Impact of Temperature on Absorption Coefficient of Pure Seawater in the Blue Wavelengths Inferred from Satellite and In Situ Measurements

State Key Laboratory of Marine Environmental Science, College of Ocean and Earth Sciences, Xiamen University, Xiamen 361102, China Research and Development Center for Ocean Observation Technologies, Xiamen University, Xiamen 361102, China School for the Environment, University of Massachusetts Boston, Boston, MA 02125, USA College of Earth, Ocean & Atmospheric Sciences, Oregon State University, Corvallis, OR 97331, USA


Introduction
The absorption coefficient of "pure" fresh water (a fw ðλÞ, in m -1 ) and "pure" seawater (a sw ðλÞ) is a basic inherent optical property (IOP) [1]; together with the incident radiation spectrum, scattering, and the optical characteristics of other constituents, they determine the apparent color of water [2]. It is thus a fundamental requirement to know the values of a fw ðλÞ and a sw ðλÞ and how (or if) they change with environmental conditions, such as temperature and salinity. To meet this desire, there is a long history in estimating a fw ðλÞ and a sw ðλÞ (Fewell and von Trojan [3], and references therein), with a fw ðλÞ values in the~370-700 nm determined by Pope and Fry [4] in laboratory measurements adopted as the "standard" by the ocean color community in the past two decades. Recently, Mason et al. [5] updated a fw ðλÞ using an improved integrating cavity and found that a fw ðλÞ values are significantly lower (by a factor of up to 5, see Figure 11 in Mason et al. [5]) than those reported in Pope and Fry [4] for wavelengths ranging from 250 to 500 nm. In addition, the values in the UV-blue domain (350-420 nm) of Mason et al. [5] are significantly lower than those reported in Lee et al. [6], with the latter considered to represent the absorption coefficient of "pure" seawater.
Further, since there are strong variations of temperature (T, in°C) in the aquatic environment, there has been a long history of interest in how (if) a fw ðλÞ and a sw ðλÞ change with T, with the first reported estimation made by Wild in 1868 (cited in Trabjerg and Hojerslev [7]). In the recent decades, and with modern instrumentation, Trabjerg and Hojerslev [7] found that a fw ðλÞ and a sw ðλÞ decrease with T. In contrast, Pegau et al. [8] obtained an increase effect of T on a sw ðλÞ, while recently both Sullivan et al. [9] and Röttgers et al. [10] indicated that T has a negligible impact on a fw ðλÞ. Note that all these reports were based on laboratory measurements with prepared "pure" water or artificial seawater and using tubes or integrating spheres with path lengths 25 cm tõ 100 cm. Because a fw ðλÞ and a sw ðλÞ values in the UV-blue domain are very low [5], change of light intensity passing through such a short tube is in the order of~10 -4 -10 -3 , which places a significant demand on the sensitivity and calibration of the sensors and systems [10], in addition to the preparation of "pure" fresh water or "pure" seawater. Such extremely small changes in light intensity, as well as the challenge to calibrate the measurement system under different temperature, might be the main reasons for the discrepancies on the relationship between a fw or a sw ðλÞ and T. As indicated in Sullivan et al. [9], the uncertainty of such measurements is around 0.001 m -1 , corresponding to approximately 45% of the a fw ð400Þ value reported in Mason et al. [5].
In this study, rather than estimating a sw ðλÞ in a laboratory setting, we took an approach of analyzing the relationship between T and the total absorption coefficient (a) at 412 nm and 443 nm obtained from~18 years of ocean color satellites and combining field measurements of chlorophyll concentration (Chl, in mg m -3 ), phytoplankton absorption coefficient (a ph , in m -1 ), and sea surface temperature (represented as T in this article). Specifically, for T in local summer months varying between~19 and 27°C and stable Chl concentration, we calculated the regression slope between að 412Þ and að443Þ and T and found that they are not different than 0 (slight negative), contrasting with the results about a sw ðλÞ reported in Trabjerg and Hojerslev [7] and Pegau et al. [8]. The results are rather similar to those of Sullivan et al. [9] and Röttgers et al. [10], although they obtained the dependence of a fw ðλÞ. We selected these two wavelengths in our analysis because (1) they are the shortest blue wavelengths for MODIS (the Moderate Resolution Imaging Spectroradiometer) and (2) they display the strongest dependence of a sw ðλÞ on T [7,8] among the MODIS channels. Note that it is unclear if the temperature effect is the same on a fw ðλÞ and a sw ðλÞ, so comparisons and discussions are focused on the T effect of a sw ðλÞ as aðλÞ from MODIS is for natural oceanic waters.

Data
2.1. HOT Time Series. Data from the ongoing Hawaii Ocean Time-series program (HOT, https://hahana.soest.hawaii .edu/hot/) were employed to validate the temporal patterns of Chl and a ph obtained from MODIS. Station ALOHA, sampled by the HOT program at nearly monthly intervals since 1988, is located at 22°45′ N, 158°00′ W in the North Pacific Gyre (the white star symbol in Figure 1) and was established to provide systematic and repeated observations of the hydrography, chemistry, and biology of the water column. The data used in this study cover 81 pairs of Chl (by fluorometric method) and T for water at 2.5-5 m from the sea surface. In addition, a ph at 5 m and 25 m were used to represent surface values of the phytoplankton absorption coefficient. Details of the cruises and measurement methods can be found in Letelier et al. [11].

MODIS Time Series
. MODIS-Aqua globally mapped 8day composite of remote-sensing reflectance (R rs ðλÞ, in sr -1 ) with a 4 km resolution, for the period of July 2002 to July 2020, processed with the most recent updates in calibration and algorithms (2018 reprocessed version), was obtained from the NASA Ocean Biology Processing Group (OBPG, http://oceancolor.gsfc.nasa.gov/). The center wavelengths of these R rs ðλÞ are 412, 443, 488, 547, and 667 nm. The concurrent MODIS-Aqua globally mapped 8-day composite of T product (2019 reprocessed version) with the same resolution was also downloaded from the OBPG website. Further, data from three areas are utilized for this effort, which are HOT, center of the South Pacific Gyre (SPG), and the entire SPG.  Journal of Remote Sensing 2.2.1. HOT. In order to obtain a statistically significant number of points having concurrent MODIS ocean color and T measurements, the data within a 10 km distance of HOT are extracted from the downloaded global MODIS data. To minimize the impact of random spikes resulting from satellite measurements and processing, for each 8 days and each band, the R rs ðλÞ mode value was calculated based on all of the R rs ðλÞ values within the 10 km distance of HOT. This mode R rs ðλÞ value was then used to represent the property of HOT for that band. The same processing scheme was applied to obtain the T data, and a time series (with a temporal resolution of 8 days) over 18 years for both R rs ðλÞ and T was assembled.

2.2.2.
Center of the South Pacific Gyre. Similarly as HOT, the data from the "center" of the South Pacific Gyre (cSPG), which is defined as 27-32°S, 115-120°W (the white box in Figure 1) was employed to evaluate the relationships between að412, 443Þ and T. This region is located within the zone of the "clearest" natural waters [12], where a sw ðλÞ play the largest role at the blue wavelengths (can account for up to~50% of að412Þ) compared to other natural waters. For this small box, the mode R rs ðλÞ and T are produced following the same procedure described above.

Entire South Pacific
Gyre. To avoid any coincidental observations that might be specific to cSPG, we expanded the analysis to the entire SPG (the red box in Figure 1) in order to further examine the impact of T on a sw ðλÞ. To emphasize the contribution from a sw ðλÞ, the analyses are limited to pixels where Chl is always less than 0.07 mg m -3 in the 18-year time series (i.e., from July 2002 to July 2020), where 0.07 mg m -3 is considered as a criterion for classifying oceanic gyre waters [13,14]. At the same time, we found that T has a seasonal variation of~10°C, sufficient to cause detectable change in a sw ð412Þ and a sw ð443Þ if the previously reported temperature dependence of a sw by Trabjerg and Hojerslev [7] and Pegau et al. [8] is real. For this larger area, the quality control of R rs ðλÞ and T at each pixel (4 km data) is based on the following criteria: R rs ðλÞ at the five bands (412, 443, 488, 547, and 667 nm) are positive and <0.05 sr -1 and the T value having qual sst ðquality flag of sea surface temperatureÞ ≤ 2, i.e., the bad and not processed T values were removed. Further, each pixel in this box is treated independently, i.e., no further spatial averaging.

Method to Obtain the Total Absorption Coefficient
3.1. Inversion of aðλÞ from R rs ðλÞ. Ideally, we should use field measured a sw ðλÞ or aðλÞ to analyze the impact of T. However, there are no such long-term data obtained in the oligotrophic ocean, and there are various levels of uncertainties from in situ measurements [15,16]; we thus used the longterm, high-quality MODIS R rs ðλÞ in the oligotrophic ocean to fill this void. Because the diffuse attenuation coefficient in the short blue wavelengths is around 0.02 m -1 for such oligotrophic waters [12,17], the penetration depth [18] can be as deep as~50 m for such waters. Thus, að412Þ and að443Þ can be considered measured equivalently with a "tube" as long as 50 m, greatly longer than the path length taken in lab measurement settings. As a result, the sensitivity of the absorption coefficient measurement is substantially improved. There are many semianalytical algorithms developed in the past decades for the inversion of aðλÞ from R rs ðλÞ [19], where most of them require biooptical models for the component absorption coefficients (e.g., a ph ) and to specify a sw ð λÞ in the process, thus preventing an independent analysis regarding the impact of T on a sw ðλÞ. The quasi-analytical algorithm (QAA) developed by Lee et al. [20] (the latest update version 6, http://www.ioccg.org/groups/Software_ OCA/QAA_v6_2014209.pdf), as described below, is used in this effort for two reasons. First, QAA does not need to model the component absorption coefficient in the inversion process, and second, it needs only the a sw ðλÞ value at one wavelength (547 nm in the present analysis). Therefore, QAA offers a feasible means to analyze the T effect on a sw ðλÞ in the shorter wavelengths. A brief description of QAA is provided below to highlight the concept and the key components.
Earlier studies [2,21] have shown that R rs ðλÞ can be expressed as where G (sr -1 ) is a model parameter. For each R rs , there are two unknowns: a and the total backscattering coefficient (b b , in m -1 ); thus, knowing a enables the calculation of b b or vice versa. For oligotrophic waters and R rs ðλÞ obtained from MODIS, að547Þ can be approximated as a sw ð547Þ; hence, b b ð547Þ can be calculated algebraically from known R rs ð547Þ and að547Þ. Further, the particle backscattering coefficient at 547 nm (b bp ð547Þ) is obtained from b b ð547Þ after subtracting b bw ð547Þ (the backscattering coefficient of pure seawater). The b bp ð547Þ is extended to the shorter wavelengths based on the power-law model of the particle backscattering coefficient [2].
with Y estimated empirically from [20] For oligotrophic waters, as R rs ð443Þ/R rs ð547Þ > 5, the Y value estimated by Equation (3) is effectively~2.0. Further, aðλÞ at 412 and 443 nm are calculated algebraically from R rs ðλÞ after b bp ðλÞ are derived following Equations (2)-(3) and b bw ðλÞ from Zhang et al. [22], with the results corresponding to að412Þ QAA and að443Þ QAA .
It is required to know the value of a sw ð547Þ for the above derivations, which we adopt from Pope and Fry [4] and Journal of Remote Sensing consider invariant for changing temperature and salinity [9,10]. In addition, it is required to know the backscattering coefficient of pure seawater (b bsw ðλÞ), with values from Zhang et al. [22] used here. Note that for T in a range of 15-30°C and salinity in a range of~33-34 PSU, the variation of b bsw ðλÞ is within~0.8%, which is negligible in the present study.
3.2. Estimation of Chl from R rs ðλÞ. As this study focuses on extremely oligotrophic waters, the band-difference algorithm in Hu et al. [23], which is more robust than the traditional band-ratio scheme for such waters, is employed for the estimation of Chl from ocean color. Specifically, a color index (CI) is defined as Because the MODIS green band is centered at 547 nm instead of 555 nm for SeaWiFS, MODIS R rs ð547Þ was converted to R rs ð555Þ by multiplying 0.93 [23]. Further, Chl is estimated from CI, 3.3. Modeling aðλÞ Based on Chl and T. The QAA shows a direct scheme to obtain aðλÞ from R rs ðλÞ. Another scheme, which is indirect and based on Chl, can also be utilized to obtain aðλÞ from R rs ðλÞ. The core assumption for this scheme is the "Case 1" concept where the variation in optical properties of such waters can be expressed using Chl [24][25][26][27][28]. Specifically, aðλÞ can be expressed as where a dg ðλÞ is the combined absorption by detrital particulate matter and gelbstoff and a pg ðλÞ = a ph ðλÞ + a dg ðλÞ. Further, a ph ðλÞ and a dg ðλÞ can be modeled as a * ph ðλÞ is the "Chl-specific" absorption coefficient, which can be modeled as a function of Chl [24,25].
with the wavelength-dependentAðλÞ and BðλÞparameters obtained from extensive measurements in oceanic waters [24]. For oceanic "Case 1" waters, a dg ð443Þ covary with Chl [25,29]; then, a relationship between a dg ð443Þ and a ph ð443Þ is set as A p value of 1.0 is used here [30]. S dg is the spectral slope for the gelbstoff absorption coefficient, and in this study, it is set as 0.014 nm -1 following Bricaud et al. [31].
Thus, for the given R rs ðλÞ and T, the total absorption coefficient (represented as aðλ, TÞ Chl ) of such "Case 1" waters could also be calculated after values of a sw ðλ, TÞ are provided, where the variation of a sw ðλÞ due to T could be characterized. Since the most recent temperature dependence of a sw was reported by Trabjerg and Hojerslev [7] and Pegau et al. [8], only their temperature relationships, respectively, were included in the comparisons. It is necessary to point out that, although there are various levels of uncertainties in the R rs to Chl and Chl to aðλÞ Chl , the role of Chl in this scheme for the total absorption coefficient is rather a "middleman." Fundamentally, it is an empirical system that allows us to estimate aðλÞ from R rs . In the empirical relationships developed between R rs and Chl as well as between Chl and a ph ðλÞ, the impact of T average is included, implicitly, in the empirical coefficients.

Temporal Patterns of Chl in Local
Summer. The temporal patterns of Chl at both HOT and cSPG obtained from MODIS are presented in Figure 2, along with Chl of HOT measured fluorometrically. The MODIS Chl is in a range of 0.04-0.16 mg m -3 at HOT, which is generally consistent with in situ Chl (0.03-0.18 mg m -3 ) during 2002-2019. Further, as would be expected, Chl decreased generally from March to May at HOT and from September to November at cSPG in response to nutrient supply and photoadaptation to higher light levels, a result of increased mean daily photon flux in the mixed layer, i.e., increased stratification and day length [11,13,32,33].
More importantly, for the summer months (July-September for HOT) where T varied in a range of 24.7-28.6°C at HOT, we observe that Chl concentrations derived from both MODIS and in situ are quite stable and consistent (see Figure 2(c)), which is in agreement with that presented in Winn et al. [33]. The slope in linear regression between Chl and T during these months is 0.0010 mg m -3°C -1 for MODIS Chl and 0.0008 mg m -3°C-1 for in situ Chl, and there is no significant difference between these slopes. These comparisons and evaluations suggest that the temporal patterns of MODIS Chl for such oligotrophic waters for the summer months are reasonable. In addition, in viewing an average Chl of 0.06 mg m -3 , the slope suggests negligible variation of Chl in the summer months (~7% change of Chl).
Comparisons between MODIS Chl and T at cSPG in December-February (austral summer) are shown in Figure 2(d). For T in a range of 19.6-27.0°C, the slope between Chl and T is nearly flat (1×10 -5 mg m -3°C-1 ), which also indicates that Chl remains constant in the summer months though T varies by~7.4°C.  Figure 3.
The að412Þ QAA and að443Þ QAA are in a range of~0.009-0.02 m -1 and~0.01-0.02 m -1 , respectively, which are consistent with those reported in Bricaud et al. [31]. The T value is in a range of 17.7-27.0°C with the difference between the climatological maximum summer and winter minimum values as~9°C.
There is a general, opposite relationship between the absorption coefficient and T (see Figure 4), with R 2 as 0.58 for 412 nm and 0.48 for 443 nm, respectively. The decrease of absorption with the increase of T is in general due to the decrease of Chl, a result of photoadaptation and stratification in the surface layer [11,13,33]. While the detailed temporal variations are important for the study of phytoplankton dynamics in the open ocean [13,34], they are out of the scope of this study, and we will focus on the relationship between aðλÞ and T in the following. In particular, as indicated in Figures 3(c) and 4, although Following the approach used to analyze the temperature patterns of Chl in local summer, a trend of aðλÞ versus T in December-February (southern summer) can be drawn and shown in Figure 5. It is found that for T in a range of 19.6-27°C, the slope between að412Þ QAA and að443Þ QAA and T is also nearly flat (slightly negative, −4 × 10 −5 m −1°C−1 ), i.e., there are no obvious increases or decreases of the total absorption coefficient for T increased by~7.4°C. For com-parison, these slopes, along with the T-dependent slopes of a sw reported in previous studies, are listed in Table 1. Note that, as indicated by Figure 2(d), there are no changes of Chl for these summer months; thus, by Equation (6), a pg are also expected to be stable; therefore, there should be a significant decrease (following Trabjerg and Hojerslev [7]) or an obvious increase (following Pegau et al. [8]) trend of a ð412Þ and að443Þ for the increase of T, as presented in Figure 5. In particular, the decrease of að412Þ is expected to be~56% following Trabjerg and Hojerslev  0:05 ± 0:3 * For data from field measurements in summer months; * * for data from MODIS in summer months. + The units of slope for Chl versus T and a (or a ph or a fw or a sw ) versus T are mg m -3°C-1 and m -1°C-1 , respectively. B1994, T1996, P1997, S2006, and R2014 represent the T-dependent slope reported in Buiteveld et al. [35], Trabjerg and Hojerslev [7], Pegau et al. [8], Sullivan et al. [9], and Röttgers et al. [10], respectively, where superscripts "fw" and "sw" represent fresh water and salt water. 7 Journal of Remote Sensing [7] (represented as aðλÞ Chl T− ), while the increase of að412Þ could be~26% following Pegau et al. [8] (represented as a ðλÞ Chl T+ ).
Can the stable að412Þ QAA and að443Þ QAA vs. T imply negligible impact of T on a sw ðλÞ, at least for T in a range of 19-27°C? In general, as shown by Equation (6), aðλÞ is a sum of a sw ðλÞ and a pg ðλÞ (i.e., a ph + a dg ). Thus, a stable a ðλÞ QAA could be a result of an increasing a sw ðλÞ with T which is compensated by a decreasing a pg ðλÞ, or a decreasing a sw ðλÞ with T is compensated by an increasing a pg ðλÞ. This begs the question on how a pg ðλÞ varies in these waters during the summer months.
We first examined the relationship between aðλÞ QAA and Chl for a given T, i.e., "fixed" a sw ðλÞ. As shown in Figures 6(a) and 6(b), for fixed T (T is in a range of 19.5-20.5°C and 20.5-21.5°C, respectively), it is found that a ðλÞ QAA highly covary with Chl (R 2 > 0:94) at cSPG. This is consistent with that found at HOT (see Figure 6(c)), where for T in a narrow range of 25-26°C (note that temperature at HOT is always higher than temperature at cSPG), a ð412Þ QAA covaries highly (R 2 = 0:77) with in situ measured Chl, with a reduced R 2 value due to uncertainties associated with field-measured Chl. These results suggested that indeed Chl is the main driver of the variation of aðλÞ QAA for such oligotrophic waters. In consequence, during the summer months, the observed constancy of Chl as a function of T (see Figures 2(b) and 2(d)) indicates that a pg ðλÞ also remains stable during this period and over this T range. This is further verified with the time series at HOT (see Figure 7), where field-measured a ph ð410Þ and a ph ð440Þ for the summer months are quite stable (the slope in linear regression between a ph ð410Þ and a ph ð440Þ and T is -1×10 -5 m -1°C-1 and -1×10 -4 m -1°C-1 , respectively). These analyses, from both field measurements and satellite observations, suggest that

4.3.
Characteristics of að412Þ QAA , að443Þ QAA , and T Time Series at SPG. We further extended the above analyses to the entire SPG, which is the regression between Chl or aðλÞ and T at each pixel in the SPG. The resulted occurrence frequency of these slopes is presented in Figure 8. Since the distribution of slope between að443Þ QAA and T derived from each pixel is almost the same as that between að412Þ QAA and T, we only present the results of að412Þ QAA and Chl. For these summer months, the slope of Chl versus T falls primarily (>91%) in the range of -0.0003 to +0.0006 mg m -3°C-1 and~73% in the range of ±0.0002 mg m -3°C-1 (see Figure 8(a)), which translates into the slope between a pg ðλÞ and T being in the order of 10 -5 m -1°C-1 when a pg ðλÞ is derived from Equations (7)- (10). The slope between a ð412Þ QAA and T is generally in the range of -0.0002 to +0.0001 m -1°C-1 with~93% in the order of 10 -5 m -1°C-1 (see Figure 8(b)). This slope, effectively flat, is significantly    Journal of Remote Sensing different from the -0.0009 m -1°C-1 reported in Trabjerg and Hojerslev [7] and the 0.0003 m -1°C-1 reported in Pegau et al. [8] for a sw ð412Þ. Note that the T difference (i.e., the difference of maximum and minimum of T for each pixel) for these months is in the range of 3.9-11.9°C, with 95% of T difference as 5-9°C (see Figure 8(c)), which are sufficient to cause detectable variations in a sw in the blue wavelengths based on Trabjerg and Hojerslev [7] and Pegau et al. [8]. Our results, obtained from measurements of natural oceanic waters, are similar to those recently reported in Sullivan et al. [9] and Röttgers et al. [10] (see Table 1), but the latter were from laboratory measurements and for a fw . With regard the challenges of taking precise measurements of a fw or a sw in a laboratory setting [5], these evaluations highlight the value of long-term ocean color satellite measurements in the oligotrophic ocean.

Discussion
5.1. Impact of Y on the Temporal Variation of að412Þ QAA and að443Þ QAA . Except for the measurement uncertainties associated with R rs ðλÞ, there are two sources of uncertainties for the analytical derivation of að412Þ QAA and að443Þ QAA via QAA. The first is the model (Equation (1)) to link R rs with a and b b , while the second is the determination of a Y value (Equation (2)). For uncertainty source 1, there are many models developed in the past [36,37]. While a different model will result in slightly different retrievals of aðλÞ QAA [38], here, the focus is on the temporal variation of aðλÞ, not the exact value of aðλÞ; thus, we do not expect that this choice of model for R rs will bring any significant impact on the temporal trend of aðλÞ as long as it is the same model used for all data. In particular, we focused on a temporal range of summertime when there are almost no visible changes of Chl (see Figure 2).
For uncertainty source 2, a spectral power value (Y) is required (Equation (2)) to calculate b bp ðλÞ from one wavelength to other wavelengths. Historically, researchers set Y value as 2.0 for open-ocean waters [20,39]. However, it is not known if a temperature-dependent Y will change the patterns. We thus carried out the following numerical experiments to evaluate the potential impact of temperature-dependent Y on að412Þ QAA and að443Þ QAA . For such a sensitivity analysis, we assumed that there could be a decrease or an increase trend of Y for the increase of T, which are expressed as Here, T r is a reference temperature which is set as 20°C; thus, Y is in a range of 1.5-2.5 for T in a range of 20-30°C under the Y T+ scheme, and 2.0-1.0 under Y T− scheme for the same T range. The resulted aðλÞ via QAA are represented as að412Þ QAA T+ and að443Þ QAA T− accordingly.
Following the approach used to analyze the trend of a ðλÞ QAA versus T in December-February, the trends of a ðλÞ QAA T+ and aðλÞ QAA T− versus T are shown in Figure 9. It is found that for these summer months, the slopes between að412Þ QAA T+ and að412Þ QAA T− and T are still nearly flat (the slope of að412Þ QAA T+ and að412Þ QAA T− is 4×10 -5 m -1°C -1 and -0.0001 m -1°C-1 , respectively). In addition, the slopes between að443Þ QAA T+ and að443Þ QAA T− and T are almost the same with those between að412Þ QAA T+ and a ð412Þ QAA T− and T. Thus, for T in a range of 19.6-27°C, although values of Y vary over a relatively wide range (Y T+ is~1.5-2.2 and Y T− is 2.0-1.3), they have a small influence on the relationship between að412Þ and að443Þ and T. This is because in these oligotrophic waters, b sw ð412Þ contributes over 50% of b b ð412Þ; thus, a change of Y has limited impact on the derived að412Þ for such waters [36]. Further, note that Y changes from 1.5 to 2.5 corresponding to changes in particle-size-class parameter from 4.5 to 5.5 (i.e., significantly more tiny particles) following Kostadinov et al. [40], a variation highly unlikely, especially under a situation where there are no obvious changes of chlorophyll concentration. Thus, 10 Journal of Remote Sensing these analyses indicate that the temporal trend between a ð412Þ and að443Þ and T obtained from MODIS for the summer months are highly reliable.

In Principle, What Is
Likely the Trend between a fw ðλÞ or a sw ðλÞ and Temperature in the Natural Environment? The discrepancies on the T trends of a fw or a sw in the blue wavelengths reported in the literature [7][8][9][10]35] beg the question of how a fw or a sw should change with T in the natural environment. We know that water has three phases of states: solid (ice), liquid, and gas (water vapor). Although the absorption coefficient of pure ice (a w−ice ) is still under debate, it appears that a w−ice is significantly higher than a fw [5,41,42], and a fw are significantly higher than that of water vapor. If a fw increases with T, values of a fw will be very high when water is approaching the boiling point. Since the absorption coefficient of water vapor is significantly lower, there must be an abrupt and significant drop of the absorption coefficient when water changes from liquid to water vapor. At the other end, if a fw increases with T, values of a fw will be very low when water is approaching ice; thus, there must be an abrupt and significant increase of the absorption coefficient when liquid water turns to ice water. In short, there will be no continuity of the absorption coefficient when water changes from ice to liquid to gas, if a fw increases with T.
The above considerations support a trend that a sw decreases with T [7], which is also supported by the slightly negative slopes between að412Þ and að443Þ and T found in this study (see Figures 5 and 8). This is consistent with the nature of water molecules that when T increases, the volume of water molecules expands, thus fewer number of water molecules per unit volume, although this change in volume could be very small, especially for T in the common range of the natural environment. On the other hand, a slope of -0.0009 m -1°C-1 reported in Trabjerg and Hojerslev [7] appears to be too steep, as a fw ð412Þ will become negative when T simply increases from 20°C to 23°C based on the latest a fw ðλÞ values presented in Mason et al. [5].

Impact of Salinity on the Absorption Coefficient of Pure Water
The a sw ðλÞ derived by Lee et al. [6] are considerably higher (higher by a factor of 2) than the a fw ðλÞ values recently reported in Mason et al. [5] for λ in the range of 350-420 nm but a bit lower than that of Mason et al. [5] for λ > 430 nm. This difference is not surprising because the waters considered in Lee et al. [6] are oceanic waters where the average salinity is about 35 PSU [43], with an average T similar to that in Mason et al. [5]. Therefore, the difference between the a sw ðλÞ values in Lee et al. [6] (a sw L15 ) and the a fw ðλÞ values in Mason et al. [5] (a fw M16 ) suggests an impact of salinity on the absorption coefficient of pure water. Assuming this impact is linearly related to salinity [10], then a slope of salinity can be calculated from the two independent determinations (represented as Ψ S−LM ) When Ψ s−LM values are compared with the salinity slopes reported in Pegau et al. [8] (represented as Ψ s−P ; see Figure 10), we find good agreement with Ψ s−P for λ in the range of~400-550 nm. In particular, these determinations show positive salinity slope at 410 nm and negative salinity slopes for λ longer than~430 nm, remarkable agreements from these independent determinations. But the Ψ s−P value is much higher than Ψ s−LM at 410 nm, which could be due to CDOM contamination in the artificial seawater solutions, or an over correction for CDOM contribution in the derivation of a sw ðλÞ in Lee et al. [6], which deserve further studies from a well-controlled experiment. On the other hand, these findings are different from that of Sullivan et al. [9] and Röttgers et al. [10], where no detectable salt effect on a fw ðλÞ was found. In view of the significant differences in a fw ðλÞ in the blue wavelengths reported between Pope and Fry [4] and Mason et al. [5], and that Röttgers et al. [10] indicated that the salinity slopes in their study are unreliable for wavelengths < 500 nm, it highlights the challenges to obtain accurate measurements of such properties in laboratory settings.

Conclusions
Based on field measured Chl, a ph , T and~18 years (from 2002 to 2020) of MODIS ocean color measurements in the oligotrophic oceans, we analyzed the relationships between að412Þ and að443Þ and T. We found that, for the summer months of the southern hemisphere (December-February) in the center of the South Pacific Gyre (SPG) where T varied from~19 to 27°C, the slope between að412Þ and að443Þ and T is nearly 0 (in the order of 10 -5 , slightly negative), which indicates stable values of a sw ðλÞ within this temperature range. Such a stable pattern is further confirmed when analyzing the entire SPG. Our results are similar to those reported in Sullivan et al. [9] and Röttgers et al. [10] regarding the impact of T on water's absorption coefficient, but the 11 Journal of Remote Sensing latter were obtained from laboratory measurements of prepared "pure" water. Further, the slight negative trend with T for að412Þ and að443Þ is consistent with the reduced number of water molecules per volume when T increases in a common natural environment, although such a change is very small. Thus, in principle, a sw ðλÞ in the blue wavelengths are decreasing with an increase of T, although the actual effect could be negligible for the purpose of retrieving ocean color products from remote-sensing observations.
Separately, based on previously reported a sw ðλÞ [6] and a fw ðλÞ [5], we calculated the salinity slope for λ in the range of~350-550 nm, with results in good agreement with that of Pegau et al. [8]. These results, from three independent determinations, do suggest an impact of salinity on a fw ðλÞ. As demonstrated in Yu et al. [44], for processing ocean color measurements in the oceanic waters, it is better to adopt a sw ðλÞ rather than a fw ðλÞ; otherwise, more uncertainties will be introduced in the retrieved a ph ðλÞ.
Note that the selection of the wavelengths in this study is constrained by the band configuration of the satellite sensor. After we obtain long-term hyperspectral R rs in the oligotrophic ocean, the above analysis can be extended to evaluate the effect of T on hyperspectral a sw ðλÞ. Separately, compared to the high demand of caution in sample preparations and sensors' calibrations in laboratory measurements of such properties, the long-term satellite data offer a unique and reliable data source to evaluate the impact of temperature on the "pure"seawater absorption coefficient, but the calibration of an ocean color satellite sensor does require a significant effort from the community.

Data Availability
The satellite and in situ data used to support the findings of this study are publicly available. MODIS-Aqua data can be downloaded from the NASA OBPG website (http:// oceancolor.gsfc.nasa.gov/), while field measurements of HOT can be found online at https://hahana.soest.hawaii.edu/hot/.