavelength:

The derivation of the AVW, at its most fundamental level, is simply a first-order measure of the dominant color of the water, as determined by the weight that each measured reflectance channel contributes to the albedo in the visible range of the spectrum. The output is not in the form of discrete classes, but instead a continuous gradient of wavelength values that represent a quantitative descriptor of weighted mean color reflected from the water's surface. At any point on this gradient, we find similarly shaped $R_{rs}$(λ) spectra represented by the same AVW number.

To reconcile the impacts of spectral band placement on variance in spectral shape, an extensive in situ hyperspectral dataset (Clark et al. 1997, Bracher et al. 2015, Vandermeulen et al. 2017, Casey et al. 2019) is used to correlate sensors of varying multi- and hyperspectral resolutions, thereby promoting product continuity of the AVW between satellite sensors. $R_{rs}$(λ) for each multispectral sensor are reconstructed from the 5,522 hyperspectral spectra, using the corresponding Relative Spectral Response (RSR) function for each satellite sensor. The hyperspectral AVW is compared to the multispectral AVW calculated for each sensor, and the coefficients from a polynomial fit are retained and applied to multispectral satellite data (see Section 4). Hyperspectral sensors undergo a slightly different procedure in l2gen. Since the multispectral coefficients are largely tuned with 1 nm spectral resolution data, hyperspectral satellite data are first interpolated to 1 nm spectral resolution using a spline interpolation function, and AVW is subsequently calculated without the use of a polynomial offset. With this correction, sensors with disparate spectral band placement (see table below) yield comparable AVW values to that of a hyperspectral sensor, further enabling an effective means of elucidating similarities or differences in spectral signatures within the constraints of two dimensions. See Vandermeulen et al. (2020) for details on a fit-for-purpose analysis performed on the AVW product multiple missions.

Sensor-specific band centers used in AVW calculations:

SensorSensor-specific band centers used in AVW calculations
MODIS-Aqua412, 443, 469, 488, 531, 547, 555, 645, 667, 678
MODIS-Terra412, 443, 469, 488, 531, 547, 555, 645, 667, 678
OLCI-S3A400, 412, 443, 490, 510, 560, 620, 665, 674, 682
OLCI-S3B400, 412, 443, 490, 510, 560, 620, 665, 674, 681
MERIS413, 443, 490, 510, 560, 620, 665, 681
SeaWiFS412, 443, 490, 510, 555, 670
HawkEye412, 447, 488, 510, 556, 670
OCTS412, 443, 490, 516, 565, 667
GOCI412, 443, 490, 555, 660, 680
VIIRS-SNPP410, 443, 486, 551, 671
VIIRS-JPSS1411, 445, 489, 556, 667
CZCS443, 520, 550, 670
MSI-S2A443, 490, 560, 665
MSI-S2B443, 490, 559, 665
OLI443, 482, 561, 655

Using the defined band centers (above) to calculate a sensor-specific AVW, the values are subsequently converted into a hyperspectral-equivalent AVW, using the following polynomial offsets:

Polynomial Coefficients
Sensor c0 c1 c2 c3 c4 c5
MODIS-Aqua 5.3223151E-09 -1.3619239E-05 1.3886726E-02 -7.0534823E+00 1.7860303E+03 -1.8010144E+05
MODIS-Terra5.2820302E-09 -1.3533547E-05 1.3817488E-02 -7.0277257E+00 1.7819361E+03 -1.7993575E+05
OLCI-S3A5.3756534E-10 -1.3823300E-06 1.4217760E-03 -7.3259519E-01 1.9025240E+02 -1.9586876E+04
OLCI-S3B5.2874737E-10 -1.3593836E-06 1.3979935E-03 -7.2032459E-01 1.8710170E+02 -1.9264929E+04
MERIS-1.8566476E-10 5.9630399E-07 -7.3760077E-04 4.4214046E-01 -1.2805555E+02 1.4733655E+04
SeaWiFS1.3889225E-08 -3.4666482E-05 3.4478423E-02 -1.7081781E+01 4.2173196E+03 -4.1487648E+05
HawkEye1.2484460E-08 -3.1200493E-05 3.1064705E-02 -1.5404026E+01 3.8058444E+03 -3.7458936E+05
OCTS4.9443860E-09 -1.2738386E-05 1.3043106E-02 -6.6374048E+00 1.6805142E+03 -1.6913709E+05
GOCI2.3513884E-10 -6.3647535E-07 6.9347646E-04 -3.8202645E-01 1.0759457E+02 -1.2026274E+04
SGLI1.6912427E-09 -4.9242779E-06 5.5741262E-03 -3.0863774E+00 8.4069664E+02 -9.0088850E+04
VIIRS-SNPP 1.6399143E-09 -4.1496452E-06 4.1742101E-03 -2.0901182E+00 5.2296625E+02 -5.2094618E+04
VIIRS-JPSS13.8180817E-10 -1.1345956E-06 1.2998933E-03 -7.2752517E-01 2.0172126E+02 -2.1958504E+04
CZCS2.5904658E-08 -6.7326637E-05 6.9802590E-02 -3.6085795E+01 9.3033343E+03 -9.5665775E+05
MSI-S2A-7.4719643E-10 1.8794584E-06 -1.8924228E-03 9.5069314E-01 -2.3623942E+02 2.3384674E+04
MSI-S2B-1.3572502E-09 3.4546589E-06 -3.5159381E-03 1.7855878E+00 -4.5046399E+02 4.5327899E+04
OLI-7.5487887E-09 1.9136261E-05 -1.9333568E-02 9.7261770E+00 -2.4338650E+03 2.4247497E+05

A calibrated, hyperspectral "equivalent" AVW is then computed as:

$AVW_{calibrated} = c0(AVW^5) + c1(AVW^4) + c2(AVW^3) + c3(AVW^2) + c4(AVW) + c5$

## 3 - Implementation

Product Short Name: avw

Level-2 Product Suite: None (available through SeaDAS command-line processing)

Level-3 Product Suite: avw (test product)

Calling in L2GEN: l2prod = avw

Each satellite will use its sensor-specific coefficients, to override the coefficients: avw_coef = [c0, c1, c2, c3, c4, c5]

Flags: PRODWARN - Pixels with negative $R_{rs}$ values can adversely impact product viability. IF $R_{rs}$_vvv < 0, PRODWARN is issued.

## 5 - References

Bracher, Astrid; Taylor, Marc H; Taylor, Bettina B; Dinter, Tilman; Röttgers, Rüdiger; Steinmetz, Francois (2015): Phytoplankton pigments, hyperspectral downwelling irradiance and remote sensing reflectance during POLARSTERN cruises ANT-XXIII/1, ANT-XXIV/1, ANT-XXIV/4, ANT-XXVI/4, and Maria S. Merian cruise MSM18/3. PANGAEA, doi: 10.1594/PANGAEA.847820

Casey, Kimberly A; Rousseaux, Cecile S; Gregg, Watson W; Boss, Emmanuel; Chase, Alison P; Craig, Susanne E; Mouw, Colleen B; Reynolds, Rick A; Stramski, Dariusz; Ackleson, Steven G; Bricaud, Annick; Schaeffer, Blake; Lewis, Marlon R; Maritorena, Stéphane (2019): In situ high spectral resolution inherent and apparent optical property data from diverse aquatic environments. PANGAEA, doi: 10.1594/PANGAEA.902230

Clark, D. K., Gordon, H. R., Voss, K. J., Ge, Y., Broenkow, W., & Trees, C. (1997). Validation of atmospheric correction over the oceans. Journal of Geophysical Research: Atmospheres, 102(D14), 17209-17217, doi: 10.1029/96JD03345

Craig, Susanne E; Lee, Zhongping; Du, Keping (2020): Top of Atmosphere, Hyperspectral Synthetic Dataset for PACE (Phytoplankton, Aerosol, and ocean Ecosystem) Ocean Color Algorithm Development. National Aeronautics and Space Administration, PANGAEA, doi: 10.1594/PANGAEA.915747

Seegers, B. N., Stumpf, R. P., Schaeffer, B. A., Loftin, K. A., & Werdell, P. J. (2018). Performance metrics for the assessment of satellite data products: an ocean color case study. Optics express, 26(6), 7404-7422, doi: 10.1364/OE.26.007404

Vandermeulen, R. A., Mannino, A., Neeley, A., Werdell, J., & Arnone, R. (2017). Determining the optimal spectral sampling frequency and uncertainty thresholds for hyperspectral remote sensing of ocean color. Optics Express, 25(16), A785-A797, doi: 10.1364/OE.25.00A785

Vandermeulen, R. A., Mannino, A., Craig, S.E., Werdell, P.J., 2020: "150 shades of green: Using the full spectrum of remote sensing reflectance to elucidate color shifts in the ocean," Remote Sensing of Environment, 247, 111900, doi: 10.1016/j.rse.2020.111900

TBD