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Abstract
Accurate estimation of the diffuse attenuation coefficient of photosynthetically active radiation, Kd(PAR), is critical for understanding and modeling key physical, chemical, and biological processes in waters. In this study, a deep learning model (DLKPAR) was developed for remotely estimating Kd(PAR). Compared to the traditional empirical algorithms and semi-analytical algorithm, DLKPAR demonstrated an improvement in the model’s stability and accuracy. By using in situ NOMAD data to evaluate the model’s performance, DLKPAR had lower root mean square difference (RMSD; 0.028 vs. 0.030-0.048 m-1) and mean absolute relative difference (MARD; 0.14 vs. 0.17-0.25) and higher R2 (0.94 vs. 0.82-0.94). The statistical results of the matchup NOMAD and Argo data to the MODIS also indicated DLKPAR improves the inversion accuracy of Kd(PAR) and could be applied to remotely estimate Kd(PAR) in the global oceans. Therefore, we anticipate that DLKPAR could yield reliable Kd(PAR) values from ocean color remote sensing, providing an accurate estimation of visible light attenuation in the upper ocean and facilitating biogeochemical cycle research.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photosynthetically active radiation (PAR, 400–700 nm), a natural component of irradiance that reaches the Earth, plays a vital role in regulating the species and distribution of algae and aquatic plants [1] and, in turn, has a significant impact on the precise estimation of primary productivity in waters [2–5]. The vertical distribution of PAR under the sea surface can be characterized by the downwelling diffuse attenuation coefficient of PAR (Kd(PAR), m-1), which represents the ability of solar radiation to penetrate the water column [6–8]. Kd(PAR) is usually determined by four optically active components, namely pure sea water, phytoplankton, chromophoric dissolved organic matter (CDOM), suspended particulate matter (SPM) [9–11]. Accurately estimating Kd(PAR) throughout the water column is crucial for understanding upper ocean ecological processes, heat budget, and biogeochemical cycles in the upper ocean [12–15].
In the past few decades, many algorithms have been proposed to quantify Kd(PAR) based on spectral measurements of seawater, mainly including empirical algorithms [6,16–18] and semi-analytical algorithms [7]. Empirical algorithms typically rely on remote sensing reflectance (Rrs, sr-1) to derive intermediate variables, which are then used to calculate Kd(PAR). For example, Morel et al. [16] use chlorophyll (Chl, mg/m3) as the intermediate variable, while Saulquin et al. [6] and Chen et al. [18] uses downwelling diffuse attenuation coefficient (Kd(λ), m-1) as the intermediate variable for their respective algorithms. Empirical formulas require sufficient data to parameterize the model and may only be valid for specific locations [19]. Semi-analytical algorithms primarily rely on Rrs to retrieve inherent optical parameters (IOPs), use IOPs to estimate Kd(PAR). Lee et al. [7] employed the widely used quasi-analytical algorithm (QAA) to derive the absorption coefficient (a, m-1) and backscatter coefficient (bb, m-1) at 490 nm. Subsequently, an inversion model is established for the profile of Kd(PAR) using simulation data obtained through Hydrolight [20]. As obtaining an adequate number of bands to characterize PAR can be challenging, scholars usually rely on a relationship between Kd(490) and Kd(PAR) in inversion algorithms [18]. However, since the blue light around 490 nm generally penetrates deepest in clear waters (e.g., Morel [21]), this can lead to an overestimation of light levels [16,22].
Deep learning algorithms are widely used in ocean color remote sensing, and have achieved promising outcomes in the inversion of apparent optical parameters (AOPs) [18,23,24], IOPs [25–27], and bio-optical parameters [28–30]. Jamet et al. [31] uses neural network to establish Kd(λ) model, but there is an assumption in the model that there is an inherent spectral relationship between Kd(λ) spectra. In fact, this assumption is not valid [19,32]. In a study on Kd(PAR), Chen et al. [18] noted that neural network models can be used to retrieve Kd(λ) from the remote sensing reflectance of the MODIS band spanning 443 to 667 nm, and establish the weight formula between Kd(PAR) and Kd(λ). However, there are three issues that need to be further considered. First, some deep learning models (e.g., Chen et al. [18]) exclude wavelength information < 440 nm, given that satellite sensors may have calibration and atmospheric correction problems at < 440 nm, especially in coastal waters. Secondly, current deep learning models generally have to develop an empirical formula to invert Kd(PAR) from Kd(λ), and an additional uncertainty may be introduced. Thirdly, not all of the current deep learning algorithms have been verified with data observed in situ [33]. Given the issues stated above, we propose a new deep learning model to estimate Kd(PAR), and the model performance is evaluated by using field in situ and satellite data. As reprocessing on satellite data may improve the quality of Rrs for wavelengths < 440 nm, and possibly more importantly, recently and proposedly launched ocean color satellites may have sensors to detect high-quality Rrs for wavelengths < 440 nm, it is essential to evaluate models which include the use of wavelength information < 440 nm. This model utilizes Rrs(λ) at seven selected wavelengths (400, 412, 443, 488, 531, 547, 667) as inputs and outputs Kd(PAR), thereby solving the issue of input wavelengths and circumventing the need for an additional empirical formula to convert Kd(λ) to Kd(PAR). This approach enables a precise estimation of the attenuation of the underwater light field and upper ocean primary productivity [34,35].
In Section 2, we present the data used for training and evaluating Kd(PAR) algorithm. Section 3 reviews the model used to calculate Kd(PAR) and the overall deep learning framework in this study. Section 4 introduces the inversion results and evaluates the performance of different Kd(PAR) models. In Section 5, we summarize our main findings and future prospectives.
2. Data
2.1 Simulated data
To determine the light field in the upper water column, a synthetic dataset was generated using Hydrolight 5.3 [20]. The models and input parameters used to calculate the water and atmospheric conditions by Hydrolight are provided below.
The Case 2 model was used to generate IOPs by Hydrolight in this study. Specifically, the absorption coefficient of the water, a(λ), is modeled as [36]:
Values of aw(λ) represents the absorption coefficient of pure seawater, which can be available from the literature [37,38]. aph(λ), ag(λ) and ad(λ) correspond to the spectral absorption coefficient of phytoplankton pigments, CDOM and SPM respectively, which are defined as: where a* c(λ) is the chlorophyll-specific absorption coefficient at λ [39], the slope parameters Sdm (∼0.007-0.015 nm-1) and Sg (∼0.01-0.02 nm-1) were taken as random values as in IOCCG-OCAG [40].The backscattering coefficient of the water, bb(λ), is modeled as [41]:
with values of backscattering coefficient of pure water, bbw(λ), from the literature [42]. The formula backscattering coefficient of phytoplankton, bbph(λ), is as follows [11]: Bph is the backscattering ratio of phytoplankton and a constant value of 1% was taken [40]. Parameters p1 (∼0.006-0.6) and p2 (∼-0.1-2) were random values within given ranges from IOCCG-OCAG [40]. Similarly, the spectral backscattering coefficient of SPM, bbdm, were modeled following: with p3 (∼0.006-0.6) and p4 (∼-0.2-2.2) also random values within given ranges, respectively.Here, we set Chl ranging from 0.01 - 50.0 mg m-3, with 20000 steps in 0.00025 mg m-3 intervals. For each Chl, ag(440) ranging from 0.01 - 2 m-1, and the concentration of SPM, which is used to generate ad(440), ranging from 0.001 - 1 g m-3 were randomly selected. The wavelengths ranged from 400 ∼ 800 nm with 1 nm intervals. The water column was set as infinitely deep, output depth was set as 50 m, the step size is set as 0.1 m to ensure sufficient resolution to calculate the profiles of the Kd(PAR). Kd(PAR), from the surface (0) to any given depth z is defined as [8]:
We used z = zpd (the penetration depth, defined as the depth where PAR(0) reaches 1/e = 37% of the surface’s value) to characterize the lower boundary of our surface layer (ranging from depths of 0-zpd). Note that even in very clear waters, Zpd is shallower than 50 m.The solar zenith angles were randomly selected from 0 to 50°, particle scattering phase function was adopted from the “Petzold-average” as defined in Mobley [11].In addition, wind speed is 5 m/s, relative humidity is 80%, horizontal visibility is 15 km, total ozone is 300 Dobson. Typical Rrs spectra are shown in Fig. 1(a). We divided the 20,000 sets of Rrs ∼ IOPs data into training and validation sets with a 8:2 ratio, resulting in 16,000 sets for training and 4,000 sets for independent validation (Table 1). The mean values and the ranges of Rrs(547) and Kd(PAR) for the training dataset and the validation dataset are also shown in Table 1.
Fig. 1. Examples of Rrs spectra used in this study: (a) synthesized Rrs spectra, (b) NOMAD Rrs spectra, (c) MODIS Rrs spectra that have matchup with BGC-Argo Kd(PAR) data.
Table 1. Statistical descriptions of Rrs(547) (taking Rrs(547) as an example) and Kd(PAR) for datasets used for model training, validation, and testing (The coefficient of variation (CV) is the ratio of standard deviation to the mean).
2.2 In situ data
To evaluate the performance of our deep learning model, this study utilized various in situ data to test its accuracy and effectiveness. The field measurement was sourced from NOMAD dataset (see Fig. 2, white circles) and BGC-Argo data (Fig. 2, yellow stars).
Fig. 2. Location of field measurements used to evaluate the Kd(PAR) algorithm. White circles represent NOMAD data measurement locations, red squares and yellow stars represent NOMAD and BGC-Argo stations matching MODIS satellites, respectively.
NOMAD (NASA’s Bio-Optics Ocean Algorithm Dataset, https://seabass.gsfc.nasa.gov/wiki/NOMAD) is used to develop, calibrate, and evaluate the correct implementation of water color remote sensing inversion algorithms. It is comprised of roughly 4500 sites and covers a period between 1995 and 2006 [43,44]. It contains water-leaving radiation, surface irradiance, Kd(PAR) measurements and associated ancillary metadata [45]. In this study, a total of 605 matched data points with both in situ Rrs(λ) and Kd(PAR) were obtained. The Rrs(λ) spectral data are shown in Fig. 1(b), with Rrs(547) ranging from 0.0012–0.014 sr-1, and Kd(PAR) ranging from 0.033–0.82 m-1 (Table 1).
BGC-Argo data consisting of data across the world, filling in the gaps in satellite coverage that arise due to low sun angles, high latitude winters, and cloud cover [8,15,46] . The device is equipped with an irradiance radiometer that measures Ed in three channels (380 or 443, 412, 490) as well as PAR, surfacing once a day around solar noon [47]. The detailed data quality control and data calculation methods are listed in Begouen Demeaux and Boss [15]. The radiometer data in BGC-Argo only covers 3 bands, which is insufficient for meeting the requirements of the current proposed algorithm. Therefore, we have extended our analysis by incorporating matchups with remote sensing data. For specific matchups rules and matchups quantity, refer to Section 2.3. Eventually, a total of 1776 matchups between MODIS Rrs spectra that have matchups with BGC-Argo Kd(PAR) data (Fig. 1(c)), with Rrs(547) ranging from 0.0015-0.020 sr-1, and Kd(PAR) ranging from 0.029-0.25 m-1 (Table 1).
About 80% of the NOMAD data were randomly selected to serve for model testing, while 16% and 4% of the data were pooled into the datasets for model training and model validation, respectively (Table 1). A similar partition was made for the BGC-Argo data.
2.3 Remote sensing data
To explore the application of our algorithm to ocean color remote sensing, we used the Moderate Resolution Imaging Spectroradiometer (MODIS) to evaluate Kd(PAR) using satellite matchups to in situ data. The MODIS visible band Level2 Rrs data was downloaded from the NASA website (https://oceancolor.gsfc.nasa.gov/).
We set a time window of ±5 hours between in situ and satellite data, and used the median value from a 5 × 5 pixel box centered at each sampling site to represent satellite measurement in which half of the pixel must be unflagged [45,48]. In addition, the quality of spectral data was determined according to the Level-2 Processing Flags (l2_flags) [49], which exclude MODIS data containing these l2_flags (atmospheric correction failures, land pixels, possible cloud or ice pollution, intense solar flash pollution, and cloud stray light or shadow pollution). In total, we obtained 71 NOMAD matchups (Fig. 2, red squares), and 1776 BGC-Argo matchups, as mentioned in Section 2.2.
2.4 Accuracy assessment
In addition to the coefficient of determination (R2) in linear regression analysis, the accuracy of the predicted Kd(PAR) is assessed with the following statistical measures: root mean square difference (RMSD), mean absolute relative difference (MARD), and bias. They are defined as follows (N is the number of samples):
3. Methods
3.1 Semi-analytical algorithm (L2005)
Based on a radiative transfer model, Lee et al. [7] used Hydrolight simulated data to propose a semi-analytical formula (L2005), which can describe the vertical variation of solar radiation in the upper layers of the global ocean. The formula is as follows:
where K1 and K2 are model parameters, with K1 for the asymptotic value at greater depths and K2 representative of the subsurface Kd(PAR) value. IOPs here represents combinations of different inherent optical properties. K1 and K2 vary with IOPs. The formula is as follows:3.2 chlorophyll-a concentration-based Kd(PAR) algorithm (M2007)
Morel et al. [16] develop an empirical formula (M2007) between Kd(490) and Kd(PAR) based on 454 LOV (Laboratoire d'Océanographie de Villefranche) datapoints collected from 1970 to 2004. M2007 is centered around the “Case 1” concept and system. The formula is as follows:
where Kd(490) comes from Here x(490) and e(490) are empirical coefficients developed from the dataset, while aw is from Pope and Fry [38], bbw from Morel [50]. [Chl] is estimated by using OC3M empirical algorithms:3.3 Kd(490)-based Kd(PAR) algorithm (S2013)
Saulquin et al. [6] developed a relationship between Kd(PAR) and Kd(490) in clear and turbid water using 404 sets of in-situ measurements and satellite matchups taken between 1995 and 2009. They utilized MERIS satellite reflectivity and the Kd(λ) proposed by [32]. The resulting revised formula is as follows:
For Kd(490) <=0.115 m-1,
For Kd(490) > 0.115 m-1,
The Kd(490) comes from
3.4 Deep-learning model for Kd(PAR) (DLKPAR)
In this study, we adopted a deep learning approach centered around the estimation of Kd(PAR) from Rrs(λ). Figure 3 illustrates the deep learning schematic we used. This algorithm was named DLKPAR (deep-learning model for Kd(PAR)). As with all deep-learning systems, DLKPAR is composed of one input layer, multiple hidden layers that are associated with many numbers of neurons, and one output layer [53–57].
Fig. 3. Schematic chart of the deep-learning-based system for estimating Kd(PAR) using Rrs(λ), named DLKPAR.
Here, we selected Keras [58] for DLKPAR based on the data characteristics. The input data of the DLKPAR model is Rrs(λ) at specific wavelengths: 400, 412, 443, 488, 531, 547, 667 nm. Due to Rrs(400) is not included in the MODIS bands, we adopted the model proposed by Wang et al. [23] to predict Rrs(400) in this study. The number of hidden layers and neurons in each layer were determined based on the achievement of the minimum loss [55]. Eventually, we found that a system of four hidden layers with 256 neurons in Layer-1, 128 in Layer-2, 64 in Layer-3, and 16 in Layer-4 performed well for DLKPAR.
For the training of DLKPAR, we employed the Rectified Linear Unit (ReLu) function as the activation function of each layer [59]. The optimization function of the training was conducted by the Adam algorithm [60]. A learning rate of 2 × 10−5 is used in this study. The training of DLKPAR was considered complete when the value of the loss function remains stable over multiple consecutive training cycles and there is no obvious downward trend, and the iteration stopped.
4. Results and discussion
4.1 Algorithm comparison with synthetic Kd(PAR) data
Initially, we conducted a Kd(PAR) assessment on the 4095 data points from the synthetic dataset (Table 1). A scatter plot and statistical analysis results are shown in Fig. 4. The synthetic dataset consisted of 4000 Hydrolight-generated simulation data, 24 NOMAD data, 71 BGC-Argo matchup data. The statistical analysis results are as follows: R2 = 0.99, RMSD = 0.039 m-1, bias = -0.0037 m-1, MARD = 0.065. As depicted in the density map (Fig. 4), the data is distributed on both sides of the 1:1 line. This finding demonstrated the high accuracy of DLKPAR Rrs(λ) data-based predictions. This is because both Rrs(λ) and Kd(PAR) are determined to the first order by a and bb. Decades ago, Barnard et al. [61] showed that Kd(PAR) could be estimated by using Kd(490), while Kd could be estimated by Rrs using algorithms [10,19,32]. Therefore, it is reasonable to believe that there are connections between Rrs and Kd(PAR), which are more complex than a simple linear relationship.
Fig. 4. Comparison between Kd(PAR) and predicted Kd(PAR) of the synthetic dataset. The numbers along the colour bar indicate the pixel density.
4.2 Algorithm comparison to in situ Kd(PAR) data
To assess the applicability of the models (L2005, M2007, S2013, DLKPAR) to global oceans and coastal waters, we evaluated the model using a dataset obtained from NOMAD. Figure 5 and Table 2 show the scatterplots of model-derived Kd(PAR) (from in situ Rrs) versus in situ Kd(PAR) for each algorithm for the NOMAD dataset.
Fig. 5. Comparison between measured Kd(PAR) and predicted Rrs-derived Kd(PAR) of the in situ NOMAD dataset: (a) L2005, (b) M2007, (c) S2013, (d) DLKPAR.
Table 2. Statistical analysis of Kd(PAR) algorithm (L2005, M2007, S2013, DLKPAR) inversion on NOMAD data (n = 484).
4.2.1 L2005
Up to now, L2005 is the only semi-analytical algorithm capable of deriving the average Kd(PAR) distribution at any given depth [8]. This algorithm is based on IOPs, and its relationship is established using the radiative transfer equation. The algorithm performed very well on the NOMAD dataset (Fig. 5(a)), with RMSD = 0.030 m-1, MARD = 0.21, and R2 = 0.94 (Table 2). It can be observed that the inversion-derived Kd(PAR) from L2005 is slightly overestimated when in situ Kd(PAR) < 0.3 m-1 (Fig. 5(a)). The possible reason for this is the presence of empirically-derived formulas and parameters in the current algorithm, such as the empirical parameters of steps 3 and 5 in QAAv6 [62]. However, it should be noted that the algorithm is universal because it is not derived from any specific in situ data. According to Xing et al. [8], caution should be exercised when using L2005 in areas with strong water stratification, as the Hydrolight modelling of the radiative transfer equation assumes a homogeneous distribution of IOPs throughout the water column.
4.2.2 M2007
Morel et al. [16] proposed an empirical relationship between Kd(490) and Chl, and expressed Kd(PAR) as a function of Kd(490) specifically for clear open ocean waters [21]. This model is used in waters where phytoplankton is the main contributor to attenuation [63]. Compared with the L2005 algorithm, this algorithm performs slightly less well with a RMSD = 0.048 m-1, MARD = 0.25, bias = 0.0092 m-1 and R2 = 0.82 (Fig. 5(b) and Table 2). Due to the increased contribution to light attenuation by CDOM and suspended particulate matters (SPM) in coastal waters, Kd(PAR) is no longer a single function of Chl [10,32]. Therefore, it is understandable that there are biased inversion results in M2007.
4.2.3 S2013
S2013 was developed to establish a relationship between Kd(PAR) and Kd(490) for both Case 1 and Case 2 waters. QAA_v6 was used to calculate a and bb to invert Kd(PAR) in both S2013 and L2005. The MARD = 0.17 of S2013 is inferior to that of L2005 (Fig. 5 (c), Table 2). The superior performance of S2013 (compared to L2005) can be explained by the utilization of the NOMAD dataset in S2013 when empirically conditioning the Kd(PAR) formula, effectively resulting in better statistical results. However, it is worth noting that this algorithm still relies on the empirical relationship between Kd(PAR) and Kd(490) [6]. As PAR penetrates the ocean, the spectral shape undergoes change with the increasing depth [64,65]. For example, with the increasing turbidity of the water column, PAR will shift from the blue-green spectrum (400-500 nm) in open waters to the green spectrum (500-550 nm) in coastal waters [66,67].
4.2.4 DLKPAR
Deep learning models are widely used in ocean color remote sensing research [68]. In this study, DLKPAR outperformed other models when applied to the NOMAD dataset (Fig. 5 (d), Table 2), with RMSD = 0.038 m-1, MARD = 0.14 and R2 = 0.94. Although deep learning models are essentially empirical models and come with associated limitations [69,70], the issue of inadequate band information during the Kd(PAR) inversion process was eliminated by using Rrs(400, 412,443,488.531,547.667) as input for Kd(PAR) inversion and employing a complex structure and combination of neurons [18]. In addition, Kd(PAR) is an AOPs of water, whose value is contingent (to a second order), upon the angular distribution of the underwater radiation field [7,71]. Rrs, as another AOP, is also determined by the inherent optical properties of the waters as well as environmental factors such as the sun zenith angle [32]. Therefore, the use of Rrs (taking into account the influence of environmental factors) as a deep learning input parameter to derive another AOP helps to minimize the impact of solar zenith on model accuracy.
4.3 Algorithm comparison with remote sensing Kd(PAR) data
Since the ultimate aim of the DLKPAR algorithm is to apply it to ocean color satellites in order to obtain a global distribution of Kd(PAR), we conducted further evaluations using Kd(PAR) derived from MODIS. The corresponding position of the satellite and in situ matching station of the NOMAD dataset are indicated by red squares in Fig. 2.
By matching NOMAD data with MODIS images, we observed that Kd(PAR) values estimated by L2005 were overestimated (Fig. 6(a)), while inversion results of M2007 were slightly inferior (Fig. 6(b)). Moreover, the inversion outputs of S2013 were slightly overestimated (Fig. 6(c)). In contrast, DLKPAR exhibited the best accuracy results (Fig. 6(d), Table 3), with RMSD = 0.051 m-1, MARD = 0.20, bias = 0.0015 m-1. Nonetheless, it should be noted that the DLKPAR model had a slightly lower R2 value of 0.78 compared to L2005 (R2 = 0.82), but still performed better than S2013 and M2007. The evaluation metrics were slightly inferior when compared with in situ data. However, this outcome is expected in satellite remote sensing of ocean color. The main source of bias in the data is the absence of an exact “match” between satellite and in situ measurements, which is primarily caused by temporal and spatial gaps [45]. In addition, the atmospheric corrections for oceans and coastal regions are imperfect [72], any existing biases in Rrs measurements will be further propagated during the inversion process of Kd(PAR).
Fig. 6. Comparison between predicted matchups MODIS Kd(PAR) and in situ Kd(PAR) of the NOMAD dataset: (a) L2005, (b) M2007, (c) S2013, (d) DLKPAR.
Table 3. Statistical analysis of Kd(PAR) predicted from algorithm (L2005, M2007, S2013, DLKPAR) inversion with NOMAD-MODIS matchups versus in-situ data (n = 71).
We employed BGC-Argo to match MODIS data to further evaluate the performance of the different inversion algorithms (Fig. 7, Table 4). In general, the inversion results of algorithms on BGC-Argo matchups with MODIS outperformed the matchups with NOMAD (with the exception of S2013), but were moderately inferior to the results obtained from in situ data. Due to the inherent limitations of the BGC-Argo instrument itself, no data originates from coastal areas, and the range of the measured Kd(PAR) is < 0.3 m-1. L2005 (Fig. 7(a)) and M2007 (Fig. 7(b)) exhibit overestimation while S2013 (Fig. 7(c)) yields underestimation. In contrast, the performance of DLKPAR is optimal, or at least similar to that in other models (Fig. 7(d)). The utilization of BGC-Argo sampling sites results in global coverage, including high latitude regions (> 60°N), which significantly enhances the comparison data for the algorithm [8]. The collaboration between BGC-Argo and satellite remote sensing data offers a valuable synergy, enabling an expansion of satellite ocean color observations beyond surface level to greater depths.
Fig. 7. Comparison between predicted MODIS Kd(PAR) and in situ Kd(PAR) of the BGC-Argo dataset: (a) L2005, (b) M2007, (c) S2013, (d) DLKPAR.
Table 4. Kd(PAR) algorithm (L2005, M2007, S2013, DLKPAR) inversion BGC-Argo matchup MODIS data results statistical analysis (n = 1420).
4.4 Kd(PAR) of the global ocean from MODIS
As illustrated in the above figures, DLKPAR demonstrates excellent inversion results for MODIS. Furthermore, Fig. 8 show cases the inversion results of global ocean MODIS climatological Kd(PAR) data using DLKPAR, applying the estimation of Kd(PAR) to a global scale. This extension contributes to providing crucial information regarding the vertical distribution of solar radiation in the upper column and aids in evaluating the underlying photochemical and photobiological processes that occur within the ocean.
Fig. 8. Global distribution of MODIS Kd(PAR) climatology data, (a) Spring, (b) Summer, (c) Autumn, (d) Winter.
As depicted in Fig. 8(a), temporal analysis revealed that Kd(PAR) was marginally higher during spring in the equatorial Pacific, primarily as a result of the influence of equatorial upwelling that led to an increase in biological activity [73]. In terms of spatial variation, the smallest Kd(PAR) was found to be 0.04 m-1 in the South Pacific Gyre (SPG, Fig. 8(b)). The reason is that the lack of nutrients leads to the limitation of phytoplankton growth in SPG, while the photodegradation limits the content of CDOM. Notably, Kd(PAR) can reach up to 0.9 m-1 in coastal areas (Fig. 8(b)), such as the Yangtze Estuary, primarily due to the influence of high SPM and CDOM from terrestrial sources [74]. In the southwest Atlantic, there was an increase in Kd(PAR) during autumn and winter (Fig. 8(c) and (d)). This elevation in Kd(PAR) restricted the downward transmission of solar radiation.
With previous algorithms, the intricate ocean environment posed significant challenges to accurately invert Kd(PAR) near the sea surface [4,6,75], which in our case, do not appear to affect DLKPAR performance, as seen in our statistical analysis. We therefore conclude that DLKAR is an effective algorithm to accurately obtain Kd(PAR), thereby facilitating the modeling of marine ecosystems and the estimation of upper ocean biological heat.
5. Summary
In this study, a large amount of simulated data was used to construct a deep learning model for inversion of Kd(PAR). Using global public datasets such as NOMAD and BGC-Argo covering Case 1 and Case 2 waters, we compared the Kd(PAR) inversion results of empirical algorithms, semi-analytical algorithms, and our deep learning algorithm (DLKPAR). The comparison results between derived and in situ measured Kd(PAR) dataset showed that the performance of DLKPAR was better than, or at least similar to, that of any other algorithms. In addition, L2005 and S2013 Kd(PAR) performed better than M2007. Our study also shows the universality of algorithms based on radiative transfer, and further illustrates the powerful ability of deep learning in solving ocean color problems. Furthermore, DLKPAR also showed better, or at least similar, inversion accuracy than other algorithms when applying to MODIS Rrs spectra.
DLKPAR uses Rrs spectra as inputs, meaning that it can be directly applied to ocean color satellite to retrieve Kd(PAR) in the global oceans. Furthermore, since Rrs in short visible wavelength (e.g. 400 nm) is used by DLKPAR, this model can also be applied to future satellites equipped with high-quality sensors to detect water-leaving radiance in short wavelengths. It may substantially improve the accuracy of the remotely sensed Kd(PAR) in coastal waters, which in turn improves our understanding on the coastal ecosystem and carbon cycle.
Funding
National Natural Science Foundation of China (#42266005); Finance Science and Technology Project of Hainan Province (ZDYF2021GXJS037); Major Science and Technology Plan Project of Hainan Province (ZDKJ202017-02-01); National Natural Science Foundation of China Key Program (#61931025); Joint Funds of the National Natural Science Foundation of China key program (U1906217); Key Laboratory of Space Ocean Remote Sensing and Application Open Fund (202301002).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data used in this study are available in either NASA SeaBASS or ocean color website, can also be obtained from the authors upon request.
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