vsf_water: Scattering of pure (saline) water
In AlexCast/rho: R Hydrology Optics

Description Usage Arguments Details Value See Also Examples

This functions calculate the angular integral (scattering coefficient) and the angular distribution (volume scattering function) of pure (saline) water scattering.

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vsf_water(lambda, S = 0, Tc = 20, psi = pi/2, P = 0)

b_water(lambda, S = 0, Tc = 20, P = 0)

`lambda`	Wavelength in vacuum (nm).
`S`	Salinity [0,40] (parts per thousand).
`Tc`	Temperature [0,30] (ºC).
`psi`	Polar scattering angle (radians).
`P`	Pressure (bar in excess of 1 ATM).

The formulation of scattering of pure (saline) water is based on the Einstein-Smoluchowski theory of scattering in a particle free media due to fluctuations of the dieletric constant (square of the refractive index) caused by random motion of molecules. This implementation follows Zhang & Hu (2009A) that revisited the equations formulated with respect to the density derivative of the refractive index, after the new determinations of Proutiere et al. (1992). The excess scattering caused by diluted salts is based on salt concentration fluctuations by incorporating the salinity derivative of the refractive index (Zhang & Hu 2009B).

The density fluctuations are given by thermodynamic statistics and since both the density, the refractive index and the isothermal compressibility of water are a function of pressure, the pressure is allowed to vary. Note however that the model is only validated for surface pressure. The default pressure therefore is 0 bar, with P defined as excess pressure to 1 ATM (in bar).

The volume scattering function is provided per polar scattering angle. In natural waters, the angular distribution of scattering is only a function of the polar angle of scattering, i.e, it is constant for all azimuths at a given polar scattering angle (Jonaz & Fournier, 2007).

Finally, this function will provide values slightly higher than the ones provided by the Water Optical Properties Processor (WOPP; Röttgers et al., 2011) due to different equations for water density. See d_water for details. The required physical constants are taken from the 2018 edition of CODATA, available from: http://physics.nist.gov/cuu/Constants/

A numeric vector with the volume scattering function (m^-1 sr^-1) of pure (saline) water for function vsf_water and a numeric vector with the scattering coefficient.

a_water, n_water

# Retrieve the volume scattering function of average seawater at 550 nm:
psi <- seq(0, pi, length.out = 180)
vsf_water(lambda = 550, S = 34.72, Tc = 3.5, psi = psi)

# Retrieve the scattering coefficient of average seawater in the visible 
range:
b_water(lambda = 400:700, S = 34.72, Tc = 3.5)