## 3 Results and Discussion  
Light scattering by pure water at 436 and 546 nm was estimated using Equation (2) for temperatures 0-60 \({}^{\circ}\)C, and the values normalized to the scattering at 25 \({}^{\circ}\)C were compared with the measurements by [PERSON] and [PERSON] [6] in Figure 1. Between the two wavelengths, the temperature variations of the scattering are almost identical, showing a minimum scattering at 24.7 \({}^{\circ}\)C \(\pm\) 0.2%. The scattering increases by 4.3% towards 0 \({}^{\circ}\)C and increases by 4.7% towards 60 \({}^{\circ}\)C at both wavelengths. The root mean square difference between our model and the measurements by [PERSON] and [PERSON] [6] is approximately 1.3% at both wavelengths. The refractive index model [24] used in Equations (2)and (3) were developed using the Austin and Halikas [16] measurements, which had a temperature precision of 0.1 \({}^{\circ}\)C. Also, the [PERSON] and [PERSON] [6] data we used for comparison in Figure 1 had a temperature precision of 0.1 \({}^{\circ}\)C as well. Therefore, we report the temperature in this study at a precision of 0.1 \({}^{\circ}\)C. We denote the temperature at which the scattering reaches the minimum as \(T_{min}\) hereafter. The predicted values of \(T_{min}\) are close to the value of 22 \({}^{\circ}\)C measured by [PERSON] and [PERSON] [6], but differ significantly in both value and trend from the [PERSON], et al. [7] model, which predicts a maximum near 15 \({}^{\circ}\)C. We believe the difference is largely due to the uncertainty in modeling \(\left(\partial n/\partial P\right)_{T}\) in Equation (4) that was used by [PERSON], et al. [7]. [PERSON] and [PERSON] [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 \(n(T)\), \(n(\lambda)\), 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, [PERSON], et al. [7] derived the temperature dependency of \(\left(\partial n/\partial P\right)_{T}\) by fitting the measurements [25] between 5 and 35 \({}^{\circ}\)C, which also explains the relatively large deviation as shown in Figure 1 when extrapolating their model beyond 35 \({}^{\circ}\)C.  
Several bulk properties of pure water needed to estimate the scattering coefficient behave \"anomalously\": density has the maximum near 4 \({}^{\circ}\)C [3]; isothermal compressibility has the minimum near 46 \({}^{\circ}\)C [4]; and the refractive index has the maximum near 0 \({}^{\circ}\)C [5]. Also, less apparent but indirectly relevant is that \(\left(\partial n/\partial P\right)_{T}\), as in Equation (4), has its minimum near 50 \({}^{\circ}\)C [5]. Clearly, anomalous light scattering by pure water results from the combination of all of these anomalous properties, as well as its direct proportionality with the temperature (Equation (2) or (4)). Even though scattering by pure water varies strongly with wavelength, with a spectral slope of \(-\)4.28 [9], the anomalous 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 shown in Figure 2a for \(b_{d}\) (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.