An empirical algorithm for determining the diffuse attenuation coefficient <i>K</i>_<i>d</i> in clear and turbid waters from spectral remote sensing reflectance

Abstract

A robust empirical algorithm to determine the diffuse attenuation coefficient K d at a wavelength of 490 nm ( K d 490 ) from spectral remote sensing reflectance has been derived from the NOMAD data set and tested against the COASTLOOC data set. Together, both data sets contain more than 3,800 observations of concomitantly acquired bio‐optical parameters in waters ranging from very clear to very turbid, of which about 2,300 have been used in this study. The proposed algorithm follows a power law of the form K d 490 = 10^( a 0 + a 1 x + a 2 x 2 + a 3 x 3 ) + a 4 , where x is the common logarithm of either of two remote sensing reflectance ratios: log 10 ( R rs 490/R rs 555 ) for clear waters and log 10 ( R rs 490/R rs 665 ) for turbid waters. Switching between the ratios is triggered when R rs 490/R rs 555 drops below a threshold value of 0.85 corresponding to a K d 490 value of approx. 0.2 m −1 . Our algorithm shows comparable performance in both clear and turbid waters. Due to its simplicity and the public availability of the underlying in situ data, localization of the algorithm by appropriate sub‐setting of the NOMAD data and/or adding other in situ data are straightforward.