# Anomalous Light Scattering by Pure Seawater

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

^{−1}) can be expressed as

_{d}represents the scattering due to density fluctuation, and b

_{c}the scattering due to fluctuation of mixing ratio (concentration). Following Zhang and Hu [9],

^{−23}m

^{2}·kg·s

^{−2}·K

^{−1}), and N

_{A}(=6.022 × 10

^{23}mol

^{−1}) are the wavelength of light, the Boltzmann constant, and Avogadro’s number; ρ, n, T, β

_{T}, S, and δ are the density, the absolute refractive index, the absolute temperature, the isothermal compressibility, the mass concentration of salts, and the depolarization ratio of the seawater; and a

_{w}and M

_{w}(=18.01528 g mol

^{−1}) are the activity and molecular weight of pure water. Also, $h(\delta )=(2+\delta )/(6-7\delta ).$

_{c}vanishes for pure water, and the scattering of light is due entirely to density fluctuation. Replacing the density derivative in Equation (2) with pressure derivative, i.e., ${(\rho \frac{\partial {n}^{2}}{\partial \rho})}_{T}=\frac{2n}{{\beta}_{T}}{(\frac{\partial n}{\partial P})}_{T}$, Equation (2) becomes the Einstein–Smoluchowski equation

_{T}, and a

_{w}can be found in Zhang and Hu [9] and Zhang et al. [11], and the Matlab code for the model can be accessed at https://goo.gl/jKAZgT. Light scattering by seawater is a function of salinity, temperature, and pressure. In this study, we focus on the temperature and salinity ranges of 0–60 °C and 0–40 psu under one atmospheric pressure, which cover the majority of natural inland, coastal, and oceanic surface water bodies. The presence of sea salts is expected to modify the value of δ through two contrasting effects: isotropic ions would decrease δ; whereas their electrostatic field would increase anisotropy, and hence the value of δ [18,19]. Both effects have been observed in pure salt solutions: δ for KNO

_{3}solution increases and δ for KCl solution decreases, with their respective concentrations [20]. To the best of our knowledge, however, no studies have been reported on how the δ of seawater would vary with salinity. For this study, we assumed a constant value of 0.039 for the depolarization ratio δ for pure water [21] and for seawater [8,9,22,23].

## 3. Results and Discussion

_{min}hereafter. The predicted values of T

_{min}are close to the value of 22 °C measured by Cohen and Eidenberg [6], but differ significantly in both value and trend from the Buiteveld, et al. [7] model, which predicts a maximum near 15 °C. We believe the difference is largely due to the uncertainty in modeling ${(\partial n/\partial P)}_{T}$ in Equation (4) that was used by Buiteveld, et al. [7]. Austin and Halikas [16] pointed out that the measurements of the refractive index of water as a function of the pressure, i.e., n(P), were of worse quality when compared to those of n(T), n(λ), or n(S). Also, it is well-known that to numerically approximate a derivative, such as $\partial n/\partial P$, as a ratio of measured values is very sensitive to the uncertainties in the measurements of n(P). In addition, Buiteveld, et al. [7] derived the temperature dependency of ${(\partial n/\partial P)}_{T}$ by fitting the measurements [25] between 5 and 35 °C, which also explains the relatively large deviation as shown in Figure 1 when extrapolating their model beyond 35 °C.

_{d}(due to density fluctuation) and Figure 2b for b

_{c}(due to concentration fluctuation). Both b

_{d}and b

_{c}vary with temperature in the same anomalous way, all exhibiting a minimum. Also, both T

_{min}for b

_{d}and T

_{min}for b

_{c}change with salinity—however, with differing patterns. T

_{min}for b

_{d}decreases about 20% from 24.6 °C to 19.1 °C for salinity varying from 0 to 40 psu, whereas over the same salinity range T

_{min}for b

_{c}increases slightly by ~3%, from 32.2 °C to 33.2 °C. In terms of absolute magnitude, b

_{d}is about 2–10 times greater than b

_{c}(Figure 2a), but in terms of change with respect to salinity, b

_{c}is about 10 times greater than b

_{d}(Figure 2b). As a result, the change of T

_{min}for the total scattering coefficient, b is dominated by b

_{c}, and increases from 24.6 °C to 27.5 °C for S from 0–40 psu (Figure 3). It is well known that T

_{max}for density [26] and T

_{min}for isothermal compressibility [27] decrease with the salinity. Here, we show for the first time that T

_{min}for light scattering increases with salinity, which is largely due to the temperature variation of scattering introduced by sea salts. Table 1 lists the variations of T

_{min}for b

_{d}, b

_{c}, and b at different salinities.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Brovchenko, I.; Oleinikova, A. Multiple Phases of Liquid Water. ChemPhysChem
**2008**, 9, 2660–2675. [Google Scholar] [CrossRef] [PubMed] - Ball, P. Water—An enduring mystery. Nature
**2008**, 452, 291. [Google Scholar] [CrossRef] [PubMed] - Vedamuthu, M.; Singh, S.; Robinson, G.W. Properties of Liquid Water: Origin of the Density Anomalies. J. Phys. Chem.
**1994**, 98, 2222–2230. [Google Scholar] [CrossRef] - Vedamuthu, M.; Singh, S.; Robinson, G.W. Properties of Liquid Water. 4. The Isothermal Compressibility Minimum near 50 °C. J. Phys. Chem.
**1995**, 99, 9263–9267. [Google Scholar] [CrossRef] - Cho, C.H.; Urquidi, J.; Gellene, G.I.; Robinson, G.W. Mixture model description of the T-, P dependence of the refractive index of water. J. Chem. Phys.
**2001**, 114, 3157–3162. [Google Scholar] [CrossRef] - Cohen, G.; Eisenberg, H. Light Scattering of Water, Deuterium Oxide, and Other Pure Liquids. J. Chem. Phys.
**1965**, 43, 3881–3887. [Google Scholar] [CrossRef] - Buiteveld, H.; Hakvoort, J.H.M.; Donze, M. The optical properties of pure water. SPIE
**1994**, 2258, 174–183. [Google Scholar] - Twardowski, M.S.; Claustre, H.; Freeman, S.A.; Stramski, D.; Huot, Y. Optical backscattering properties of the “clearest” natural waters. Biogeosciences
**2007**, 4, 1041–1058. [Google Scholar] [CrossRef] - Zhang, X.; Hu, L. Estimating scattering of pure water from density fluctuation of the refractive index. Opt. Express
**2009**, 17, 1671–1678. [Google Scholar] [CrossRef] [PubMed] - Zhang, X.; Hu, L. Scattering by pure seawater at high salinity. Opt. Express
**2009**, 17, 12685–12691. [Google Scholar] [CrossRef] [PubMed] - Zhang, X.; Hu, L.; He, M.-X. Scattering by pure seawater: Effect of salinity. Opt. Express
**2009**, 17, 5698–5710. [Google Scholar] [CrossRef] [PubMed] - Zhang, X.; Hu, L.; Twardowski, M.S.; Sullivan, J.M. Scattering by solutions of major sea salts. Opt. Express
**2009**, 17, 19580–19585. [Google Scholar] [CrossRef] [PubMed] - Morel, A. Etude Experimentale de la diffusion de la lumiere par l’eau, les solutions de chlorure de sodium et l’eau de mer optiquement pures. J. Chim. Phys.
**1966**, 10, 1359–1366. [Google Scholar] [CrossRef] - Morel, A. Note au sujet des constantes de diffusion de la lumiere pour l’eau et l’eau de mer optiquement pures. Cahiers Oceanogr.
**1968**, 20, 157–162. [Google Scholar] - Einstein, A. Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes. Annalen der Physik
**1910**, 338, 1275–1298. [Google Scholar] [CrossRef] - Austin, R.W.; Halikas, G. The Index of Refraction of Seawater; SIO Ref. No. 76-1; Scripps Institute of Oceanography: La Jolla, CA, USA, 1976; p. 121. [Google Scholar]
- Proutiere, A.; Megnassan, E.; Hucteau, H. Refractive index and density variations in pure liquids: A new theoretical relation. J. Phys. Chem.
**1992**, 96, 3485–3489. [Google Scholar] [CrossRef] - Morel, A. Optical Properties of Pure Water and Pure Sea Water. In Optical Aspects of Oceanography; Jerlov, N.G., Nielsen, E.S., Eds.; Academic Press: New York, NY, USA, 1974; pp. 1–24. [Google Scholar]
- Shifrin, K.S. Physical Optics of Ocean Water; American Institute of Physics: New York, NY, USA, 1988; p. 285. [Google Scholar]
- Pethica, B.A.; Smart, C. Light scattering of electrolyte solutions. Trans. Faraday Soc.
**1966**, 62, 1890–1899. [Google Scholar] [CrossRef] - Farinato, R.S.; Rowell, R.L. New values of the light scattering depolarization and anisotropy of water. J. Chem. Phys.
**1976**, 65, 593–595. [Google Scholar] [CrossRef] - Zhang, X. Molecular Light Scattering by Pure Seawater. In Light Scattering Reviews 7; Kokhanovsky, A., Ed.; Springer: Heidelberg, Germany, 2013; pp. 225–243. [Google Scholar]
- Werdell, P.J.; McKinna, L.I.; Boss, E.; Ackleson, S.G.; Craig, S.E.; Gregg, W.W.; Lee, Z.; Maritorena, S.; Roesler, C.S.; Rousseaux, C.S.; et al. An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing. Prog. Oceanogr.
**2018**, 160, 186–212. [Google Scholar] [CrossRef] - Quan, X.; Fry, E.S. Empirical equation for the index of refraction of seawater. Appl. Opt.
**1995**, 34, 3477–3480. [Google Scholar] [CrossRef] [PubMed] - O’Connor, C.L.; Schlupf, J.P. Brillouin Scattering in Water: The Landau—Placzek Ratio. J. Chem. Phys.
**1967**, 47, 31–38. [Google Scholar] [CrossRef] - Millero, F.J.; Chen, C.-T.; Bradshaw, A.; Schleicher, K. A new high pressure equation of state for seawater. Deep-Sea Res.
**1980**, 27, 255–264. [Google Scholar] [CrossRef] - Lepple, F.K.; Millero, F.J. The isothermal compressibility of seawater near one atmosphere. Deep-Sea Res.
**1971**, 18, 1233–1254. [Google Scholar] [CrossRef]

**Figure 1.**The temperature variations of light scattering by pure water, calculated using the Zhang and Hu [9] model (i.e., Equation (2)) at 436 and 546 nm and normalized by their respective values at 25 °C, are compared with the estimates using the Buiteveld, et al. [7] model and with the measurements by Cohen and Eisenberg [6]. Note that the normalized variations estimated by the Zhang and Hu model overlap with each other at the two wavelengths.

**Figure 2.**Light scattering by pure seawater at 546 nm as a function of temperature and salinity. (

**a**) b

_{d}, the scattering due to density fluctuation; and (

**b**) b

_{c}, the scattering due to concentration fluctuation. Lines of progressive colors from blue to red correspond to different salinities from 0 to 40 psu, at 5 psu increments. The dotted line in each plot connects T

_{min}at different salinities.

**Figure 3.**Total scattering coefficient by pure seawater at 546 nm as a function of temperature and salinity. Lines of progressive colors from blue to red correspond to different salinities from 0 to 40 psu at 5 psu increments. The dotted line connects T

_{min}at different salinities.

**Table 1.**Temperatures (T

_{min}in °C) at which the scattering of light at 546 nm by pure seawater due to density fluctuations (b

_{d}), concentration fluctuations (b

_{c}), and their total (b) reach the minimum for various salinities (S).

S (psu) | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
---|---|---|---|---|---|---|---|---|---|

b_{d} (m^{−1}) | 24.6 | 24.0 | 23.4 | 22.7 | 22.0 | 21.2 | 20.5 | 19.8 | 19.1 |

b_{c} (m^{−1}) | 32.2 | 32.3 | 32.5 | 32.7 | 32.8 | 33.0 | 33.1 | 33.2 | |

b (m^{−1}) | 24.6 | 25.3 | 25.9 | 26.3 | 26.6 | 26.9 | 27.2 | 27.3 | 27.5 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Hu, L. Anomalous Light Scattering by Pure Seawater. *Appl. Sci.* **2018**, *8*, 2679.
https://doi.org/10.3390/app8122679

**AMA Style**

Zhang X, Hu L. Anomalous Light Scattering by Pure Seawater. *Applied Sciences*. 2018; 8(12):2679.
https://doi.org/10.3390/app8122679

**Chicago/Turabian Style**

Zhang, Xiaodong, and Lianbo Hu. 2018. "Anomalous Light Scattering by Pure Seawater" *Applied Sciences* 8, no. 12: 2679.
https://doi.org/10.3390/app8122679