April 23, 2020
Author: Emmanuel Boss
Water contributes to both absorption and scattering by Sea Water. In clear ocean waters water eﬀect on ocean color in the visible cannot be neglected and hence have to be taken into account. In addition in the NIR water often dominates absorption. Temperature and salinity aﬀect both absorption and scattering by water and hence need to be taken into account when the optical properties of water are computed.
This model ﬁt well data from 200-1100nm with an average error of (Zhang and Hu (2009)).
Absorption by water
Absorption as a rich structure due to the the excitation of the diﬀerent vibrational modes of the water molecule. You can access a compendium of published research on water absorption and values. Water absorption is aﬀected by temperature and salinity (See Sullivan et al. (2006) for latest results on the subject).
Elastic scattering by water According to Einstein-Smolucjowski theory, elastic scattering of light by water is due to ﬂuctuations in the dielectric constant in space caused by random motion of molecules (see Zhang and Hu (2009) and Zhang et al. (2009) for a recent review). Elastic scattering by water has similarities in angular shape and spectral behavior to Rayleigh scattering, however with important diﬀerences. For example, the VSF:
where is the deploarization ratio. Several depolarization ratios have been suggested with providing the best ﬁt to data (Zhang et al. (2009)).
Elastic scattering by sea water depends on salinity ( increase for range of salinities observed in the oceans), much less so of temperature ( between 0 and ) and pressure ( for an increase in P of 100bar).
Rather than repeat the derivations from Zhang and Hu (2009) and Zhang et al. (2009), we provide a link to a matlab function that provide their results and computes the scattering coeﬃcient and the VSF of water at 90 degrees for a given wavelength, salinity and temperature. We summarize their results using a few plots (for a code produced by Zhang here.
Raman scattering by water In Raman scattering a fraction of the incident light of wavenumber is absorbed and re-emitted at wavenumber where is the Raman shift of a vibrational mode of the water molecule (Desiderio (2000)). For water (Ge et al. (1993)). Remember that wavelength and wavenumber are related through . The emission wavelegnth (in [nm]) is then:
If represents the irradiance of the incident light  and the volume Raman scattering function , then the total power scattered into the full solid angle for a of water (, ) is: . The value of for an excitation wavelength of (20,492) is (Desiderio (2000)). In many case we are interested in quanta emitted per quanta absorbed (e.g. for Monte Carlo simulations or to calculate the eﬀect on IOPs, See Desiderio (2000)) in which case: .
To compute for another wavelength ():
Raman scattering is used to calibrate the intensity of the source of a LIDAR system as the signal leaving the ocean is proportional to the intensity of the source Hoge et al. (1988).