The spectral absorption coefficient of pure water［a_w，cm^-1］is a basic inherent optical property（IOP）^［1］，which characterizes the capacity of pure water to absorb light. It plays an important role in regulating the propagation of solar radiation in aquatic environment as well as heating of the upper water column，which is also a critical optical property applied in the calibration of in situ absorption sensors^［2-3］ and utilized in the “black” pixel assumption in atmosphere correction^［4］.

Many studies in the past have shown that the a_w has two distinct characteristics. On the one hand，the values of a_w vary enormously from UV-visible to near-infrared，spanning several orders of magnitude^［5-6］. On the other hand，due to difficulties in the preparation of “pure” water and in meeting the high sensitivity requirement of instrument to measure this optical property，there are also large variations of reported a_w values in the literature^［7-11］, and even from the same laboratory^［14-15］.

Further，it has also been indicated that the values of a_w depend on environmental influences，such as temperature（T）and salinity^[14-15]，but the reported dependence on temperature in the literature also varies. For instance，for wavelengths in the 350-500 nm range，Pegau et al.^［16］ found that a_w increases with T，while Röttgers et al.^［14］ found it slightly decreases with T. Recently，using ~20 years of satellite data measured at the ocean gyres，Wei et al.^［5］ found that the impact of temperature on a_w in the blue bands is consistent with that reported in Röttgers et al.^［14］. For the temperature dependence of a_w in the near-infrared（NIR）domain，Röttgers et al.^［14］ indicated spectrally opposite impacts（see Fig. 1），where a_w increased with T between 740 nm and 835 nm，but decreased with T between 795 nm and 890 nm. However，for such spectral behaviors，there are no independent，out-of-laboratory measurements，to verify the results.

Laboratory measurement of a_w is not an easy task^{［12，14］}. It requires very careful preparation of the sample - “pure” water^［17-18］，as well as sensitive and well calibrated instrumentation^［13］. In particular，when the objective is to study the impact of T on a_w，the impact of T on the measurement system has to be shielded off also，and otherwise artifacts could be introduced to the impact of T on a_w，which could be an important source of the different temperature dependences reported in the literature.

In this study，to avoid the above-mentioned difficulties in laboratory measurements，we use remote-sensing reflectance [R_rs(λ)，sr^-1］of highly turbid waters in the NIR to analyze the response of a_w to different temperatures. This is based on that R_rs is in general a function of b_b/（a+b_b），where b_b is the total backscattering coefficient and a is the total absorption coefficient. For the NIR domain，the absorption coefficient of gelbstoff can be ignored，and a can be expressed as the following after considering T-dependent a_w，

where $T_{\mathrm{0}}$ is the reference temperature（set as 20 ℃），Ψ_T is the temperature correction coefficient of a_w，and a_pis the absorption coefficient of particulates. Since the scattering contribution from pure water can be ignored for turbid waters，R_rs in the NIR can be approximated as^［19-20］

where b_bp is the backscattering coefficient of suspended particles，while G is the model coefficient，which in the first order approximates 0.05 sr^-1. In the NIR domain，the spectral shapes of both a_p and b_bp are flat and do not show spectrally selective temperature dependences. Thus if the dependence of a_w in NIR at difference wavelengths is opposite，we should expect to see a twist of R_rs spectral shapes in the NIR（740-850 nm here，more specifically）.

To analyze this response of a_w on temperature，we thus carried out controlled experiments to measure hyperspectral R_rs of very turbid waters at different temperatures. A high turbidity is required to obtain adequate R_rs measurements in the NIR domain，where the values of a_w are very high^［21］，and thus it is required to have high b_bp（which is driven by sediments or turbidity）to ensure adequate R_rs signal in the NIR. The following of this article then describes the experimental settings and the results obtained.

To evaluate the impact of temperature on a_w in the NIR（740-850 nm）domain，we designed an outdoor experimental system to measure R_rsof highly turbid waters under controlled temperature. It includes a large black customized tank（see Fig. 2）with a height of 0.6 m and a diameter of 2.2 m to contain turbid waters. This tank was placed on an empty area on the campus of Xiamen University in China，where there were no objects in the nearby to block the radiation from the sun and sky. Water from a nearby lake was used to fill the tank，and a large amount of fine sediments were added to obtain highly turbid water. Gentle stirring of this water-sediment mixture was carried out to keep it well mixed and that the sediments not sunk quickly.

The temperature of this water-sediment mixture was adjusted by adding a large number of crushed ice cubes and heating rods，which resulted in a temperature range of 7 to 51 ℃. The temperature of the water body was measured simultaneously from five different spots near the surface when radiometric measurements were taken，where the temperature resolution was 0.1 ℃，which is sufficient for this study. An average of the temperature readings from the five spots was used to represent the temperature for each set of radiometric measurements.

The experiments were carried out on 4 December^{and 13 December，2021 between 10：00 and 14：00，under cloudless blue-sky day and low wind. The impacts of the tank wall and tank bottom on the water-leaving radiance at the center of this tank are negligible as the Secchi disk depth is ∼0.15 m after adding high loads of sediments into such lake waters.}

To obtain R_rs in the NIR，the spectrometer（SE SR1901）of Spectral Evolution（USA）was used to collect the required radiance. SE SR1901 has a wavelength range of 280-1900 nm，with a spectral resolution of ~2 nm and a field of view of 4°. The spectrometer has two probes，one is with a cosine collector used for measuring downwelling irradiance，the other is used for measuring radiance，and both are factory calibrated where their equivalent radiation noises are orders lower than the radiance to be measured in this study. In order to avoid potential mismatch in radiometric and spectral calibrations between the two probes，we just used the probe for radiance，and the downwelling irradiance was calculated from measuring the radiance reflected from a standard gray card，which has a reflectance of 20%.

For such controlled environment，we took the AWA^［22-24］ to measure the total upwelling radiance（L_t）and the sky radiance（L_sky）in the reciprocal angle of L_t for the determination of water-leaving radiance（L_w）that is required for the calculation of R_rs. The angular geometry^［22］ for the measurement of L_t is 40° from nadir with an azimuth angle of 135° away from the sun. The radiance leaving a standard gray card（L_plaque）was measured using the same spectrometer. From these measurements，R_rs was calculated as follows^［25］：

where ρ is the reflectance（0.2）of the gray card，F is the Fresnel reflectance of the air-sea surface and takes a value of 0.023 because we restrict the measurements to cloudless and calm water conditions. Δ reflects a residual correction of surface-reflected radiance that might not be completely corrected from the subtraction of FL_sky，and is determined by setting the average value of R_rs（1600-1650 nm）to 0 based on Lee et al.^［6］，since SE SR1901 covers wavelength up to 1980 nm.

We first added a large amount of crushed ice to the turbidity water. Gentle stirring was carried out to make the ice melted and the water well mixed. After no floating ice visible on the water surface，we recorded the temperature and measured L_t，L_sky，and L_plaque in turn via AWA. Each property was measured 10 times to ensure stable and reliable data. After that，the water was gradually warmed，and generally it took ~40 minutes for each increase of 10 ℃. The temperature range of liquid water in the nature environment is about -2-30 ℃，but we expand the higher end to 51 ℃ in order to more clearly observe the impact of temperature on a_w. Finally，we took radiometric measurements at 14 different temperatures，which were 7，10，12，15，17，20，25，27，29，32，37，42，47，and 51 ℃. For each temperature scale，it took approximately 2 minutes to complete the measurement cycle，where the ambient light field could be considered stable and the variation of water temperature was within ~0.5 ℃，and thus it is appropriate to consider these measurements were completed under the “same” environmental conditions and the “same” temperature.

In addition，we also collected water samples from the surface to measure the IOPs of the water-sediment mixture，which include the absorption coefficients of suspended particles（a_p）and gelbstoff（a_g）that corresponding to each set of R_rsmeasurement at different temperatures. The absorption coefficients of the water samples were all measured with a dual-beam PE Lambda 950 spectrophotometer equipped with an integrating sphere（150 mm in diameter）in the laboratory. The spectrum of a_p was measured by the transmittance-reflectance（T-R）method^［26］ after the water sample was filtered by GF/F filters for 30 mL following the filter-pad technique^［27］ and a_g spectrum was measured according to the method from Bricaud et al.^［28］.

The resulted R_rs spectra at different temperatures obtained on 4 December，2021 are presented in Fig. 3（a），where the lowest temperature was 7 ℃ and the highest temperature was 29 ℃，while Fig. 3（b）shows R_rs spectra obtained on 13 December，2021，with temperature varied from 17 ℃ to 51 ℃. Overall，the values（the averaged coefficient of variation is less than 2%）of the measured R_rs are in a range of 0.005-0.03 sr^-1 for the spectral window of 700-900 nm，which are similar to those of high-sediment-load waters of the Changjiang River estuary^［6］，so do the spectral shapes of these measured R_rs. These characteristics indicate that the obtained R_rs spectra indeed are those of high sediment waters. Note that while gentle stirring of the water-sediment mixture was carried out for each set of measurements，it cannot guarantee it is the same kind of water-sediment mixture for each radiometric measurement，thus not surprise to observe variations in the R_rs values. This is also evidenced by the absorption spectra of the particulates（see Fig. 4）obtained from the water samples，where a_p（700-900 nm）changed a lot for water samples collected under different temperature. However，as presented and discussed below，the key is the spectral curvature of R_rs（λ）in the 700-900 nm range，and thus the minor variations of R_rs（λ）values are acceptable for this study.

To highlight the variation of R_rs spectral shape in the NIR，all R_rs spectra under different T are normalized to R_rs（770），represented as R_{rs_Nor}（λ）：

The reason to select 770 nm as the reference point is that a_w（770）is insensitive to T（see Fig. 1）^［1，17］. The resulted R_{rs_Nor}（NIR）spectra are presented in Fig. 5. Because a_w（740）［and a_w（835）］increases with T and a_w（795）decreases with T，we should expect a twist of R_{rs_Nor} between 740 nm and 795 nm，which is clearly shown in Fig. 5，where R_{rs_Nor}（740）［and R_{rs_Nor}（835）］decreases with the increase of T，but the opposite is observed for R_{rs_Nor}（795）. Further，there is another “standing” point at ~820 nm where R_{rs_Nor}（820）is found nearly insensitive to T，which is consistent with Ψ_T（820）as 0^{［14，17］}.

The opposite responses of R_rs（λ₁）and R_rs（λ₂）to the change of T were further quantitatively analyzed by the relative difference（$D_{R_{\mathrm{r}\mathrm{s}}}$）between R_rs（λ₁）and R_rs（λ₂），calculated as：

For comparison，we also calculated the relative difference between a_w（λ₁）and a_w（λ₂）（${D_a}_{\mathrm{w}}$）for these temperatures：

where the values of a_w（λ_i，T₀）（i=1，2）were taken from Kou et al.^［21］ for 725-900 nm，while values of Ψ_T were taken from Rottgers et al.^［14］. Note that this relative difference is a measure of the spectral curvature of R_rs and a_w，respectively.

Fig. 6（a）shows the changes of $D_{R_{\mathrm{r}\mathrm{s}}}$ and ${D_a}_{\mathrm{w}}$（λ₁ as 740 nm and λ₂ as 795 nm）for T in a range of 7-51 ℃. For this temperature range，${D_a}_{\mathrm{w}}$（740∶795）increased from ~0.03 to 0.20，this twist of a_w shape is expected based on Eq. 1 and the values of Rottgers et al.^［14］. On the other hand，$D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）decreased from ~0 to -0.09，indicating a relatively narrower change of $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）compared to ${D_a}_{\mathrm{w}}$（740∶795）. This reduced range of $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）is due to the impact of a_p（see Eq. 1），which has a high value for the water-sediment mixture of this study even at NIR bands（see Fig. 4）. Although the spectral shape of a_p does not change with T，because R_rs is a measure of the total absorption，thus the high a_p value dampens the change of $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）.

The opposite relationships with T for ${D_a}_{\mathrm{w}}$（740∶795）and $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）basically reflect that R_rs is inversely related to the absorption coefficient（see Eq. 2）. To highlight the change of $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）due to the change of a_w with T，Fig. 6（b）shows a scatterplot between $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）and ${D_a}_{\mathrm{w}}$（740∶795），where the correlation coefficient r between the two is -0.98，which highlights the significant cause and effect relationship between R_rs and a_w.

Similar results were found for $D_{R_{\mathrm{r}\mathrm{s}}}$ and ${D_a}_{\mathrm{w}}$ of the wavelength pair 795 nm and 835 nm，but this time ${D_a}_{\mathrm{w}}$ decreases with temperature，and thus $D_{R_{\mathrm{r}\mathrm{s}}}$ increases with temperature［see Fig. 7（a）］. As Fig. 6（b），Fig. 7（b）shows the scatterplot between ${D_a}_{\mathrm{w}}$（795∶835）and $D_{R_{\mathrm{r}\mathrm{s}}}$（795∶835），with an r value as -0.88，also very significant. The reason for this slightly lower r value compared to the correlation between ${D_a}_{\mathrm{w}}$（740∶795）and $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）is not clear yet，likely due to sharp changes of R_rs for wavelengths around 835 nm（see Fig. 3），and thus a resolution of the sensor could impact the results. Also，R_rs（835）is much lower than R_rs（795），and a slight error in the measurement of R_rs will thus impact more on$D_{R_{\mathrm{r}\mathrm{s}}}$（795∶835）. Nevertheless，the strong correlation（0.88 and higher）between the $D_{R_{\mathrm{r}\mathrm{s}}}$ and ${D_a}_{\mathrm{w}}$ provides a clear support about the wavelength dependence of a_w obtained by Rottgers et al.^［14］ for these bands.

Because R_rs is also related to b_bp and a_p（see Eq. 2），some changes of $D_{R_{\mathrm{r}\mathrm{s}}}$ could be a result of the changes of b_bp and/or a_p. To evaluate these potentials，the change of $D_{R_{\mathrm{r}\mathrm{s}}}$caused by changes of a_p and b_bp are shown in Fig. 8，where the value of a_w is kept as that at 20 ℃. For the wide changes of a_p［（a_p（740）in a range of ~0.5-1.5 m^-1］and b_bp［b_bp（555）in a range of 0.1-1.0 m^-1］，it is found that $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）is in a range of -0.075 to -0.069，a range significantly narrower than the change of $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）under different temperatures（see Fig. 8）. Thus it is safe to conclude that the changes of $D_{R_{\mathrm{r}\mathrm{s}}}$（740∶795）［and $D_{R_{\mathrm{r}\mathrm{s}}}$（795∶835）］measured for different temperatures were driven by changes of ${D_a}_{\mathrm{w}}$.

From the measured R_rs of highly turbid waters under different temperature，it is clear that the change of spectral curvature of R_rs in the 740-850 nm range is driven by the spectrally varying change of a_w at different temperatures. More importantly，this change in R_rs shape is consistent with that predicted by the latest laboratory measurements of Rottgers et al.^［14］. Therefore，this experiment and results provide an independent evaluation and confirmation of the spectrally opposite impact of temperature on a_w，which further provide confidence on using the Ψ_T，at least in the 740-850 nm range of Rottgers et al.^［14］，in field measurements and/or satellite ocean color data processing. However，because the a_w values for wavelengths longer than 900 nm are extremely high，although the Ψ_T values are even higher for some wavelengths longer than 900 nm（Rottgers et al.^［14］），our system may not be sensitive enough to measure the change of R_rs shape for those longer wavelengths，and thus the Ψ_T values of these bands still wait to be confirmed.