The relation between the total Raman scattering coefficient of water (b(r)) and the Raman scattering cross section of liquid water is clarified. Consideration of the experimental configurations used to derive the Raman scattering cross section of water relative to benzene leads to a revised value of b(r) for water. In certain applications in marine optics it is necessary to scale b(r) to effect a change from implicit units of energy to quanta.