# Diffuse attenuation coefficient for downwelling irradiance at 490 nm (Kd)

## 1 - Product Summary

This algorithm returns the diffuse attenuation coefficient for downwelling irradiance at 490 nm ($Kd\_490$) in m-1, calculated using an empirical relationship derived from in situ measurements of $Kd\_490$ and blue-to-green band ratios of remote sensing reflectances (Rrs).

Implementation of this algorithm is contingent on the availability of Rrs in the blue-green spectral region (e.g., 490 - 565 nm). CZCS, OCTS, MODIS-Aqua and -Terra, MERIS, SeaWiFS, VIIRS, and others are all supported.

Algorithm Point of Contact: P. Jeremy Werdell, NASA Goddard Space Flight Center

## 2 - Algorithm Description

##### Inputs:

$R_{rs}$ near 490 nm and between 547 and 565 nm

##### Output:

$Kd\_490$, diffuse attenuation coefficient of downwelling irradiance at 490 nm in m-1

##### General Algorithm:

The algorithm is a fourth-order polynomial relationship between a ratio of $R_{rs}$ and $Kd\_490$:

$$log_{10}\left(K_{bio}\left(490 \right ) \right )=a_0 + \sum_{i=1}^{4}a_i\left(log_{10}\left(\frac{R_{rs}\lambda_{blue}}{R_{rs}\lambda_{green}}\right) \right )^{i}$$

$$Kd\_490=K_{bio}\left(490\right) + 0.0166$$

the coefficients for which are sensor-specific:

sensor blue green a0 a1 a2 a3 a4
KD2S SeaWiFS 490 555 -0.8515 -1.8263 1.8714 -2.4414 -1.0690
KD2M MODIS 488 547 -0.8813 -2.0584 2.5878 -3.4885 -1.5061
KD2E MERIS 490 560 -0.8641 -1.6549 2.0112 -2.5174 -1.1035
KD2V VIIRS 490 550 -0.8730 -1.8912 1.8021 -2.3865 -1.0453
KD2O OCTS 490 565 -0.8878 -1.5135 2.1459 -2.4943 -1.1043
KD2C CZCS 443 520 -1.1358 -2.1146 1.6474 -1.1428 -0.6190
KD2L OLI/Landsat 8 482 561 -0.9054 -1.5245 2.2392 -2.4777 -1.1099

The coefficients were derived using version 2 of the NASA bio-Optical Marine Algorithm Data set (NOMAD).

## 3 - Implementation

Click get_Kd.c to view source code.

##### Calling in L2GEN
 l2prod = Kd_490 each satellite will use its sensor-specific coefficients and wavelengths (e.g., SeaWiFS defaults to KD2S) to override the coefficients: kd2_coef = [a0,a1,a2,a3,a4] to override the wavelengths: kd2_wave = [numerator wavelength, denominator wavelength] 

## 4 - Assessment

Satellite-to-in-situ validation results are available from the SeaWiFS Bio-Optical Archive and Storage System (SeaBASS):

KD2S KD2M KD2E
KD2V KD2O KD2C

#### Algorithm verification: comparison with alternate models

KD2S is compared with (Morel et al. 2007) (both Rrs- and Chl-driven) and (Lee 2005)

## 5 - References

Austin, R. W., & Petzold, T. J. (1981). The determination of the diffuse attenuation coefficient of sea water using the Coastal Zone Color Scanner.  In: J.F.R. Gower, Ed., Oceanography from Space, Plenum Press, New York, 239-256, http://dx.doi.org/10.1007/978-1-4613-3315-9_29

Lee, Z.-P. (2005). A model for the diffuse attenuation coefficient of downwelling irradiance. Journal of Geophysical Research, 110(C2). http://dx.doi.org/10.1029/2004jc002275

O'Reilly, J.E. & 24 co-authors (2000). SeaWiFS Postlaunch Calibration and Validation Analyses, Part 3. NASA Tech. Memo. 2000-206892, Vol. 11, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, 49 pp.

Yeh, E-N. & 7 co-authors (1997). Case Studies for SeaWiFS Calibration and Validation, Part 4. NASA Tech. Memo. 104566, Vol. 41, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, 35 pp.

Werdell, P. J. & Bailey, S. W. (2005). An improved bio-optical data set for ocean color algorithm development and satellite data product validation. Remote Sensing of Environment 98, 122-140, http://dx.doi.org/10.1016/j.rse.2005.07.001.