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Abstract
Inherent optical properties (IOPs) of typical ocean waters have been derived from a worldwide database of measured parameters. The optical quality of the world’s oceans can be described in terms of their Jerlov water type, ranging from the clearest Jerlov I to the most turbid Jerlov 9C. These Jerlov classifications are defined in terms of an apparent optical property known as the downwelling diffuse attenuation coefficient (${K_d}$). There is a need to relate these Jerlov water types to their IOPs, namely their absorption coefficient, $a$, and scattering coefficient, $b$. However, robust values of $a$ and $b$ for Jerlov water types have not previously existed. This study used the World-wide Ocean Optics Database to derive a series of experimentally measured $a$ and $b$ values for six Jerlov water types. Using data science techniques to group measurements in time and space, over 13.5 million data points were consolidated into 53 measured values for $a$ and $b$. Established models were subsequently applied to generate a complete table of absorption and scattering coefficients from 300 to 800 nm for Jerlov IB to Jerlov 5C. The analysis includes the influence of changes in the solar zenith angle and the scattering phase function. These data are recommended for use in applications where IOPs are required to describe Jerlov water types.
1. INTRODUCTION
Quantifying the optical quality of oceans and other water bodies has wide-ranging applications, including the monitoring of ecosystem stability [1], underwater imaging [2], optical communications [3], and remote sensing [4]. In the absence of precise optical quality data for specific locations, standard values of optical quality parameters permit the behavior of “typical” environments to be described and simulated in these and other contexts.
In 1951, Swedish oceanographer Jerlov proposed such a classification of ocean types based on their optical transparency [5]. The proposal was built upon experimental measurements across the world’s oceans, most notably from the 1947/1948 Albatross expedition [6]. Jerlov used a photometer with optical filters to measure the amount of light reaching different depths of the ocean across the visible spectrum. By comparing this downwelling irradiance at a given depth to the irradiance measured at the surface, the downwelling diffuse attenuation coefficient, ${K_d}$(${{\rm m}^{- 1}}$), was derived. These Jerlov classifications have evolved since they were first defined, and now constitute a series of five open ocean and five coastal water types, ranging from the clearest Jerlov I to the most turbid Jerlov 9C [7,8]. The characteristics of these 10 water types are summarized in Table 1, while Fig. 1 shows their ${K_d}$ spectral profiles.
Table 1. Summary of the Features of the Jerlov Water Types
Fig. 1. Downwelling diffuse attenuation coefficient, ${K_d}$(${{\rm m}^{- 1}}$), for each of the 10 Jerlov water types [8].
${K_d}$ is known as an apparent optical property (AOP), as it depends on the characteristics of the ocean water and the ambient light from the sun and the sky, as well as the sea state [9]. Many experimental investigations of ${K_d}$ have taken place across the world’s oceans [10–15], in some cases permitting the distribution of Jerlov water types to be mapped [8,16,17]. While the standard Jerlov values for ${K_d}$ can be used in the aforementioned applications, there are other optical parameters that can also be useful to describe different aspects of optical water quality.
Inherent optical properties (IOPs), in contrast to AOPs, only depend on the characteristics of the water itself [18,19]. The total beam attenuation coefficient, $c$(${{\rm m}^{- 1}}$), is one such IOP and is measured using a narrow collimated beam of light to determine the total loss of light across a defined path length. $c$ is the sum of two IOPs: the absorption coefficient, $a$(${{\rm m}^{- 1}}$), and the scattering coefficient, $b$(${{\rm m}^{- 1}}$) ($c = a + b$). $a$ represents the fraction of light absorbed by the water, primarily due to chlorophyll, colored dissolved organic matter (CDOM), and non-algal particulates, as well as the water molecules themselves. $b$ represents the fraction of light scattered by the water, primarily due to suspended particles and water molecules. Both $a$ and $b$ can be measured individually, again using a narrow, collimated light beam with an appropriate detection geometry.
Models of varying complexity exist [20–26] that can predict values for ${K_d}$, $a$, and $b$ based on the optical properties of pure water [21,27–32], together with the concentrations of the various pigments and particles within the ocean. Theoretical and empirical conversions exist between AOPs and IOPs [33–38], with the recent work of Solonenko and Mobley [38] being the most pertinent regarding IOPs for Jerlov water types.
Solonenko and Mobley presented equations for $a$ and $b$ across the visible waveband that were dependent on a set of five input parameters. Using a theoretical conversion from $a$ and $b$ to ${K_d}$, these input parameters were optimized to give the best match to each of the Jerlov water type ${K_d}$ values. The result was a table of $a$ and $b$ values across the visible waveband to accompany the ${K_d}$ values for each of the Jerlov water types. To the best of our knowledge, this was the first time such a comprehensive conversion had been published, and it provides a valuable resource for anyone interested in simulating “typical” ocean types. During the use of these data, however, the authors noticed some potential discrepancies between the derived values of ${K_d},a$, and $b$, and those published from various experimental studies (e.g., [39–42]). In some cases, it appeared that the values of Solonenko and Mobley predicted too little absorption and too much scatter.
The authors set out to analyze existing measured data for ${K_d}$, $a$, and $b$, in order to derive an experimentally validated set of IOPs that could be related to the Jerlov water types. A vast repository of such measured data exists in the World-wide Ocean Optics Database (WOOD), created in 1997 at Johns Hopkins University [43] and currently hosted by the NOAA National Centers for Environmental Information [44]. This database has already been used by Smart to derive empirical relationships between optical parameters [45] and by Neuner et al. to predict the link between ${K_d}$ and backscatter [46]. Derivation of IOPs for the Jerlov water types was not the aim of either of these research efforts, although Neuner et al. used machine learning to assign Jerlov water types to paired ${K_d}$ and $c$ data.
The basic principle of the present study was to use the WOOD data to match ${K_d}$ values to Jerlov water types, and then to identify corresponding $a$ and $b$ values that were recorded at the same time and location. This would allow measured $a$ and $b$ values to be directly related to Jerlov water types.
2. METHODS
A. Software Tools
A data analysis was conducted using the Python programming language version 3.9.4 running from the Spyder development environment version 5.0.1 on the Windows 10 operating system. The main Python libraries used were the pandas data analysis library version 1.2.4 [47,48] and the NumPy scientific computing library version 1.20.2 [49]. Some additional data manipulations took place in Microsoft Excel 2016. Map visualizations were generated using MATLAB version R2019b with other plots created using GraphPad Prism version 8.0.1.
B. Data Source
WOOD composes experimentally measured parameters from the world’s oceans, collated from hundreds of different cruises and research teams over many decades [44]. Forty-one individual parameters are available for download, including material concentrations (e.g., ammonium, chlorophyll, and nitrates) and optical properties (e.g., fluorescence, backscatter, and reflectance). Each of these parameters is contained within its own downloadable text file, with a line of data representing each discrete measurement (referred to as a “cast”). Each line of data has a standardized format, consisting of 25 columns that describe the source of the data (cruise and author information), measurement environment (location, date, and time), equipment used (instrument type and wavelength of the measurement), data information (accuracy and editing history), and other metadata. The measured data are held in two columns–one containing an array of depths (in meters) at which readings were taken and the other with a corresponding array of measured values at those depths.
For this study, the parameters of interest from WOOD are the downwelling diffuse attenuation coefficient (${K_d}$), absorption coefficient ($a$), scattering coefficient ($b$), and beam attenuation coefficient ($c$). The columns of interest from the downloaded files are the cruise ID number (identifying the cruise that measured the data), the latitude, longitude, date, and time of the cast, a code denoting the quality of the data, the wavelength of the measurements, the depths of measurements, and the measured values themselves. The raw files contain 141,039 casts (= lines of data) for ${K_d}$, 27,269 for $a$, 5,820 for $b$, and 57,149 for $c$. With each cast containing measurements at multiple depths, in total there are over 13.5 million measurements across the four files.
C. Cleaning the Data
The first task was to clean the data of unsuitable, erroneous, and unreliable entries. Values for $a$, $b$, and $c$ were all directly measured (predominantly using absorption meters or transmissometers), while 35% of ${K_d}$ values were directly measured, and the remainder were indirectly measured through conversion from measured pigment and chlorophyll concentrations using established relationships [24,50]. These indirectly measured ${K_d}$ values were removed from the dataset, as their derivations are linked to IOPs; therefore, their presence could bias the outcomes of this study. Subsequent data cleaning applied the same method to all four datasets. Building from the procedure of Neuner et al. [46], the metadata were used to filter out any incorrectly categorized data or data labeled as poor quality or with poor calibration. Entries with invalid or null values for date, time, or wavelength were also removed. Entries that only contained depths deeper than 10 m were removed from the datasets, as Jerlov classified ocean types by their properties in the upper layers between 0 and 10 m of depth due to the homogeneity exhibited in this region [5]. The measurement values of the remaining entries were averaged over all measured depths of 10 m or shallower. This reduced the measured value column from a series of arrays (showing the values at various depths) to a single measured value for each cast that was averaged over data from the first 10 m of depth. The impact of this initial data cleaning was to reduce the number of casts to 47,099 (representing a 67% loss of data) for ${K_d}$, 20,764 (24% loss) for $a$, 4,504 (23% loss) for $b$, and 42,904 (25% loss) for $c$.
D. Grouping ${{K}_d}$ Data into Data Collection Campaigns
Next, the casts for ${K_d}$ were grouped into a number of data collection “campaigns,” with a campaign defined as a group of casts from the same cruise that were taken at approximately the same time and location. The time span for a campaign was set as a maximum of 12 h after the first cast of a campaign, while the matching of geographic locations was taken within $\pm {0.5}$ degrees of latitude and longitude from the first cast. Locations that were significantly inland were identified by the visual inspection of a map plot and then removed from the data (${\sim}{0.4}\%$ of campaigns). The result was a set of 3,061 data collection campaigns.
Within some campaigns, casts were repeated for the same wavelength of measurement. Therefore, ${K_d}$ values were averaged, where more than one measurement existed in the same campaign for a given wavelength. This process reduced the dataset to a discrete set of wavelengths and ${K_d}$ values for each campaign, totaling 18,653 lines of data across the 3,061 campaigns. This gives a mean of ${6.1}\;{\pm}\;{4.7}$ wavelength entries per campaign (maximum of 18 wavelengths for a campaign, minimum of 1, median of 6). The measurement wavelengths ranged from 305 to 710 nm with a total of 78 unique wavelengths.
E. Assigning Jerlov Water Types to ${{K}_d}$ Campaigns
It was now possible to assign a Jerlov water type to each of the 3,061 campaigns by comparing the ${K_d}$ values at each wavelength to the ${K_d}$ values of each Jerlov water type (shown in Fig. 1). The Jerlov water type with the minimum mean absolute percentage error (MAPE) was taken as the matching Jerlov water type for a given campaign. To provide further cleaning of the data, a MAPE limit of 25% was imposed; then outlier ${K_d}$ values were removed that were more than $\pm {2}$ standard deviations (SDs) away from the average value for a given wavelength and Jerlov water type. This reduced the number of campaigns to 2,710 (11% data loss). All 10 Jerlov water types were present, with Jerlov II being the most common (660 campaigns) and Jerlov 7C the least common (52 campaigns). A full breakdown of the resulting Jerlov water types can be found in Table 2, with an additional analysis of the results in Section 3.A.
Table 2. Number of Campaigns Matched to Each Jerlov Water Type for the Three Measured Parameters
F. Assigning Jerlov Water Types to $a$, $b$ Campaigns
The cruise ID, latitude, longitude, date, and time of each cast in the absorption and scattering datasets were compared to the campaigns identified in the ${K_d}$ data. Where matching campaigns were identified (using the same criteria as used for the original grouping of campaigns from ${K_d}$ data), any duplicated wavelengths for the same campaign were averaged. Of the 2,710 data collection campaigns identified in the ${K_d}$ data, 205 were matched to absorption data, and 27 were matched to scattering data.
Exploiting the beam attenuation coefficient data allowed additional campaign matches to be made to scattering data, using the relation $c = a + b$. $c$ data were matched to the ${K_d}$ campaigns, which discovered that data existed at matching wavelengths for 177 campaigns that were present in the $a$ and $c$ data, but not in the $b$ data. This allowed $b$ data to be generated ($b = c - a$) for the matching campaigns and wavelengths. After this process, there was only one campaign that was not common to $a$ and $b$; this campaign was removed to give a matched set of 204 campaigns in both $a$ and $b$ datasets. Figure 2 shows the geographic locations for the campaigns identified for ${K_d}$ and $a,b$.
Fig. 2. World maps showing the 2,710 campaign locations for ${K_d}$ values (left), and the 204 campaign locations for $a$ and $b$ values (right).
Table 3. Number of Values Averaged across All Campaigns, for Each Jerlov Water Type, to Arrive at the Final Averages for $a$, $b$a
With the $a$ and $b$ data now grouped into campaigns, the Jerlov water types of each campaign (as derived using the ${K_d}$ data) could now simply be assigned to the $a$ and $b$ data according to their associated campaign. The 204 matched campaigns included eight of the 10 Jerlov water types (missing the clearest Jerlov I and the most turbid Jerlov 9C), with Jerlov III being the most common (81 campaigns) and Jerlov IA and 7C being the least common (one campaign each). Table 2 details the number of matching campaigns against each Jerlov water type.
G. Deriving ${a},{b}$ versus Wavelength for Each Jerlov Water Type
Measured $a$ and $b$ values for each Jerlov water type were grouped by the wavelength and then averaged to give a single $a$ and $b$ value at each wavelength for each Jerlov water type. The outliers were removed at the $\pm {2}$ SD level, after which a new average was created. Entries with less than five values contributing to the final average were removed, leaving data for six of the 10 Jerlov water types (Jerlov IB to Jerlov 5C). Table 3 lists the number of entries for each wavelength/Jerlov combination that were used to create the final average values. The results from this analysis are given in Sections 3.B and 3.C.
H. Deriving a Matched Set of $a$, $b$, and ${{ K}_d}$ Values
It was desirable to generate a matched set of $a,b,$ and ${K_d}$ values so that mathematical conversions from $a$ and $b$ to ${K_d}$ could be assessed against the measured data to test their consistency. This required finding entries from all three datasets that were collected at the same time and location (i.e., from the same campaign) and at the same wavelength. The 204 campaigns of the $a$ and $b$ data were correlated to the same campaigns for the ${K_d}$ data to identify where there was a match in wavelength and campaign. This yielded 170 campaigns with up to four matching wavelengths (412, 510, 532, and 555 nm). Data for eight Jerlov water types remained (Jerlov IA to 7C), although with only one campaign available for Jerlov IA and Jerlov 7C, and only four campaigns for Jerlov IB. These matched sets of data for $a,b$, and ${K_d}$ were subsequently used to assess their consistency according to existing mathematical conversions from $a$ and $b$ to ${K_d}$ (see Section 3.D).
3. RESULTS
A. Downwelling Diffuse Attenuation Coefficient and Jerlov Water Types
Figure 3 demonstrates the assignment of Jerlov water types to measured ${K_d}$ data. The 4,375 measured data points spanning the 660 campaigns that matched closest to Jerlov II (after removal of the outliers and imposition of the MAPE limit of less than 25%) are shown. It can be seen that these data fall along the standard Jerlov II data curve, and relatively few points stray across the neighboring Jerlov IB or Jerlov III curves. This is by the design of the fitting process, and similar trends are shown for other Jerlov water types.
Fig. 3. Measured downwelling diffuse attenuation coefficient, ${K_d}$(${{\rm m}^{- 1}}$), values classified as Jerlov II. The spectral profiles for Jerlov IB, II, and III are shown for comparison.
B. Absorption Coefficient and Jerlov Water Types
The measured data for $a$ are compared to the values predicted by Solonenko and Mobley [38] in Fig. 4. For all water types, the measured data above 600 nm provide a good match to values predicted by Solonenko and Mobley. At these wavelengths, the absorption values converge for the different water types, as the principal absorber is the water itself. At shorter wavelengths, however, the measured data generally show higher absorption than the predicted values. The largest differences are in the Jerlov II and Jerlov III water types and around 500 nm, where chlorophyll has its greatest influence. Overall, 24 of the 53 measured values are within $\pm {25}\%$ of the predicted values.
Fig. 4. Comparison of the measured values for $a$ derived by this study, and the predicted values published by Solonenko and Mobley [38] across six Jerlov water types. The error bars on the measured values show their SDs.
Table 4. Comparison of Measured to Predicted Values for $a$ and $b$ at 510 nm
A numerical comparison of $a$ data for 510 nm is shown in Table 4. At this wavelength, the measured data are higher than the predicted values for all of the presented Jerlov water types. The smallest difference is for Jerlov 5C, where the predicted value is 25% too low, while Jerlov III shows the largest difference of 51%.
C. Scattering Coefficient and Jerlov Water Types
The measured data for $b$ are compared to the values predicted by Solonenko and Mobley [38] in Fig. 5. At Jerlov IB, the measured data are greater than the predicted data at all wavelengths and, at Jerlov II to Jerlov 5C, the measured data are lower than the predicted data for most wavelengths, particularly 555 nm and below. Only 11 of the 53 measured values are within $\pm {25}\%$ of the predicted values.
Fig. 5. Comparison of the measured values for $b$ derived by this study, and the predicted values published by Solonenko and Mobley [38] across six Jerlov water types. The error bars on the measured values show their SDs.
A numerical comparison of $b$ data for 510 nm is shown in Table 4. At this wavelength, the difference between the measured and predicted data is 5% for Jerlov 1C and 19% for Jerlov 5C while, for all other water types, the differences are at least 54%. The differences in the scattering coefficient are generally greater than those for absorption, with the greatest difference in scattering being at Jerlov III, where the predicted value is 2.6 times greater than the measured value.
D. Consistency with ${{ K}_d}$ Calculations
The parameters $a,b$, and ${K_d}$ are linked through scattering processes, and their relationship can be studied to test the self-consistency of the measured data and its compliance with models. ${K_d}$ is dominated by absorption, and its value exceeds $a$ because scattered light follows a longer jagged path through the medium, experiencing more absorption as it penetrates. Several authors have explored the relationship between the three parameters in terms of the phase function which describes the angular profile of scattering in the medium [33,35,37,38,51]. Different models predict different analytical relationships between the dimensionless ratios ${K_d}/a$ (describing the extent to which the diffuse loss is increased) and $b/a$ (describing the relative strength of scattering). These relationships can be tested directly against the measured parameters.
The simplest of these relationships is a linear relationship from Shannon [33]:
where $n$ is a fitting parameter. More complete analyses from Morel and Loisel [37] and from Solonenko and Mobley [38] take into account the influence of the solar zenith angle and the different scattering characteristics of water molecules and particles, based on the work of Haltrin [51], Kirk [35], and others. Morel and Loisel analyze several different depths and several different illumination conditions. The case that is most relevant to this current paper refers to “optical depth” $\zeta = {1}$, illuminated by the sun in a black sky. For this case, the relationship between ${K_d}/a$ and $b/a$ is given asThe matched set of $a,b$, and ${K_d}$ measured data derived in Section 2.H was used to test consistency with these three equations, with the results summarized in Table 5. A total of 473 matched sets of measured data were available, which were reduced to 424 matched sets after removal of those where the value of ${K_d}/a$ was less than 1. The value of $n$ for Eq. (1) was set to minimize the MAPE, with a resulting value of $n = {10}$. The value of $\eta$ was calculated for each individual data point, using the measured value of $b$ and a wavelength-dependent value of ${b_{\rm{water}}}$ determined from the formula given in Solonenko and Mobley. The calculated values of $\eta$ lay between 0 and 0.044, so the scattering was always dominated by particulate scattering. An attempt was made to derive solar angles (in order to calculate $\mu$) from the time, date, and position of each measurement, but the averaging of multiple measurements at multiple points in time prevented such an analysis. The parameter $\mu$ had to be treated as a fitting parameter, and its value was chosen to minimize the MAPE, using two different values to describe oceanic and coastal types as suggested by Solonenko and Mobley. This fitting process in Eq. (2) yielded slightly different values of $\mu$ (0.89 oceanic, 0.85 coastal) than were proposed by Solonenko and Mobley [38] (0.98 and 0.85, respectively). The same fitting process applied to Eq. (3) optimized at $\mu = {1.02}$ for oceanic and 0.97 for coastal types. In all cases, $\mu$ influenced the value of ${K_d}$ more strongly than did $\eta$ for both Eqs. (2) and (3).
Table 5. Accuracy of Fitting the Three Different ${K_d}/a$ Equations to the Sets of $a$, $b$, $K_d$ Data
The closest match to the measured data was achieved by Eqs. (2) and (3), both with a MAPE of 13% and with 85% of the calculated ${K_d}$ values being within $\pm {25}\%$ of the measured ${K_d}$ values. It is likely that the fits could be further improved if individual values of $\mu$ were available for each data point. The Shannon equation (1) achieves a reasonable fit in spite of its simplicity.
Figure 6 illustrates the relationship between ${K_d}/a$ and $b/a$ for the 181 matched sets of measured data for waters classified as Jerlov III (at wavelengths 412, 510, 532, and 555 nm). Also included are lines showing the relationships predicted from the three equations, all of which provide a reasonable match. In Eqs. (2) and (3), $\eta$ was set to the average value across all of the Jerlov III data points ($\eta = {0.011}$). The experimental points exhibit considerable scatter due to variations in solar zenith angle (different $\mu$), variations in scattering characteristics ($\eta$ depends both on the wavelength and on $b$), as well as other uncontrolled effects.
Fig. 6. Jerlov III measured data points against the predictions of Eq. (1) from Shannon, Eq. (2) from Morel and Loisel, and Eq. (3) from Solonenko and Mobley.
As a further self-consistency check, the final averaged measured values of $a$ and $b$ (53 values of each parameter, as shown in Sections 3.B and 3.C) were input to the three equations and their calculated ${K_d}$ values compared to their corresponding Jerlov ${K_d}$ values (see results in Table 5). The simplest equation (1) performed the best (MAPE of 14%, 77% of calculated ${K_d}$ within $\pm {25}\%$ of Jerlov ${K_d}$), with the other two equations also providing a reasonable match.
E. Proposed Absorption and Scattering Coefficients for Jerlov Water Types
With measured $a$ and $b$ values for up to 10 wavelengths (412–715 nm) available for six Jerlov water types, it was possible to generate full spectral profiles for $a$ and $b$ across 300–800 nm by fitting the measured data to existing models. This study used the equations of Solonenko and Mobley [38], which are based on the work of Gordon [52], Morel [24,37], and Bricaud [53] for absorption relationships, and Haltrin [51] for scattering relationships.
The absorption coefficient, $a$, is related to the relative contributions from pure water, ${a_w}$, chlorophyll, ${a_{\rm{chl}}}$, and CDOM, ${a_{\rm{cdom}}}$, according to
where $\lambda$ is the wavelength (nm), $A$ and $E$ are wavelength-dependent parameters from [54], Chl is the chlorophyll concentration (${{\rm mg\cdot m}^{- 3}}$) specific to each Jerlov water type, $M$ (unitless) and $\alpha$ (${{\rm nm}^{- 1}}$) are fitting parameters specific to each Jerlov water type, and ${a_w}$ was taken from Buiteveld et al. [30].The scattering coefficient, $b$, is related to the contributions from pure water, ${b_w}$, and particles, ${b_p}$:
where ${B_s}({{\rm g\cdot m}^{- 3}})$ and ${B_{l}}({{\rm g\cdot m}^{- 3}})$ are the concentrations of small and large particles, respectively.The fitting variables (${\rm Chl},M,\alpha$ for absorption, and ${B_s},{B_l}$ for scattering) were optimized, using the Microsoft Excel Solver add-in for the best MAPE fit to the measured $a$ and $b$ data for each Jerlov water type, without any constraints on their magnitudes or ratios. Therefore, the resulting values for ${\rm Chl},{B_s}$, and ${B_l}$ should be treated as fitting parameters, rather than the physical properties they represent.
Table 6 shows the optimized fitting parameters for the absorption and scattering equations to give the best fit to the measured $a$ and $b$ data, together with the associated MAPE values. Figures 7 and 8 show the resulting spectra plotted with the measured values derived by this study, while Fig. 9 and Table 7 provide values for $a$ and $b$ from 300 to 800 nm for Jerlov IB to Jerlov 5C. The MAPE values for the fits were 9% or less in all cases. Fifty-two of the 53 measured absorption values are within $\pm {25}\%$ of the optimized model values, while 53 of the 53 measured scattering values are within $\pm {25}\%$ of the optimized model values. Although it can be seen from the equations in Section 3.D that multiple combinations of $a$ and $b$ could lead to the same value of ${K_d}$ (i.e., there are no unique solutions), for this study, we are using directly correlated, measured values for all three parameters; therefore, the uniqueness of the solution is implicit.
Table 6. Optimized Fitting Parameters for the Absorption and Scattering Models to Match to the Measured Values Derived in This Study, Together with MAPE Values for the Fitsa
Fig. 7. Optimized absorption spectra, together with the measured values derived by this study. The error bars on the measured values show their SDs.
Fig. 8. Optimized scattering spectra, together with the measured values derived by this study. The error bars on the measured values show their SDs.
Table 7. Proposed Absorption and Scattering Coefficients for Jerlov IB to Jerlov 5C
The $a$ and $b$ values from Table 7 are recommended for use in future applications, where IOPs are required for Jerlov water types. Our implementation of the absorption and scattering models, together with tabulated input and output data, is available to download [55].
4. CONCLUSION AND DISCUSSION
Measured IOPs have been derived for Jerlov water types by exploiting a vast database of measured ocean parameters and applying data science techniques. Established models have been used to extend the wavelength range of the derived absorption and scattering coefficients, with values presented for 300–800 nm across six Jerlov water types from Jerlov IB to Jerlov 5C. These data are recommended for use in applications where IOPs are required to describe Jerlov water types.
The measured values of the absorption and scattering coefficients were shown to be consistent with three existing models for conversion to the downwelling diffuse attenuation coefficient. Furthermore, it was shown that the simplest relation by Shannon [Eq. (1) with ${n} = {10}$] gives an excellent match for most purposes, and its accuracy was comparable to the much more complex Eqs. (2) and (3).
There are several limitations to the data that should be highlighted. First, there were insufficient measured data to derive IOPs for the two clearest Jerlov water types (I and IA) and the two most turbid (7C and 9C). Referring to Table 2 for the relative popularity of these water types in ${K_d}$ measurements, it would seem that Jerlov I and Jerlov IA are particularly common water types; therefore, their omission here is notable. However, the other two missing water types appear to be rarer; therefore, the absence of data for these water types is possibly of less significance.
Of the Jerlov water types that were included, the data for Jerlov IB and Jerlov 5C were particularly sparse. They just reached the threshold of having five values to be averaged for a given wavelength. However, it can be seen from the measured data plots in Figs. 4 and 5 that these data had comparable SDs to the other water types.
Data for the other presented water types were very robust indeed, although with a limited number of wavelengths. As many as 79 different values were averaged (e.g., 510 nm at Jerlov III), and it should be emphasized that each of those 79 measurements was already built from the averaging of multiple measurements within the same campaign. Measured data for up to 10 wavelengths were available for most water types, ranging from 412 to 715 nm. The use of a model to interpolate between (and extrapolate beyond) these points is another limitation to be highlighted, although it was based on established models that have been developed over several decades.
In terms of the individual data measurements themselves, there are some caveats to their provenance. The vast majority of scattering coefficient data (177 out of 204 campaigns) were indirectly derived from the matching absorption coefficient and total attenuation coefficient data. Ideally, there would be directly measured values for $a,b$, and ${K_d}$ at the same time and location, but clearly this is rarely the case.
The grouping of data into “data collection campaigns” was a key component of the initial data preparation, and it was found to be very robust to the chosen boundaries. It was decided that the grouping should encompass a 12 h period within $\pm {0.5}$ degrees of longitude and latitude of the starting location. While it was assumed that water quality would not change within these parameters, clearly it could cause some issues if a vessel was moving, for example, from a coastal to an open water area. To check the impact of these choices, other combinations of time and location boundaries were tested. Choosing much tighter constraints of 1 h per campaign within $\pm {0.1}$ degrees of longitude and latitude, 99% of the final averaged values of absorption and scattering coefficients were within $\pm {25}\%$ of the values found with the more generous boundaries, and the majority of values (74%) were within $\pm {10}\%$. The consistency is because the same data are effectively still being averaged to derive the final numbers, but the numbers are grouped into a different number of campaigns (325 separate campaigns for the tighter grouping versus 204 campaigns for the more generous grouping used in the analysis). Although some of these additional campaigns may fall into different Jerlov classifications, this is clearly not significant enough to affect the final numbers.
One limitation that is apparent from the world map plot of $a$ and $b$ data (Fig. 2) is the lack of geographic diversity in the locations of the measured data used. While ${K_d}$ values are available from around the world (also shown in Fig. 2), the campaigns matched to $a$ and $b$ data are limited to a relatively narrow swathe of locations $-185$ of the 204 campaign locations were between 20 and 45° north of the equator. However, diversity in Jerlov water types does exist across these locations, and that is the key concern for this work.
The historical evolution of oceanic water quality is another unknown is this study. It is possible that the spectral dependence of ${K_d},a$, and $b$ could have changed since the initial Jerlov data were collected around 75 years ago. That could potentially lead to inaccuracies when comparing more recently gathered experimental data to the original Jerlov values.
The outputs of this study were generated via a complex data analysis pipeline; therefore, all of the source code and data have been published openly to ensure reproducibility [55]. It is intended that other researchers may reproduce the results herein and refine the methodology further. This may reveal additional insights into the data and potentially uncover new ways of deriving the IOPs of Jerlov water types.
The ultimate extension to this study would be a cruise to make full-spectrum direct measurements of $a,b$, and ${K_d}$, correlated in time and space, distributed across the world’s oceans, and encompassing all 10 Jerlov water types. In the absence of such an experimental campaign, newly reported experimental measurements of IOPs and AOPs should be referenced to this dataset to monitor its accuracy and relevance. Furthermore, the methods used to derive this dataset should be repeated with any substantial new measured data as they become available.
Funding
Defence Science and Technology Laboratory.
Acknowledgment
The authors are grateful to reviewers at Applied Optics for their valuable feedback on this paper. © Crown copyright (2022), Dstl. This material is licensed under the terms of the Open Government Licence except where otherwise stated. To view this license, visit http://www.nationalarchives.gov.uk/doc/open-government-licence/version/3 or write to the Information Policy Team, The National Archives, Kew, London TW9 4DU, or email: psi@nationalarchives.gov.uk.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [55].
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