The latest model for light scattering by pure seawater was used to investigate the anomalous behavior of pure water. The results showed that water exhibits a minimum scattering at 24.6 °C, as compared to the previously reported values of minimum scattering at 22 °C or maximum scattering at 15 °C. The temperature corresponding to the minimum scattering also increases with the salinity, reaching 27.5 °C for S = 40 ps

Hu, Lianbo

Zhang, Xiaodong

English

UND Scholarly Commons (University of North Dakota)

University of North DakotaUND Scholarly CommonsEarth System Science and Policy FacultyPublications Department of Earth System Science and Policy12-2018Anomalous Light Scattering by Pure SeawaterXiaodong ZhangUniversity of North Dakota, xiaodong.zhang2@UND.eduLianbo HuFollow this and additional works at: https://commons.und.edu/essp-facThis Article is brought to you for free and open access by the Department of Earth System Science and Policy at UND Scholarly Commons. It has beenaccepted for inclusion in Earth System Science and Policy Faculty Publications by an authorized administrator of UND Scholarly Commons. For moreinformation, please contact zeineb.yousif@library.und.edu.Recommended CitationZhang, Xiaodong and Hu, Lianbo, "Anomalous Light Scattering by Pure Seawater" (2018). Earth System Science and Policy FacultyPublications. 4.https://commons.und.edu/essp-fac/4applied  sciencesArticleAnomalous Light Scattering by Pure SeawaterXiaodong Zhang 1,* ID and Lianbo Hu 1,21 Department of Earth System Science and Policy, University of North Dakota, Grand Forks, ND 58202, USA;hulb@ouc.edu.cn2 Ocean Remote Sensing Institute, Ocean University of China, Qingdao 266001, China* Correspondence: zhang@aero.und.edu; Tel.: +1-701-777-6087Received: 17 May 2018; Accepted: 19 July 2018; Published: 19 December 2018Abstract: The latest model for light scattering by pure seawater was used to investigate the anomalousbehavior of pure water. The results showed that water exhibits a minimum scattering at 24.6 ◦C, ascompared to the previously reported values of minimum scattering at 22 ◦C or maximum scatteringat 15 ◦C. The temperature corresponding to the minimum scattering also increases with the salinity,reaching 27.5 ◦C for S = 40 psu.Keywords: light scattering; light scattering by pure water; light scattering by pure seawater;anomalous properties of water1. IntroductionLight scattering by pure water or pure seawater is a fundamental quantity in aquatic optics.Because of hydrogen bonding, many bulk properties of water exhibit anomalous behavior withtemperature that is unlike any other liquids [1,2]. For example, liquid water has a maximum densitynear 4 ◦C [3], a minimum isothermal compressibility near 46 ◦C [4] and a maximum refractive indexnear 0 ◦C [5]. The scattering seems to behave “anomalously” too [6]. Cohen and Eisenberg [6]measured the scattering at 436 and 546 nm by pure water at temperatures from 5 to 65 ◦C, and founda scattering minimum at approximately 22 ◦C that is consistent with their theoretical estimate usingthe Einstein–Smoluchowski equation and the temperature variation of the isothermal compressibility.Using the same Einstein-Smoluchowski equation, with inputs re-evaluated using newer experimentalresults, Buiteveld et al. [7] improved the estimate of light scattering by pure water, which showed abetter agreement with the spectral values measured by Morel [8]. However, their model predicts amaximum scattering at 15 ◦C, which differs from Cohen and Eisenberg [6] not only in value but inthe behavior as well. To the best of our knowledge, few other studies have explored the temperaturebehavior of scattering by water. In addition, it is still unknown whether and how this temperaturedependence of scattering by water would vary in the presence of sea salts.2. MethodsRecently, Zhang and coworkers refined the models for light scattering by pure water [9], by pureseawater [10,11], and by simple sea salt solutions [12] using the improved measurements of the keythermodynamic parameters, and their models agree with the spectral scattering measurements [13,14]for both pure water and seawater within the experimental errors (2%). Localized fluctuation in densityfor pure water, as well as additional fluctuations in the mixing ratio of salt ions and water for pureseawater, lead to microscopic inhomogeneities in the refractive index (n) [15], which in turn causescattering of light. Since the fluctuations in density and mixing ratio are independent, the scatteringcoefficient of seawater, b (m−1) can be expressed asb = bd + bc, (1)Appl. Sci. 2018, 8, 2679; doi:10.3390/app8122679 www.mdpi.com/journal/applsciAppl. Sci. 2018, 8, 2679 2 of 6where bd represents the scattering due to density fluctuation, and bc the scattering due to fluctuation ofmixing ratio (concentration). Following Zhang and Hu [9],bd =8π3λ4(ρ∂n2∂ρ)2TkTβTh(δ), (2)and following Zhang et al. [11]bc =8π3λ4NA(∂n2∂S)2 MwρS−∂ ln aw/∂Sh(δ), (3)where, respectively, λ, k (=1.38064852 × 10−23 m2·kg·s−2·K−1), and NA (=6.022 × 1023 mol−1) are thewavelength of light, the Boltzmann constant, and Avogadro’s number; ρ, n, T, βT, S, and δ are thedensity, the absolute refractive index, the absolute temperature, the isothermal compressibility, the massconcentration of salts, and the depolarization ratio of the seawater; and aw and Mw (=18.01528 g mol−1)are the activity and molecular weight of pure water. Also, h(δ) = (2 + δ)/(6 − 7δ).In Equation (1), bc vanishes for pure water, and the scattering of light is due entirely todensity fluctuation. Replacing the density derivative in Equation (2) with pressure derivative, i.e.,(ρ ∂n2∂ρ )T= 2nβT (∂n∂P )T , Equation (2) becomes the Einstein–Smoluchowski equationbd =32π3λ4n2βT(∂n∂P)2TkTh(δ) (4)which was used by Cohen and Eisenberg [6] and Buiteveld et al. [7] in evaluating the temperaturedependence of scattering by pure water. Historically, Equation (4) was often used becausethe isothermal piezo-optic coefficient (∂n/∂P)T was relatively easier to measure, even thoughthe uncertainty was high as compared to n(T), n(λ), or n(S) [16]. However, recent theoreticaldevelopment [17] has greatly improved our knowledge in (ρ∂n/∂ρ)T . This, together with thedevelopment of Equation (3) to explicitly account for the effect of salinity on scattering [11], hasadvanced our capability for modeling scattering by seawater [9–11], and our confidence in usingEquations (1)–(3) to evaluate its temperature effect. The formulae used in the equations to estimaten, ρ, βT, and aw can be found in Zhang and Hu [9] and Zhang et al. [11], and the Matlab code forthe model can be accessed at https://goo.gl/jKAZgT. Light scattering by seawater is a function ofsalinity, temperature, and pressure. In this study, we focus on the temperature and salinity ranges of0–60 ◦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 valueof δ through two contrasting effects: isotropic ions would decrease δ; whereas their electrostatic fieldwould increase anisotropy, and hence the value of δ [18,19]. Both effects have been observed in puresalt solutions: δ for KNO3 solution increases and δ for KCl solution decreases, with their respectiveconcentrations [20]. To the best of our knowledge, however, no studies have been reported on how theδ of seawater would vary with salinity. For this study, we assumed a constant value of 0.039 for thedepolarization ratio δ for pure water [21] and for seawater [8,9,22,23].3. Results and DiscussionLight scattering by pure water at 436 and 546 nm was estimated using Equation (2) fortemperatures 0–60 ◦C, and the values normalized to the scattering at 25 ◦C were compared with themeasurements by Cohen and Eisenberg [6] in Figure 1. Between the two wavelengths, the temperaturevariations of the scattering are almost identical, showing a minimum scattering at 24.7 ◦C ± 0.2%.The scattering increases by 4.3% towards 0 ◦C and increases by 4.7% towards 60 ◦C at both wavelengths.The root mean square difference between our model and the measurements by Cohen and Eisenberg [6]is approximately 1.3% at both wavelengths. The refractive index model [24] used in Equations (2)Appl. Sci. 2018, 8, 2679 3 of 6and (3) were developed using the Austin and Halikas [16] measurements, which had a temperatureprecision of 0.1 ◦C. Also, the Cohen and Eisenberg [6] data we used for comparison in Figure 1 hada temperature precision of 0.1 ◦C as well. Therefore, we report the temperature in this study ata precision of 0.1 ◦C. We denote the temperature at which the scattering reaches the minimum asTmin hereafter. The predicted values of Tmin are close to the value of 22 ◦C measured by Cohen andEidenberg [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 inmodeling (∂n/∂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 tonumerically approximate a derivative, such as ∂n/∂P, as a ratio of measured values is very sensitive tothe uncertainties in the measurements of n(P). In addition, Buiteveld, et al. [7] derived the temperaturedependency of (∂n/∂P)T by fitting the measurements [25] between 5 and 35◦C, which also explainsthe relatively large deviation as shown in Figure 1 when extrapolating their model beyond 35 ◦C.Figure 1. The temperature variations of light scattering by pure water, calculated using the Zhang andHu [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 byCohen and Eisenberg [6]. Note that the normalized variations estimated by the Zhang and Hu modeloverlap with each other at the two wavelengths.Several bulk properties of pure water needed to estimate the scattering coefficient behave“anomalously”: density has the maximum near 4 ◦C [3]; isothermal compressibility has the minimumnear 46 ◦C [4]; and the refractive index has the maximum near 0 ◦C [5]. Also, less apparent butindirectly relevant is that (∂n/∂P)T , as in Equation (4), has its minimum near 50◦C [5]. Clearly,anomalous light scattering by pure water results from the combination of all of these anomalousproperties, as well as its direct proportionality with the temperature (Equation (2) or (4)). Even thoughscattering by pure water varies strongly with wavelength, with a spectral slope of −4.28 [9], theanomalous temperature behavior of scattering varies little with wavelength (Figure 1).The scattering coefficient at 546 nm as a function of temperature for different salinities is shownin Figure 2a for bd (due to density fluctuation) and Figure 2b for bc (due to concentration fluctuation).Both bd and bc vary with temperature in the same anomalous way, all exhibiting a minimum. Also,both Tmin for bd and Tmin for bc change with salinity—however, with differing patterns. Tmin for bddecreases about 20% from 24.6 ◦C to 19.1 ◦C for salinity varying from 0 to 40 psu, whereas over thesame salinity range Tmin for bc increases slightly by ~3%, from 32.2 ◦C to 33.2 ◦C. In terms of absolutemagnitude, bd is about 2–10 times greater than bc (Figure 2a), but in terms of change with respect tosalinity, bc is about 10 times greater than bd (Figure 2b). As a result, the change of Tmin for the totalAppl. Sci. 2018, 8, 2679 4 of 6scattering coefficient, b is dominated by bc, and increases from 24.6 ◦C to 27.5 ◦C for S from 0–40 psu(Figure 3). It is well known that Tmax for density [26] and Tmin for isothermal compressibility [27]decrease with the salinity. Here, we show for the first time that Tmin for light scattering increases withsalinity, which is largely due to the temperature variation of scattering introduced by sea salts. Table 1lists the variations of Tmin for bd, bc, and b at different salinities.Figure 2. Light scattering by pure seawater at 546 nm as a function of temperature and salinity. (a) bd,the scattering due to density fluctuation; and (b) bc, 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 psuincrements. The dotted line in each plot connects Tmin at different salinities.Figure 3. Total scattering coefficient by pure seawater at 546 nm as a function of temperature andsalinity. Lines of progressive colors from blue to red correspond to different salinities from 0 to 40 psuat 5 psu increments. The dotted line connects Tmin at different salinities.Table 1. Temperatures (Tmin in ◦C) at which the scattering of light at 546 nm by pure seawater dueto density fluctuations (bd), concentration fluctuations (bc), and their total (b) reach the minimum forvarious salinities (S).S (psu) 0 5 10 15 20 25 30 35 40bd (m−1) 24.6 24.0 23.4 22.7 22.0 21.2 20.5 19.8 19.1bc (m−1) 32.2 32.3 32.5 32.7 32.8 33.0 33.1 33.2b (m−1) 24.6 25.3 25.9 26.3 26.6 26.9 27.2 27.3 27.5Appl. Sci. 2018, 8, 2679 5 of 6In conclusion, using the latest scattering models for water and seawater, we find that waterexhibits an anomalous light scattering behavior, with a minimum occurring at 24.6 ◦C for pure water,and that this minimum increases with the salinity, reaching 27.5 ◦C at 40 psu. This temperature behaviorchanges little spectrally. Caution should be exercised when using the Buiteveld, et al. [7] model, whichpredicts a temperature behavior of scattering that is inconsistent with the measurements [6] or theresults of this study.Author Contributions: X.Z. and L.H. conceived and designed the experiments; X.Z. wrote the paper.Funding: National Aeronautics and Space Administration (NASA) (NNX13AN72G, NNX15AC85G) and NationalScience Foundation (NSF) (1355466, 1459168).Acknowledgments: We thank three anonymous reviewers and Dariusz Stramski for their comments, which haveimproved the manuscript.Conflicts of Interest: The authors declare no conflict of interest. The funding sponsors had no role in the designof the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; and in thedecision to publish the results.References1. Brovchenko, I.; Oleinikova, A. Multiple Phases of Liquid Water. ChemPhysChem 2008, 9, 2660–2675. 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Anomalous Light Scattering by Pure Seawater

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Anomalous Light Scattering by Pure Seawater

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