Next Article in Journal
Seaweed Potential in the Animal Feed: A Review
Previous Article in Journal
On-Line Multi-Class Segmentation of Side-Scan Sonar Imagery Using an Autonomous Underwater Vehicle
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

A New Algorithm to Estimate Diffuse Attenuation Coefficient from Secchi Disk Depth

1
Facultad de Ciencias Marinas, Universidad Autónoma de Baja California, Ensenada 22860, Baja California, Mexico
2
Alumni PhD postgraduate program in Coastal Oceanography, Facultad de Ciencias Marinas, Universidad Autónoma de Baja California, Ensenada 22860, Baja California, Mexico
3
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92037, USA
4
Institut d’Investigació per a la Gestió Integrada de Zones Costaneres (IGIC), Universitat Politècnica de València (UPV), 46730 Grau de Gandia, Spain
5
Departamento de Plancton y Ecología Marina, Instituto Politécnico Nacional, Centro Interdisciplinario de Ciencias Marinas (IPN-CICIMAR), La Paz 23096, Baja California Sur, Mexico
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2020, 8(8), 558; https://doi.org/10.3390/jmse8080558
Submission received: 24 June 2020 / Revised: 20 July 2020 / Accepted: 22 July 2020 / Published: 25 July 2020

Abstract

:
The vertical diffuse attenuation coefficient K d ( PAR ) is used for calculating the euphotic zone, the first optical depth that is important for primary productivity models. Currently, K d   ( PAR ) can be estimated using an irradiometer or a Secchi disk ( SD ). The main objective of this work is to define a model that can be applied to a wide range of optical marine conditions to estimate K d   ( PAR ) by SD . We used irradiance profiles and SD depth ( Z S D ) from 679 stations in various marine regions. Three parametric models were developed, and their statistical performance was evaluated in view of previous approaches reported and remote sensing data. The best results were obtained with an adaptive model representing three cases: clear-water, turbid-water, and a transition zone (R2 = 0.965, MAE = 0.083, RMSD = 0.239, BIAS = 0.01, and MPI = 0.854). Previous models considering a single optical depth figure at which the S D disappears did not capture the marine optical complexity. Our classification of 113 stations with spectral absorption data into Jerlov water types indicated that no unique correspondence existed between estimated K d (PAR) and water type, making it ambiguous to associate compatible inherent optical properties and chlorophyll with Z S D . Although obtaining K d ( PAR ) from Z S D is simple/low-cost, care should be taken in the methodology used to measure Z S D to ensure consistent results across different optical marine conditions.

1. Introduction

Sunlight in the electromagnetic spectrum region between 400 and 700 nm, known as photosynthetically active radiation (PAR) [1], plays an important role in the physics, biology, and chemistry of the oceans [2]. PAR is directly linked to biological processes such as photosynthesis, which constitutes the base of the food chain in marine ecosystems [1,3,4,5]. In other words, primary productivity largely depends on the sunlight field in the water column, which decreases exponentially with depth.
In the late 19th century, Pietro Angelo Secchi (1866) [6] pioneered studies on the field of light penetration in water and developed a method for determining water transparency based on a white disk (made of a non-refractive material) 30201350 cm in diameter, now known as Secchi disk ( SD ) [7]. The principle for the use of the SD consists of determining the depth at which it is no longer visible to the naked eye [8]. This depth is defined as the Secchi disk depth ( Z S D ), being inversely proportional to the amount of dissolved or particulate matter present in the water column; therefore, the Z S D reading can be used as an indicator of turbidity [9,10].
During the 20th century, it was possible to quantify the light field in water, noting that light decreases exponentially with depth. This decrease can be measured using the vertical spectral diffuse attenuation coefficient ( K d ) , an apparent optical property (AOP) [11] that reflects the attenuation caused by water molecules [12] and the amount and type of compounds in water (phytoplankton, organic and inorganic particles, and colored dissolved organic matter (CDOM)) [13].
Since primary productivity, which controls the evolution of marine ecosystems, largely depends on the sunlight environment in the water column, knowing K d is essential to describe its variability. For instance, K d can be used for calculating the depth of the euphotic zone ( Z e u ) (i.e., the depth at which 99% of the surface light is attenuated) and the first optical depth (qualitatively, the ocean layer that produces the color signal of the ocean recorded by satellites) [1]. K d is also important for primary productivity models, which are based on the potential of the phytoplankton community to react to different light intensities [14].
K d can be estimated directly, using irradiance sensors measuring the flow of PAR photons in the water column ( K d (PAR)) [1], or indirectly, using a SD [7]. The former provides more accurate data; however, is not routinely used in oceanographic cruises due to its high cost, but only in those focused on bio-optical measurements or primary productivity, or for the calibration of ocean color sensors [9,15,16,17,18]. On the other hand, SD is routinely used in most oceanographic cruises [18,19,20,21,22]. The approximation most commonly used is that K d (PAR) is inversely proportional to Z S D [9] (Equation (1)), which yields empirical constants. Considering the criteria of Kirk [1] and Gallegos et al. [23], these empirical constants represent the optical depth ( O D S D ) at which the Secchi disk disappears:
K d ( P A R ) = O D S D Z S D
Poole and Atkins (1929) [9] were the first to propose an O D S D value from 14 measurements recorded in the English Channel, with Z S D values ranging from 2 to 35 m. These authors proposed estimating K d (PAR) with an O D S D of 1.70. In 1970, at a time when technological progress made it possible to manufacture submersible photometers/irradiance-meters, Holmes [15] revisited this topic; using data from 13 stations in Santa Barbara (California, USA), he derived a value of 1.44. However, the data used by Holmes [15] came from an area with Z S D values ranging from 2 to 12 m, i.e., conditions that were more turbid than those reported by Poole and Atkins [9]. The above studies support using an O D S D of 1.70 for clear water and 1.44 for turbid water (v.gr. Barbosa and Domingues, 2009 [22]).
The above values (i.e., 1.70 and 1.44) were estimated from a limited dataset (14 and 13 stations), which is why several researchers have subsequently sought to re-evaluate these values. Megard and Berman (1989) [16] recorded 24 measurements in the southeastern Mediterranean Sea and estimated an average value of 1.54 for areas with Z S D ranging from 6 to 46 m.
In the marine environment, K d   ( PAR ) has been estimated from Z S D using O D S D values ranging from 1.22 to 1.70 [22]. Recently, according to the new Secchi Disk Theory [23] and the approach proposed in the Fifth IOCCG Report [24], Lee et al. (2018) [18] proposed to unify all O D S D values into a single figure. These authors used the Hydrolight computer code [25] to simulate the light field in the water column under different optical conditions (from oligotrophic to eutrophic, oceanic and coastal, including phytoplankton blooms). These simulations yielded an average O D S D of 1.48.
Another approach used to estimate K d   ( PAR ) through SD without involving O D S D involves the development of empirical models based on a nonlinear relationship between K d (PAR) and 1/ Z S D :
K d ( P A R ) = a ( Z S D ) b
where a and b are the empirical coefficients of the model, which vary according to the study area. The majority of the work on models given by Equation (2) has been conducted for inland water bodies [26,27,28]. For marine environments, Montes-Hugo and Alvarez-Borrego [17] proposed values of 1.45 and 1.10 for a and b, respectively, for coastal waters in the northeast of Baja California and southern California, an area with Z S D from 2 to 12 m.
Jerlov [29] classified oceanic water into five types (I, IA, IB, II, and III) and coastal water into five types (1, 3, 5, 7, and 9), based on hyperspectral K d ( K d   ( λ ) ) for each wavelength), where a larger number indicates higher turbidity. Each of the 10 Jerlov water types has a typical light absorption coefficient associated ( a ( λ )   m o d e l ) [30]. This absorption coefficient takes into account pure sea water absorption, a w ( λ ) , chlorophyll-based absorption, a p h y ( λ ) , and CDOM absorption, a C D O M ( λ ) [30] (Equation (3)):
a ( λ ) m o d e l = a w ( λ ) + a p h y ( λ ) + a C D O M ( λ )
where λ is wavelength.
Based on the above, estimating K d   ( PAR ) from Z S D measurements has proven to be a useful, cost-effective methodology to detect changes in marine ecosystems. However, it is essential that the K d   ( PAR ) estimates be robust and objective, since a miscalculation of K d ( PAR ) would lead to errors in estimates of euphotic zone and first optical depths. The main objective of this work is to establish an empirical relationship that could be applied to a wide range of optical conditions occurring in marine environments. A second objective is to examine whether the K d ( PAR ) derived from Z S D could be related to a specific optical water type (in Jerlov’s sense), which would broaden the application of the SD approach and enhance its usefulness as a descriptor of water optical properties. Likewise, and considering that the current development of spectroradiometer-type remote sensors allows producing synoptic measurements of K d at 490 nm ( K d ( 490 ) ), this study considered data from these remote sensors as one of the models to evaluate.

2. Materials and Methods

In this study, we compiled 679 pairs of K d   ( PAR ) and Z S D data recorded under well-illuminated (sunny) conditions, with an irradiance meter and SD , respectively. These encompass conditions from clear oceanic to turbid coastal waters (Figure 1a,b). The source of data was as follows: 212 data pairs from the Tara Ocean Consortium [31] (Figure 1a); 195 from the NASA SeaBass archive (Chesapeake bay and CALCOFI zone) [32]; 103 from Gallegos et al. [21]; 74 from the Phytoplankton Ecology Group (POPEYE) database at Universidad Autónoma de Baja California; 71 from Montes-Hugo and Alvarez-Borrego [17]; 24 from Megard and Berman [16]. Hereafter, K d ( PAR ) recorded from irradiance-meter data will be named K d i n   s i t u .
K d i n   s i t u for NASA SeaBass [32] and POPEYE data was estimated for each station based on PAR measurements, in accordance with the criteria of Kirk [1], expressed in Equation (4):
l n ( P A R ( Z ) ) = l n ( P A R ( 0 ) ) K d i n   s i t u   Z
where K d i n   s i t u is the slope of a linear model and the dependent variable is the natural logarithm of irradiance as a function of depth ( Z ). For the Tara Ocean Consortium data [31], K d i n   s i t u was estimated from Z e u using the following equation [1]:
Z e u = 4.6 K d i n   s i t u
The K d i n   s i t u data of Megard and Berman [16], Montes-Hugo and Alvarez-Borrego [17], and Gallegos et al. [21] were taken from those reported in the respective publications.
Based on Steyerberg [33] and the IOCCG report [34], the database was randomly split into two groups. Group 1 was used for the development of models; it comprises 478 data pairs (70% of total data). Group 2 was used for validation purposes; it comprises 201 data pairs (30% of total data). To reduce the random error in the selection of the two datasets and to test the robustness of models, 10 replicates were obtained by randomly selecting 10 different datasets for modeling, along with the respective validation datasets.
Three parametric models were tested to predict K d   ( P A R ) based on Z S D ; the model with the best fit was selected as per the criteria of Xu et al. [35] for least-squares analysis. The first approximation (model a) was based on Equation (1), where K d   ( PAR ) is calculated using fixed (or single) estimates of O D S D ; the second (model b) was based on the nonlinear empirical relationship between K d i n   s i t u and 1 Z S D (Equation (2)); and the third (model c) followed the concepts of Equation (2); in the latter model, Z S D was split into three zones, namely two extreme cases (clear and turbid waters) and a transition zone, as follows:
l o g 10 ( K d ) = p 1 + p 2 × l o g 10 ( Z S D ) ,   if   l o g 10 ( Z S D ) < p 3
l o g 10 ( K d ) = p 5 + p 6 × l o g 10 ( Z S D )   if   l o g 10 ( Z S D ) p 4
In the transition zone, where p 3 l o g 10 ( Z S D ) < p 4 , l o g 10 ( K d ) is modeled as a linear combination of the two models:
l o g 10 ( K d ) = ( p 1 + p 2 × l o g 10 ( Z S D ) ) × p 4 l o g 10 ( Z S D ) p 4 p 3 + ( p 5 + p 6 × l o g 10 ( Z S D ) ) × l o g 10 ( Z S D ) p 3 p 4 p 3
The model parameters p1, p2, p3, p4, p5, and p6 are retrieved through the least-squares fitting.
Moreover, K d   ( 490 ) values were derived from measurements with a 1 × 1 km-resolution spectroradiometer in monthly multi-sensor composites. The sensors used were Ocean Color and Temperature Scanner from August 1996 to July 1997 (OCTS_v2014.0), Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) from September 1997 to December 2010 (SeaWiFS_v2018.0), Moderate Resolution Imaging Spectroradiometer-MODIS TERRA from February 2000 to date (MODIST_v2018.0), Medium Resolution Imaging Spectrometer (MERIS) from April 2002 to March 2012 (MERIS_R3), Moderate Resolution Imaging Spectroradiometer-MODIS-AQUA from July 2002 to date (MODISA_v2018.0), and Visible and Infrared Imager/Radiometer Suit (VIIRS) Suomi-NPP from January 2012 to date (VIIRS_v2018.0). Sensor data to construct these images were downloaded from [36] to 1B level and processed at levels 2 and 3 using SeaDAS 7.5.1. (National Aeronautics and Space Administration) The multi-sensor composites were performed following the criteria by [37,38].
To determine the performance from the above models, three statistical descriptors were calculated: mean absolute error (MAE) (Equation (9)), root-mean-square error (RMSD) (Equation (10)), and analysis of bias (BIAS) (Equation (11)).
M A E = | ( K d i n   s i t u K d m o d e l ) | n
R M S D = ( K d i n   s i t u K d m o d e l ) 2 n
where n is the total number of data included in this analysis, K d i n   s i t u K d m o d e l is residual observations, and | ( K d i n   s i t u K d m o d e l ) | is the absolute value of residuals.
B I A S = a v e r a g e   ( K d i n   s i t u K d m o d e l )
where BIAS is the residual mean.
According to MAE and RMSD, lower values represent better results, whereas BIAS values closer to zero mean better results. To determine which is the best model, a model performance index (MPI) was estimated (Equation (12)) based on the three statistic descriptors mentioned above:
M P I = 1 ( ( R M A E p ) + ( R R M S D p ) + ( R | B I A S | p ) 3 )
where R M A E is the MAE rank, R R M S D is the RMSD rank, R | B I A S | is the rank of absolute BIAS values, and p is the total number of models to be compared. Ranks and their respective matches were calculated following the criteria of [39,40,41]. MPI ranges from 0 to 1, where values closer to 1 mean a better model.
To accomplish the objective of examine whether the K d   ( P A R ) derived from Z S D could be related to a specific optical water type (in Jerlov’s sense), we compiled in-situ absorption coefficient data ( a ( λ ) i n   s i t u ). These were available for 113 stations only. The data for the POPEYE database and the CALCOFI zone were processed following the protocol of Mitchell et al. [42], whereas the data for the Chesapeake Bay area were analyzed following the protocol of Mueller and Austin [43]. Pope and Fry [12]) values were used for a w ( λ ) . a ( λ ) i n   s i t u spectra were classified into the different Jerlov water types. The classification was obtained by comparing a ( λ ) i n   s i t u with a ( λ ) m o d e l using a least-squares fitting method based on Xu et al. [35]. The statistical significance of this fit was determined through a goodness-of-fit test following Zar [44]. POPEYE absorption data ranged from 400 to 700 nm, and SeaBaSS data from 400 to 650 mm. Thus, the goodness-of-fit test was carried out with different degrees of freedom, according to each dataset (POPEYE: α = 0.05, χ C r i t 2 = 21.02, df = 12; SeaBASS: α = 0.05, χ C r i t 2 = 18.30, df = 10).

3. Results and Discussion

Our database includes both oceanic and coastal stations (Figure 1), so the models presented in this work were developed and evaluated considering a wide range of optical conditions. The three models proposed in this work represent K d i n   s i t u and Z S D values ranging from 0.030 to 3.217 m−1. and 0.3 to 50 m, respectively.
Model a based on Equation (1) and that gives rise to Equation (13) yielded an O D S D of 1.37 (R2 = 0.957), which is lower than O D S D values reported in the literature. Typically, studies performed in the 20th century considered that low O D S D values resulted from increased turbidity [13,45]. However, the authors of [18] mentioned that in addition to the above, a factor to consider is that when K d   ( PAR ) is estimated using shallow depths, this tends to be higher than values estimated for deeper layers. This trend is most evident in oceanic stations with deeper Z e u relative to stations where light penetration is lower. In other words, lower O D S D values may be obtained when the calculation of K d   ( PAR ) considers the light profile from the surface to a depth close to Z e u , or at least to Z S D [18]. In determining O D S D , K d i n   s i t u was calculated using light profiles close to Z e u or Z S D .
K d m o d e l   a = 1.37 Z S D
Model b was based on a nonlinear fit between K d i n   s i t u and Z S D , (Equation (14)), assuming that this represents the continuous function of the empirical relationship between K d   ( P A R ) and Z S D . This model resulted in regression coefficients a = 1.18 and b = 0.92 (R2 = 0.957). These coefficients are lower relative to those reported by Montes-Hugo and Álvarez-Borrego [17] (a = 1.45 and b = 1.10), likely because of the narrower sampling interval (1–12 m) used by these authors.
K d m o d e l   b = 1.18 ( Z S D ) 0.92
Model c is adaptive and followed the same approach as model b, i.e., it comprises three equations that consider three Z S D ranges (Equations (15)–(17)) (R2 = 0.965). These Z S D ranges represent two contrasting conditions: turbid water with Z S D < 2.20 m (Equation (15)) and clear water with Z S D ≥ 5.37 m (Equation (17)); plus a transition zone with 2.20 m ≤ Z S D < 5.37 m (Equation (16)).
K d m o d e l   c = 1.16 ( Z S D ) 0.62
K d m o d e l   c = exp ( ( 0.15 l o g Z S D × 0.62 ) × 1.68 l o g Z S D 0.89 + ( 0.48 l o g Z S D × 0.72 ) × l o g Z S D 0.79 0.89 )
K d m o d e l   c = 0.62 ( Z S D ) 0.72
The equation for the transition zone (Equation (16)) is more complex since attempting to discern stations located between these two extremes (turbid-to-clear vs. clear-to-turbid stations), while keeping continuity in Z S D over the entire Z S D range. This partitioning into Z S D ranges in the model c allowed us to reduce variability in the data, i.e., achieve a better fit for each case, therefore providing better performance overall.
For evaluating models a, b, and c, K d i n   s i t u (Equations (4) and (5)) was compared versus K d m o d e l   a (Equation (13)), K d m o d e l   b (Equation (14)), and K d m o d e l   c (Equations (15)–(17)) (Figure 2), as well as versus K d estimated from the different models for marine waters reported in the literature (Table 1). These comparisons were evaluated based on MAE (Equation (9)), RMSD (Equation (10)), BIAS (Equation (11)), and MPI (Equation (12)). The above showed that model c (Figure 2c) yielded the best fit (lowest MAE, RMSD, BIAS close to zero, and MPI closest to one), MAE of 0.083, RMSD of 0.239, BIAS of 0.01, and MPI of 0.854.
Table 1 represents an improvement versus previous methods, showing that model c yields the best performance considering the statistical descriptors and the index mentioned above. In particular, with respect to the most recent model [18], model c yields a MAE reduction of 0.051, an RMSD reduction of 0.046, and a MPI increase of 0.5.
If models developed for particular or regional marine conditions are considered, such as the model of Lugo-Fernández et al. [46], which divide their conditions for use into summer and non-summer for the north Gulf of Mexico an area influenced by the Mississippi river mouth, highly dispersed results may be obtained as this area is affected by high inland CDOM inputs. Additionally, we consider that the conditions in this model depend on river flows rather than seasonality. Given that our database includes stations from both northern and southern hemispheres, the criteria for applying this model become complex. As an example, we assessed the model of Montes-Hugo and Álvarez-Borrego [17], which was developed only for coastal waters in northeast Baja California and southern California; we observed that the application of this model to different marine conditions yields suboptimal results, thus highlighting the constraints in generalizing empirical models that were originally established from a limited range of conditions.
The evaluation of models a and b revealed that the use of a single O D S D value [9,15,16,18] for different optical conditions of water resulted in higher RMSD (Table 1), relative to using two values, i.e., the 1.70 figure proposed by Poole and Atkins [9] for clear waters and the 1.44 figure estimated by Holmes [15] for turbid waters. If we consider the broad range of optical conditions that occur in the marine environment, the above confirms that a single value is certainly not representative of the range of optical conditions. In addition, it was noted that model b yields lower RMSD values relative to O D S D .
The three equations adequately represented the range of optical diversity in marine environments (from clear ocean waters to very turbid coastal waters) in a simplified way, and the model can be used even under conditions of phytoplankton blooms such as those described in Santamaria-del-Angel et al. [47] and Aguilar-Maldonado et al. [48].
In order to estimate K d ( 490 ) values from remote sensors for comparison versus K d i n   s i t u and K d figures estimated with the models in Table 1, 1 km-resolution multi-sensor images were constructed. From the original 679 data, only 383 were used for this comparison. Table 2 evidences that model c is the best model, yielding an MPI of 0.814, whereas the models with the worst fit to K d i n   s i t u were the model of Pooole and Atkins [9] and the satellite model, with an MPI of 0.074. To note, the model of [9] was derived from only 14 data that are not representative of the range of optical conditions in the ocean.
For its part, the satellite model represents K d (490), which is a spectral portion of the K d (PAR) measured in situ. Austin and Petzoid [49] proposed the first approach of K d   ( 490 ) using the ratio between leaving-water radiances (Lwr) between 443 and 550 nm (Lwr443/Lwr550), as well as the K d   ( 490 ) for optically pure seawater and some linear approximation coefficients. A number of approaches have been developed from there, such as those of [32], which essentially have yielded improved estimates of the coefficients used, being specific to each sensor.
Additionally, several authors have estimated Z S D from satellite images, mostly focusing on inland water bodies [50,51,52,53,54]. In the marine environment, Kim et al. [55] estimated Z S D from K d (490) based on concepts derived from [56,57,58]. All these point to the need to measure other intrinsic optical properties, such as backscattering at least at 490 nm. As this work did not have in-situ backscattering observations available, we might think that these could be estimated through standard models such as the Generalized Inherent Optical Property (GIOP) model; however, Betancur-Turizo et al. [59] warn that care should be taken with these models because, by being too simplified, they do not reflect the variability of the parameter in a reliable way. This cautionary statement has been addressed recently. The works by Jiang et al. [60] and Liu et al. [61] have aimed to improve these estimates to obtain more accurate satellite Z S D values for various types of water. It is clear that this is a dynamic and constantly evolving line of research.
Although data derived from satellite observations are promising and this subject of research needs to be further refined in the future, we recommend further monitoring of marine optical properties while observing the data quality, and complementing in-situ reflectance measurements.
Based on the above and following the criteria established by [62], the use of multi-sensor data will allow us, in the long term, an improved integration of in-situ measurements and satellite images. This will result in time series that will be suitable for use in marine monitoring programs, defining weekly, monthly, seasonal, and annual variability scales, as well as their trends.
Figure 3 compares K d i n   s i t u and K d m o d e l calculated using model c and the model of Lee et al. [18]. The results show that both models performed similarly for K d i n   s i t u values lower than 0.1 m−1 (clear waters). In more optically complex waters ( K d > 2 m−1), the difference between in-situ and modelled data increases. The model of Lee et al. [18] tends to fit a positive exponential (J-shaped) function departing from the 1:1 line, while model c is a closer fit to the 1:1 line. This is evident for the full database (679 observations) and for two independent cruises with different optical conditions (Cal9709: oceanic/coastal conditions; Ties9802: estuarine conditions).
The primary objective of this work is to define a model applicable to a wide range of optical conditions in marine environments. Under this premise, model c in an adaptive model that yields better predictions relative to models that consider an O D S D value only. In order to use this model in field cruises, a table was added as supplementary material for K d   ( P A R ) (Table S1), derived from this model and based on Z S D . The most accurate estimate of K d   ( P A R ) with model c allows obtaining better results in the calculation of primary productivity, which is a major variable that can be used in studies ranging from understanding the global carbon cycle to fisheries aspects [63]. A proper understanding of primary organic production will not only allow estimating the total organic matter produced in the oceans, but also supports the comparison of ocean regions as potential food sources [14].
Figure 4a shows K d values associated with the three Z S D ranges. The clear water case, i.e., Z S D ≥ 5.37 m, corresponds to K d i n   s i t u values of less than 0.2 m−1 (blue circles); the turbid water case, i.e., Z S D < 2.20 m, to K d i n   s i t u values above 0.4 m−1 (brown circles); and the transition zone, to intermediate K d i n   s i t u values. In general, K d   ( P A R ) is inversely related to Z S D [1,9], but with a variable dependence according to the Z S D range, a behavior due to the differential influence of the components that contribute to light attenuation as Z S D change [21].
The analysis of a ( λ ) i n   s i t u resulted in 92 stations classified into a Jerlov water type; the remaining 21 stations failed to meet the criteria for inclusion into a given water type. Intermediate water types were therefore added, i.e., 2, 4, 6, and 8 (Figure 5), supporting the allocation of a water type to the 113 a ( λ ) i n   s i t u spectra.
Figure 6 illustrates the classification procedure into Jerlov water types. Four stations were selected as examples, which were contrasted according to a goodness-of-fit test based on a least-squares fitting method [35]. In each panel of Figure 6, a ( λ ) i n   s i t u of the selected stations and a ( λ ) m o d e l of different types of water (II, 4, 6, and 8) are displayed with the respective χ C a l 2 values that represent the integration of the square distances between a ( λ ) i n   s i t u and a ( λ ) m o d e l . The water type for which χ C a l 2 is minimum was selected (if the value was zero, this would imply a perfect fit, i.e., a ( λ ) i n   s i t u is equal to a ( λ ) m o d e l ). In Figure 6a, station D05 presented a χ C a l 2 = 1.46, this being the smallest value relative to all other stations, indicating that it must be classified as a type-II water. In Figure 6b, the lowest χ C a l 2 corresponded to station B06, so it was classified as type 4. For water type 6, which is exemplified in Figure 6c, station 247 showed the lowest χ C a l 2 . When stations were contrasted with water type 8 (Figure 6d), station 071 had the lowest χ C a l 2 .
The classification into Jerlov water types yielded the results shown in Table 3, with 48 oceanic stations (i.e., types I–III) and 65 coastal stations (i.e., types 1–9). No water type 3 was found in the reduced data set. Figure 4b shows that the clear water case ( Z S D ≥ 5.37 m.) comprises all the ocean groups (I, IA, IB, II, III) and the most transparent coastal groups (1–4), with K d i n   s i t u values of less than 0.2 m−1. The turbid-water case ( Z S D < 2.20 m) included the most turbid coastal waters (5–9), with K d i n   s i t u values above 0.4 m−1. Additionally, the transition zone shows the interaction between groups 4, 5, 6, and 7, comprising stations ranging from clear (4) to turbid (5–7) waters, where some stations (for example, group 6) show turbid waters while other stations in the same group belong to the transition zone. Figure 4b also shows an overlap of water types for a given Z S D in the group of oceanic waters. This also occurs for the group of clear coastal waters that includes types 1, 2, and 4, with an overlap between the few type 2 and type 1 cases. In addition, if data representing type 3 were available, these would presumably overlap with type 4. Finally, and consistent with the above, the group of turbid coastal waters (types 5–9) exhibits an overlap between optical types. These results show that the relationship between Z S D   ( or   deduced   K d   ( P A R ) ) and water type, as determined from a (λ), is not unique (i.e., a given Z S D or range of Z S D values may be associated to different water types), thus limiting the ability to derive specific inherent optical properties from Z S D as the only variable, even in statistic terms. This is hardly surprising, since K d   ( P A R ) is non-spectral and depends not only on a (λ) but also on spectral particulate backscattering [23]. Note that the model proposed by Solonenko and Mobley [30] to associate the inherent optical properties with Jerlov water type does not consider the contribution of non-phytoplankton particulate material, which comprises phytoplankton detritus plus other organic and mineral particles. They argue that it is sufficient to model absorption as a function of chlorophyll and CDOM in both Case-1 and Case-2 waters, and even for the most turbid waters. In areas highly influenced by non-phytoplankton particulate matter (e.g., mineral sources), however, the absorption of these components likely influences the association of the inherent optical properties with water type. Therefore, Jerlov’s classification needs to be adapted to account for such scenarios in turbid coastal environments, including coastal lagoons, estuaries, and river mouths.
Considering the 113 data that were optically classified into the different Jerlov water types (Table 3), a model might theoretically be derived for each type of water; however, the number of observations for some optical types is small. It was therefore decided to split the 113 data into two groups, oceanic and coastal, and work only with those types of water including more than 10 observations, aiming of derive a specific model for each. For estimating the models, observations for each type of water (oceanic, coastal, III, 1, and 7) were randomly sorted into two groups (50% for modeling and 50% for validation purposes). Once the models were obtained, these were applied to the dataset to validate them, and contrasted against model c, which is the best model from the previous analyses. These comparisons are shown in Table 4. In this case, MPI (Equation (12)) was not suitable due to the small number of observations; thus, the best model was the one showing the lowest MAE (Equation (9)) and RMSD (Equation (10)) values, and the BIAS (Equation (11)) value closest to zero.
Model c is the best fit in all cases because this model contemplates three intervals of Z S D ; also, in each interval, this model makes an approximation based on a nonlinear model (Equation (2)). Consequently, this is an adaptive model that estimates the best combination regardless of the optical type of water being analyzed. In this regard, we consider that the development of model c simplifies of the estimate K d based on Z S D regardless of the type of water. Model c can be applied to different marine optical conditions; however, it is advisable to continue obtaining measurements of Jerlov’s water types to determine the contribution of each individual component present in seawater to the calculation of K d .
Continuing with the simultaneous measurement of Z S D and K d with an irradiance-meter will facilitate obtaining better coefficients in each equation of the adaptive model. Additional measurements should be performed, especially in turbid coastal waters, including coastal lagoons, estuaries, and river mouths.
There is the need to implement marine monitoring systems to detect changes in ecosystems. Water turbidity may provide information on environmental alterations, and the monitoring thereof based on estimations of K d   ( PAR ) from Z S D using empirical models such as model c is sufficiently accurate and cost-effective. The potential sources of error in these estimates, which were analyzed by Preisendorfer [10], should however be kept in mind to ensure that the results obtained reflect the true variability across water parcels.

4. Conclusions

K d is a valuable tool for monitoring both spatio-temporal changes and long-term trends in the water column. The estimation of K d based on Z S D measurements is a low-cost methodology that can be used systematically in oceanographic campaigns due to its easy application/implementation. However, to ensure consistent results, care must be taken regarding the methodology to measure Z S D . The classical approaches for calculating K d from Z S D , based on a single O D S D value, do not accurately represent the broad range of optical conditions that occur in the marine environment. The adaptive model proposed in this work represents the optical diversity under various conditions, ranging from clear ocean waters to highly turbid coastal waters. It provides continuity across Z S D and, importantly, improves K d retrieval under clear, turbid, and transition scenarios. This model calculates K d considering three ranges of Z S D values, as described by the following equations:
If   Z S D < 2.20   m ,   then   K d m o d e l   c = 1.16 ( Z S D ) 0.62 If   2.20   m Z S D < 5.37   m ,   then K d m o d e l   c = exp ( ( 0.15 l o g Z S D × 0.62 ) × 1.68 l o g Z S D 0.89 + ( 0.48 l o g Z S D × 0.72 ) × l o g Z S D 0.79 0.89 ) If   Z S D 5.37   m ,   then   K d m o d e l   c = 0.62 ( Z S D ) 0.72
The marine optical water classification is a potential approach in studies addressing the relationship between K d   ( PAR ) and optical characteristics. However, our classification of 113 stations with absorption data into Jerlov water types indicated that no unique water type could be related to a given Z S D or K d   ( PAR ) , thus making it difficult to use Z S D measurements to infer the optical properties and chlorophyll concentrations of particular water types. This is likely due to the fact that K d   ( PAR ) is the overall result of the variability in both the quantity and type of material (dissolved or particulate matter) present in the water column. In addition, it should be noted that different optical types may occur at the same time in the water column, so that K d   ( PAR ) may result from the combination of different water types. Given this complexity, data derived from satellite observations are promising and this field of research should be further refined in the future.

Supplementary Materials

The following are available online at https://www.mdpi.com/2077-1312/8/8/558/s1. Table S1. Derived K_d from model c using Z_SD ranging from 0.5 to 50 m.

Author Contributions

Conceptualization, A.C.-R., E.S.-d.-Á., A.G.-S., R.F., M.-T.S.-F., J.L.-C., L.S.-V. and L.E.-P.; Data curation, A.C.-R. and E.S.-d.-Á.; Formal analysis, A.C.-R., E.S.-d.-Á., R.F. and J.T.; Funding acquisition, E.S.-d.-Á., A.G.-S., R.F. and L.S.-V.; Investigation, A.C.-R., E.S.-d.-Á., A.G.-S., R.F., M.-T.S.-F., J.T., J.L.-C., L.S.-V. and L.E.-P.; Methodology, A.C.-R., E.S.-d.-Á., A.G.-S., R.F., M.-T.S.-F., J.T., J.L.-C., L.S.-V. and L.E.-P.; Project administration, E.S.-d.-Á., A.G.-S., R.F. and L.S.-V.; Resources, E.S.-d.-Á., A.G.-S. and R.F.; Supervision, A.C.-R., E.S.-d.-Á., A.G.-S., R.F., M.-T.S.-F., J.T., J.L.-C., L.S.-V. and L.E.-P.; Validation, A.C.-R., E.S.-d.-Á., R.F. and J.T.; Visualization, A.C.-R., E.S.-d.-Á., R.F. and J.T.; Writing—original draft, A.C.-R., E.S.-d.-Á., A.G.-S., R.F., M.-T.S.-F. and J.L.-C.; Writing—review and editing, A.C.-R., E.S.-d.-Á., R.F., M.-T.S.-F. and J.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the projects "Influencia de remolinos de mesoescala sobre hábitats de larvas de peces (con énfasis en especies de importancia comercial) en la zona de mínimo de oxígeno del océano pacífico frente a México: océano abierto y efecto de islas" (“Influence of Mesoscale Eddies on the Habitats of Fish Larvae (with Emphasis on Species of Commercial Importance) in the Oxygen Minimum Layer of the Pacific Ocean off Mexico: Open Ocean and Effect of Islands”) (SEP-CONACyT 236864), “Fronteras de la Ciencia: Probando paradigmas sobre la expansión de la zona del mínimo de oxígeno: reducción del hábitat vertical del zooplancton y su efecto en el ecosistema pelágico mediante métodos de muestreo autónomos” (“Frontiers of Science: Testing Paradigms on the Expansion of the Oxygen Minimum Layer: Reduction of the Vertical Habitat of Zooplankton and its Effect on the Pelagic Ecosystem through Autonomous Sampling Methods” (CONACYT 8662), “Flujo atmosférico de metales bioactivos y sus solubilidad en el Golfo de California: un escenario hacia el cambio climático” (“Atmospheric Flow of Bioactive Metals and their Solubility in the Gulf of California: a Scenario toward Climate Change (UABC-IIO), “Regionalización dinámica de la Bahía de Todos Santos mediante imágenes de color del océano” (“Dynamic Regionalization of Todos Santos Bay through Ocean Color Images” supported by the 18th Internal Call at UABC, ANTARES (IAI CRN393), SIMAC-CONACYT; “Dinámica Costera En Inmediaciones De San Felipe, B.C. (“Coastal Dynamics in the Vicinity of San Felipe, B.C.”); “Condiciones Oceanográficas Del Área De Refugio Para La Protección De La Vaquita Marina e Inmediaciones” (“Oceanographic Conditions in the Reserve Area for the Protection of the Vaquita and Adjacent Areas" (Secretariat of the Navy); “Estudio integral para la determinación del polígono para vertimientos de materiales producto del dragado en bahía Sebastián Vizcaíno, B.C.” (“Integral Study to Determine the Polygon for Emptying Dredged Materials in Bahia Sebastian Vizcaino, B.C.”) (Secretariat of the Navy), SIMAC-2000107017 (CICESE); and “Ecological Monitoring of the Upper Gulf of California” (PANGAS-Packard Foundation); INP-CICIMAR: SIP 1721,20160514-CONACYT 236864). M.-T.S.-F. was beneficiary of two post-doctoral research grants, one by the Spanish Ministry of Education Culture and Sports number CAS18/00107, and one by the Valencian Conselleria d’Educació, Investigació, Cultura i Esport number BEST/2017/217; both in support of her stay at The Universidad Autónoma de Baja California (México) during advisory time.

Acknowledgments

The authors wish to thank Consejo Nacional de Ciencia y Tecnología (CONACyT) for the grant awarded to the first author in her studies. Thanks also to the SIMBIOS NASA Program, Universidad Autónoma de Baja California, Instituto de Investigaciones Oceanológicas, Centro de Investigación Científica y de Educación Superior de Ensenada, Secretaría de Marina Armada de México, Dirección General Adjunta de Oceanografía, Hidrografía y Meteorología, Instituto Politécnico Nacional. Maria Elena Sánchez-Salazar edited the English manuscript.

Conflicts of Interest

The authors declare no conflict of interest. The funding sponsors played no role in the design of the study; the collection, analysis, or interpretation of data; the drafting of the manuscript; or the decision to publish the results.

References

  1. Kirk, J.T.O. Light and Photosynthesis in Aquatic Ecosystems, 3rd ed.; Cambridge University Press: Cambridge, UK, 2011; p. 649. [Google Scholar]
  2. Frouin, R.; Ramon, D.; Boss, E.; Jolivet, D.; Compiègne, M.; Tan, J.; Bouma, H.; Jackso, T.; Franz, B.; Platt, T.; et al. Satellite Radiation Products for Ocean Biology and Biogeochemistry: Needs, State-of-the-Art, Gaps, Development Priorities, and Opportunities. Front. Mar. Sci. 2018, 5, 3. [Google Scholar] [CrossRef] [Green Version]
  3. Platt, T.; Denman, K.L.; Jassby, A.D. Modeling the Productivity of Phytoplankton, in the Sea: Ideas and Observations on Progress in the Study of the Seas; Goldberg, E.D., Ed.; John Wiley: New York, NY, USA, 1977; pp. 807–856. [Google Scholar]
  4. Falkowski, P.G.; Raven, J.A. Aquatic Photosynthesis; Blackwell Science: Malden, MA, USA, 1997; p. 375. [Google Scholar]
  5. Antoine, D.; Babin, M.; Berthon, J.; Bricaud, A.; Gentili, B.; Loisel, H.; Maritorena, S.; Stramski, D. Shedding Light on the Sea: André Morel’s Legacy to Optical Oceanography. Annu. Rev. Mar. Sci. 2014, 6, 1–21. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  6. Secchi, A. Schreiben des Herrn Prof. Secchi, Directors der Sternwarte des Collegio Romano, an den Herausgeber. Astron. Nachr. 1866, 68, 63. [Google Scholar] [CrossRef] [Green Version]
  7. Wernard, M.R. On the history of the Secchi Disk. J. Eur. Opt. Soc.-Rapid 2010, 5, 100135. [Google Scholar] [CrossRef] [Green Version]
  8. Davies-Colley, R.J.; Vant, W.N.; Smith, D.G. Colour and Clarity of Natural Waters. Science and Management of Optical Water Quality; Ellis-Horwood: New York, NY, USA, 1993; p. 310. [Google Scholar]
  9. Poole, H.H.; Atkins, W.R.G. Photo-Electric Measurements of Submarine Illumination throughout the Year. J. Mar. Biol Assoc. UK 1929, 16, 297–324. [Google Scholar] [CrossRef] [Green Version]
  10. Preisendorfer, R.W. Secchi disk science: Visual optics of natural waters. Limnol. Oceanogr. 1986, 31, 909–926. [Google Scholar] [CrossRef] [Green Version]
  11. Lund-Hansen, L.C. Diffuse Attenuation Coefficients Kd(PAR) at the Estuarine North Sea–Baltic Sea Transition: Time-Series, Partitioning, Absorption, and Scattering. Estua Coast. Shelf Sci. 2004, 61, 251–259. [Google Scholar] [CrossRef]
  12. Pope, R.M.; Fry, E.S. Absorption Spectrum (380–700 nm) of Pure Water. II. Integrating Cavity Measurements. Appl. Opt. 1997, 36, 8710–8723. [Google Scholar] [CrossRef]
  13. Prieur, L.; Sathyendranath, S. An Optical Classification of Coastal and Oceanic Waters Based on the Specific Spectral Absorption Curves of Phytoplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials. Limnol. Oceanogr. 1981, 26, 671–689. [Google Scholar] [CrossRef]
  14. Santamaría-del-Ángel, E.; Millán-Núñez, R.; González-Silvera, A.; Cajal-Medrano, R. Producción Primaria Fitoplanctónicas. En Manuales del cuerpo Académico de Ecología del Fitoplancton de la Facultad de Ciencias Marinas de la Universidad Autónoma de Baja California; Series White Papers POPEYE 41 p; Universidad Autónoma de Baja California, Facultad de Ciencias Marinas: Ensenada, Mexico, 2005. [Google Scholar] [CrossRef]
  15. Holmes, R.W. The Secchi disk in turbid coastal waters. Limnol. Oceanogr. 1970, 15, 688–694. [Google Scholar] [CrossRef]
  16. Megard, R.O.; Berman, T. Effects of algae on the Secchi transparency of the southeastern Mediterranean Sea. Limnol. Oceanogr. 1989, 34, 1640–1655. [Google Scholar] [CrossRef]
  17. Montes-Hugo, M.A.; Álvarez-Borrego, S. Empirical relations to estimate PAR attenuation in San Quintín Bay, using Secchi depth and sighting range. Cienc Mar. 2005, 31, 685–695. [Google Scholar] [CrossRef]
  18. Lee, Z.; Shang, S.; Du, K.; Wei, J. Resolving the Long-Standing Puzzles about the Observed Secchi Depth Relationships. Limnol. Oceanogr. 2018, 63, 2321–2336. [Google Scholar] [CrossRef]
  19. Harvey, E.T.; Walve, J.; Andersson, A.; Karlson, B.; Kratzer, S. The effect of optical properties on Secchi depth and implications for eutrophication management. Front. Mar. Sci. 2019, 5, 496. [Google Scholar] [CrossRef] [Green Version]
  20. Steinmetz, H.; Staudinger, M.; Balch, W.M. Analyzing the Effects of Coccolithophore Concentration on the Relationship between Vertical Absorption Coefficient and Secchi Disk Depth. Student Showcase. 2019. Available online: https://scholarworks.umass.edu/sustainableumass_studentshowcase/26 (accessed on 10 June 2020).
  21. Gallegos, C.L.; Werdell, P.J.; McClain, C.R. Longterm changes in light scattering in Chesapeake Bay inferred from Secchi depth, light attenuation, and remote sensing measurements. J. Geophys. Res. 2011, 116, C00H08. [Google Scholar] [CrossRef]
  22. Barbosa, A.; Domingues, R. Effects of Nutrient and Light Enrichment on Phytoplankton Growth. In Practical Experiments Guide for Ecohydrology; Chícharo, L., Wagner, I., Chicharo, M., Lapinska, M., Zalewski, M., Eds.; UNESCO: Venice, Italy, 2009; pp. 27–30. [Google Scholar]
  23. Lee, Z.; Shang, S.; Hu, C.; Du, K.; Weidemann, A.; Hou, W.; Lin, J.; Lin, G. Secchi disk depth: A new theory and mechanistic model for underwater visibility. Remote Sens. Environ. 2015, 169, 139–149. [Google Scholar] [CrossRef] [Green Version]
  24. IOCCG. Remote Sensing of Inherent Optical Properties: Fundamentals, Tests of Algorithms, and Applications. In Reports of the International Ocean Colour Coordinating Group No. 5; Lee, Z.P., Ed.; IOCCG: Dartmouth, NS, Canada, 2006; p. 126. [Google Scholar]
  25. Mobley, C.D.; Sundman, L.K. HydroLight 5.2 User’s Guide; Sequoia Scientific: Seattle, WA, USA, 2013. [Google Scholar]
  26. Padial, A.A.; Thomaz, S.M. Prediction of the light attenuation coefficient through the Secchi disk depth: Empirical modeling in two large Neotropical ecosystems. Limnology 2008, 9, 143–151. [Google Scholar] [CrossRef]
  27. Ficek, D.; Zapadka, T. Variability of bio-optical parameters in Lake Jasień Północny and Lake Jasień Południowy. Limnol. Rev. 2010, 10, 67–76. [Google Scholar] [CrossRef] [Green Version]
  28. Zhang, Y.; Liu, X.; Yin, Y.; Wang, M.; Qin, B. Predicting the light attenuation coefficient through Secchi disk depth and beam attenuation coefficient in a large, shallow, freshwater lake. Hydrobiologia 2012, 693, 29–37. [Google Scholar] [CrossRef]
  29. Jerlov, N.G. Optical Oceanography; American Elsevier Publishing Company Incorporation: New York, NY, USA, 1968; p. 194. [Google Scholar]
  30. Solonenko, M.G.; Mobley, C.D. Inherent optical properties of Jerlov water types. Appl. Opt. 2015, 54, 5392–5401. [Google Scholar] [CrossRef]
  31. Tara Oceans Consortium, Coordinators; Tara Oceans Expedition. Environmental Context of All Samples from the Tara Oceans Expedition (2009–2013), about Mesoscale Features; PANGAEA: Bremerhaven, Germany, 2016. [Google Scholar] [CrossRef]
  32. Werdell, P.J.; Bailey, S.W. An improved bio-optical data set for ocean color algorithm development and satellite data product validation. Remote Sens. Environ. 2005, 98, 122–140. [Google Scholar] [CrossRef]
  33. Steyerberg, E.W. Validation of Prediction Models. In Clinical Prediction Models. Statistics for Biology and Health, 2nd ed.; Springer: Cham, Germany, 2019; pp. 329–344. [Google Scholar]
  34. IOCCG. Synergy between Ocean Colour and Biogeochemical/Ecosystem Models 2020; IOCCG Report Series, No. 19; Dutkiewicz, S., Ed.; International Ocean Colour Coordinating Group: Dartmouth, NS, Canada, 2020. [Google Scholar] [CrossRef]
  35. Xu, W.; Chen, W.; Liang, Y. Feasibility Study on the Least Square Method for Fitting Non-Gaussian Noise Data. Phys. A Stat. Mech. Appl. 2017, 492, 1917–1930. [Google Scholar] [CrossRef] [Green Version]
  36. Ocean Color Data. Available online: https://oceandata.sci.gsfc.nasa.gov/ (accessed on 5 July 2020).
  37. Kahru, M.; Kudela, R.M.; Anderson, C.R.; Mitchell, B.G. Optimized merger of ocean chlorophyll algorithms of MODIS-Aqua and VIIRS. IEEE Geosci. Remote Sens. 2015, 12, 11. [Google Scholar] [CrossRef] [Green Version]
  38. Kahru, M.; Di Lorenzo, E.; Manzano-Sarabia, M.; Mitchell, B.G. Spatial and temporal statistics of sea surface temperature and chlorophyll fronts in the California Current. J. Plankton Res. 2012, 34, 749–760. [Google Scholar] [CrossRef] [Green Version]
  39. Wilcoxon, F. Individual Comparisons by Ranking Methods. Biom. Bull. 1945, 1, 80–83. [Google Scholar] [CrossRef]
  40. Wilcoxon, F.; Katti, S.K.; Wilcox, R.A. Critical Values and Probability Levels for the Wilcoxon Rank Sum Test and the Signed Rank Test; American Cyanamid Co., & Lederle Lab.: Pearl River, NY, USA, 1963. [Google Scholar]
  41. Wilcoxon, F.; Katti, S.K.; Wilcox, R.A. Critical Values and Probability Levels for the Wilcoxon Rank Sum Test and the Wilcoxon Signed Rank Test. In Selected Tables in Mathematical Statistics; Amer Mathematical Society: Providence, RI, USA, 1970; Volume 1, pp. 171–259. [Google Scholar]
  42. Mitchell, B.G.; Bricaud, A.; Carder, K.; Cleveland, J.; Ferrari, G.M.; Gould, R.; Kahru, M.; Kishino, M.; Maske, H.; Moisan, T.; et al. Determination of Spectral Absorption Coefficients of Particles, Dissolved Material and Phytoplankton for Discrete Water Samples. In Ocean Optics Protocols for Satellite Ocean Color Sensor Validation; Revision 2; Fargion, G.S., Mueller, J.L., McClain, C.R., Eds.; Goddard Space Flight Space Center: Greenbelt, MD, USA, 2000; pp. 125–153. [Google Scholar]
  43. Mueller, J.L.; Austin, R.W. Ocean Optics Protocols for SeaWIFS Validation; Revision 1; SeaWiFS Technical Report Series; Hooker, S.B., Firestone, E.R., Acker, J.G., Mueller, J.L., Austin, R.W., Eds.; Goddard Space Flight Space Center: Greenbelt, MD, USA, 1995; p. 25.
  44. Zar, J.H. Biostatistical Analysis, 5th ed.; Prentice-Hall: New Jersey, NJ, USA, 2010; p. 944. [Google Scholar]
  45. Koenings, J.P.; Edmundson, J.A. Secchi disk and photometer estimates of light regimes in Alaskan lakes: Effects of yellow color and turbidity. Limnol. Oceanogr. 1991, 36, 91–105. [Google Scholar] [CrossRef]
  46. Lugo-Fernández, A.; Gravois, M.; Montgomery, T. Analysis of Secchi depths and light attenuation coefficients in the Louisiana-Texas shelf, northern Gulf of Mexico. Gulf Mex. Sci. 2008, 26, 14–27. [Google Scholar] [CrossRef] [Green Version]
  47. Santamaría-del-Ángel, E.; Millán-Núñez, R.; Soto, I.; González-Silvera, A.; Wolny, J.; Cerdeira-Estrada, S.; Cajal-Medrano, R.; Muller-Karger, F.; Padilla-Rosas, Y.X.S.; Mercado-Santana, A.; et al. Phytoplankton Blooms: New Initiative Using Marine Optics as a Basis for Monitoring Programs. In Coastal Ecosystems: Experiences and Recommendations for Environmental Monitoring Programs; Nova Science Publisher: New York, NY, USA, 2015; Chapter 4. [Google Scholar]
  48. Aguilar-Maldonado, J.A.; Santamaría-del-Ángel, E.; González-Silvera, A.; Cervantes-Rosas, O.; López, L.M.; Gutiérrez-Magness, A.; Cerdeira-Estrada, S.; Sebastiá-Frasquet, M.T. Identification of Phytoplankton Blooms under the Index of Inherent Optical Properties (IOP Index) in Optically Complex Waters. Water 2018, 10, 129. [Google Scholar] [CrossRef] [Green Version]
  49. Austin, R.W.; Petzold, T.J. The Determination of the Diffuse Attenuation Coefficient of Sea Water Using the Coastal Zone Color Scanner. In Oceanography from Space; Springer: Boston, MA, USA, 1981; pp. 239–256. [Google Scholar]
  50. Hicks, B.J.; Stichbury, G.A.; Brabyn, L.K.; Allan, M.G.; Ashraf, S. Hindcasting water clarity from Landsat satellite images of unmonitored shallow lakes in the Waikato region, New Zealand. Environ. Monit. Assess. 2013, 185, 7245–7261. [Google Scholar] [CrossRef]
  51. Butt, M.J.; Nazeer, M. Landsat ETM+ Secchi Disc Transparency (SDT) retrievals for Rawal Lake, Pakistan. Adv. Space Res. 2015, 56, 1428–1440. [Google Scholar] [CrossRef]
  52. Rodrigues, T.; Alcântara, E.; Watanabe, F.; Imai, N. Retrieval of Secchi disk depth from a reservoir using a semi-analytical scheme. Remote Sens. Environ. 2017, 198, 213–228. [Google Scholar] [CrossRef] [Green Version]
  53. Leite, H.R.; de Oliveira, F.A.; Drago, D.; Muraro, A.; Teixeira, L.F.; Hainosz, F.S.; Prochnow, R.M.; Quicu, S.T.; Nascimento, C. Natural effects on remote sensing of water quality parameters data: A case study on available algorithms at the Jupia Reservoir, Brazil. In Remote Sensing of the Ocean, Sea Ice, Coastal Waters, and Large Water Regions; International Society for Optics and Photonics: Washington, DC, USA, 2019; Volume 11150, p. 1115006. [Google Scholar]
  54. Nouchi, V.; Kutser, T.; Wüest, A.; Müller, B.; Odermatt, D.; Baracchini, T.; Bouffard, D. Resolving biogeochemical processes in lakes using remote sensing. Aquat. Sci. 2019, 81, 27. [Google Scholar] [CrossRef] [Green Version]
  55. Kim, S.H.; Yang, C.S.; Ouchi, K. Validation of the semi-analytical algorithm for estimating vertical underwater visibility using MODIS data in the waters around Korea. Korean J. Remote Sens. 2013, 29, 601–610. [Google Scholar] [CrossRef] [Green Version]
  56. Tyler, J.E. The Secchi Disk. Limnol. Oceanogr. 1968, 13, 1–6. [Google Scholar] [CrossRef]
  57. Doron, M.; Babin, M.; Mangin, A.; Hembise, O. Estimation of light concentration, and horizontal and vertical visibility in oceanic and coastal waters from surface reflectance. J. Geophys. Res. 2007, 112, C06003. [Google Scholar] [CrossRef] [Green Version]
  58. Doron, M.; Babin, M.; Hembise, O.; Mangin, A.; Garnesson, P. Ocean transparency from space: Validation of algorithm estimating Secchi depth using MERIS, MODIS and SeaWiFS data. Remote Sens. Environ. 2011, 115, 2986–3001. [Google Scholar] [CrossRef]
  59. Betancur-Turizo, S.P.; González-Silvera, A.G.; Santamaría-Del-Ángel, E.; Millán-Núñez, R.; Millán-Núñez, E.; García-Nava, H.; Godínez, V.M.; Sánchez-Velasco, L. Variability in the Light Absorption Coefficient by Phytoplankton, Non-Algal Particles and Colored Dissolved Organic Matter in the Northern Gulf of California. Open J. Mar. Sci. 2018, 8, 20–37. [Google Scholar] [CrossRef] [Green Version]
  60. Jiang, D.; Matsushita, B.; Setiawan, F.; Vundo, A. An improved algorithm for estimating the Secchi disk depth from remote sensing data based on the new underwater visibility theory. ISPRS J. Photogramm. 2019, 152, 13–23. [Google Scholar] [CrossRef]
  61. Liu, Y.; Xiao, C.; Li, J.; Zhang, F.; Wang, S. Secchi Disk Depth Estimation from China’s New Generation of GF-5 Hyperspectral Observations Using a Semi-Analytical Scheme. Remote Sens. 2020, 12, 1849. [Google Scholar] [CrossRef]
  62. Arabi, B.; Salama, M.S.; Pitarch, J.; Verhoef, W. Integration of in-situ and multi-sensor satellite observations for long-term water quality monitoring in coastal areas. Remote Sens. Environ. 2020, 239, 111632. [Google Scholar] [CrossRef]
  63. Djavidnia, S.; Ott, M.; Seeyave, S. (Eds.) Oceans and Society: Blue Planet; Cambridge Scholars Publishing: Newcastle upon Tyne, UK, 2014. [Google Scholar]
Figure 1. Location of stations; the color bar indicates the bathymetry, in meters. (a) Stations of the Tara Ocean Stations Consortium [31] and Megard and Berman [16]. (b) Stations of the NASA SeaBass file [32], POPEYE database, Gallegos et al. [21], and Montes-Hugo and Alvarez-Borrego [17].
Figure 1. Location of stations; the color bar indicates the bathymetry, in meters. (a) Stations of the Tara Ocean Stations Consortium [31] and Megard and Berman [16]. (b) Stations of the NASA SeaBass file [32], POPEYE database, Gallegos et al. [21], and Montes-Hugo and Alvarez-Borrego [17].
Jmse 08 00558 g001
Figure 2. Comparative analysis between the attenuation coefficient estimated in situ ( K d i n   s i t u ) and the attenuation coefficients modeled. (a) K d m o d e l   a , (b) K d m o d e l   b , and (c) K d m o d e l   c .
Figure 2. Comparative analysis between the attenuation coefficient estimated in situ ( K d i n   s i t u ) and the attenuation coefficients modeled. (a) K d m o d e l   a , (b) K d m o d e l   b , and (c) K d m o d e l   c .
Jmse 08 00558 g002
Figure 3. Comparison of K d i n   s i t u vs. K d   m o d e l calculated with the model of Lee et al. [18] (circles) and with model c (crosses), for the full database (black) and for two cruises with different optical conditions: Cal9709 (yellow and blue); Ties9802 (red and green).
Figure 3. Comparison of K d i n   s i t u vs. K d   m o d e l calculated with the model of Lee et al. [18] (circles) and with model c (crosses), for the full database (black) and for two cruises with different optical conditions: Cal9709 (yellow and blue); Ties9802 (red and green).
Jmse 08 00558 g003
Figure 4. (a) Relationship between Z S D and K d   i n   s i t u according to three Z S D ranges (679 stations); (b) relationship between Z S D and K d   i n   s i t u according to Jerlov water type (113 stations with absorption data).
Figure 4. (a) Relationship between Z S D and K d   i n   s i t u according to three Z S D ranges (679 stations); (b) relationship between Z S D and K d   i n   s i t u according to Jerlov water type (113 stations with absorption data).
Jmse 08 00558 g004
Figure 5. Intermediate water types (dashed lines), added to the original Jerlov coastal water types.
Figure 5. Intermediate water types (dashed lines), added to the original Jerlov coastal water types.
Jmse 08 00558 g005
Figure 6. Least-squares fitting method for four selected stations. The black line indicates a ( λ ) m o d e l values for the different water types; the dotted line, a ( λ ) i n   s i t u for stations. χ C r i t 2 marks the maximum allowable tolerance for the fit. (a) Example of the fit for type II, where station D05 gave the best fit; (b) example of the fit for type 4, where station B06 gave the best fit; (c) example of the fit for type 6, where station 247 gave the best fit; (d) example of the fit for type 8, where station 071 gave the best fit.
Figure 6. Least-squares fitting method for four selected stations. The black line indicates a ( λ ) m o d e l values for the different water types; the dotted line, a ( λ ) i n   s i t u for stations. χ C r i t 2 marks the maximum allowable tolerance for the fit. (a) Example of the fit for type II, where station D05 gave the best fit; (b) example of the fit for type 4, where station B06 gave the best fit; (c) example of the fit for type 6, where station 247 gave the best fit; (d) example of the fit for type 8, where station 071 gave the best fit.
Jmse 08 00558 g006
Table 1. Evaluation of K d i n   s i t u versus Z S D models.
Table 1. Evaluation of K d i n   s i t u versus Z S D models.
ReferenceEquation Z S D   Intervals   ( m ) MAERMSDBIASMPI
Poole and Atkins [9] K d = 1.7 / Z S D 1.9–350.1820.2850.2170.104
Poole and Atkins [9]
Holmes [15]
K d = 1.7 / Z S D
K d = 1.4 / Z S D
1.9–35
2–12
0.1250.2730.1200.416
Megard and Berman [16] K d = 1.54 / Z S D 6–460.1420.2850.1180.229
Lee et al. [18] K d = 1.48 / Z S D All intervals0.1340.2850.0780.354
Montes-Hugo and Álvarez-Borrego [17] K d = 1.45 / ( Z S D ) 1.10 1–120.1410.359−0.0130.250
Model a K d = 1.37 / Z S D All intervals0.1180.2850.0030.583
Model b K d = 1.18 / ( Z S D ) 0.92 All intervals0.0970.2650.0020.708
Model cEquations (15)–(17)<2.20
Transition zone
≥5.37
0.0830.2390.0010.854
Table 2. Evaluation of K d i n   s i t u versus Z S D and satellite models.
Table 2. Evaluation of K d i n   s i t u versus Z S D and satellite models.
ReferenceEquation Z S D   Intervals   ( m ) MAERMSDBIASMPI
Poole and Atkins [9] K d = 1.7 / Z S D 1.9–350.0410.073−0.0280.074
Poole and Atkins [9] Holmes [15] K d = 1.7 / Z S D
K d = 1.4 / Z S D
1.9–35
2–12
0.0340.063−0.0060.460
Megard and Berman [16] K d = 1.54 / Z S D 6–460.0320.063−0.0110.425
Lee et al. [18] K d = 1.48 / Z S D All intervals0.0310.062−0.0050.740
Montes-Hugo and Álvarez-Borrego [17] K d = 1.45 / ( Z S D ) 1.10 1–120.0340.0030.0210.425
Model a K d = 1.37 / Z S D All intervals0.0290.0630.0070.592
Model b K d = 1.18 / ( Z S D ) 0.92 All intervals0.0320.0720.0090.388
Model cEquations (15)–(17)<2.200.0260.0620.0050.814
K d satellite model (490)Standard SeaDAS productTransition zone
≥5.37
0.0790.1870.0150.074
Table 3. Number of observations (N) classified into a Jerlov water type for the 113 stations with a.
Table 3. Number of observations (N) classified into a Jerlov water type for the 113 stations with a.
DescriptorsOceanicCoastal
Water TypeIIAIBIIIII123456789
N244826212-6571468
Table 4. Evaluation of the K d i n   s i t u versus a specific model by water type and model c. The bold show the best results.
Table 4. Evaluation of the K d i n   s i t u versus a specific model by water type and model c. The bold show the best results.
Water TypeModelEquationMAERMSDBIAS
Oceanic groupModel c
Model oceanic
Equations (15)–(17)
K d = 0.089 / ( Z S D ) 0.518
0.016
0.550
0.018
0.020
0.016
0.055
Coastal groupModel c
Model coastal
Equations (15)–(17)
K d = 1.79 / ( Z S D ) 0.978
0.149
0.346
0.260
0.469
0.037
−0.343
IIIModel c
Model III
Equations (15)–(17)
K d = 0.37 / ( Z S D ) 0.673
0.011
0.027
0.009
0.010
0.011
0.027
1Model c
Model 1
Equations (15)–(17)
K d = 0.66 / ( Z S D ) 0.784
0.021
0.027
0.027
0.027
0.016
0.025
7Model c
Model 7
Equations (15)–(17)
K d = 0.95 / ( Z S D ) 0.667
0.051
0.105
0.053
0.074
−0.032
0.105

Share and Cite

MDPI and ACS Style

Castillo-Ramírez, A.; Santamaría-del-Ángel, E.; González-Silvera, A.; Frouin, R.; Sebastiá-Frasquet, M.-T.; Tan, J.; Lopez-Calderon, J.; Sánchez-Velasco, L.; Enríquez-Paredes, L. A New Algorithm to Estimate Diffuse Attenuation Coefficient from Secchi Disk Depth. J. Mar. Sci. Eng. 2020, 8, 558. https://doi.org/10.3390/jmse8080558

AMA Style

Castillo-Ramírez A, Santamaría-del-Ángel E, González-Silvera A, Frouin R, Sebastiá-Frasquet M-T, Tan J, Lopez-Calderon J, Sánchez-Velasco L, Enríquez-Paredes L. A New Algorithm to Estimate Diffuse Attenuation Coefficient from Secchi Disk Depth. Journal of Marine Science and Engineering. 2020; 8(8):558. https://doi.org/10.3390/jmse8080558

Chicago/Turabian Style

Castillo-Ramírez, Alejandra, Eduardo Santamaría-del-Ángel, Adriana González-Silvera, Robert Frouin, María-Teresa Sebastiá-Frasquet, Jing Tan, Jorge Lopez-Calderon, Laura Sánchez-Velasco, and Luis Enríquez-Paredes. 2020. "A New Algorithm to Estimate Diffuse Attenuation Coefficient from Secchi Disk Depth" Journal of Marine Science and Engineering 8, no. 8: 558. https://doi.org/10.3390/jmse8080558

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop