# Accurate estimation of photosynthetic available radiation from multispectral downwelling irradiance profiles

Jaime Pitarch, Edouard Leymarie, Vincenzo Vellucci, Luca Massi, Hervé Claustre, Antoine Poteau, David Antoine, Emanuele Organelli

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## To cite this version:

Jaime Pitarch, Edouard Leymarie, Vincenzo Vellucci, Luca Massi, Hervé Claustre, et al. Accurate estimation of photosynthetic available radiation from multispectral downwelling irradiance profiles. Limnology and Oceanography: Methods, 2025, 10.1002/lom3.10673. hal-04961529

HAL Id: hal-04961529

https://hal.science/hal-04961529v1

Submitted on 21 Feb 2025

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Distributed under a Creative Commons Attribution 4.0 International License
LIMNOLOGY
and
OCEANOGRAPHY: METHODS

<figure><img src="image_3.png" /></figure>

Limnol. Oceanogr.: Methods 2025
© 2025 The Author(s). Limnology and Oceanography: Methods published by Wiley Periodicals LLC on behalf of Association for the Sciences of Limnology and Oceanography.
doi: 10.1002/lom3.10673

NEW METHODS

Accurate estimation of photosynthetic available radiation
from multispectral downwelling irradiance profiles

Jaime Pitarch,<sup>1,*</sup> Edouard Leymarie,<sup>2</sup> Vincenzo Vellucci,<sup>3,4</sup> Luca Massi,<sup>5</sup> Hervé Claustre,<sup>1</sup> ²
Antoine Poteau,<sup>2</sup> David Antoine,<sup>2,6</sup> Emanuele Organelli<sup>1</sup>

¹National Research Council of Italy (CNR), Institute of Marine Sciences (ISMAR), Rome, Italy; ²Sorbonne Université, CNRS, Laboratoire d'Océanographie de Villefranche, LOV, Villefranche-sur-Mer, France; ³Sorbonne Université, CNRS, Institut de la Mer de Villefranche, IMEV, Villefranche-sur-Mer, France; ⁴Sorbonne Université, CNRS, OSU Stations Marines, STAMAR, Paris, France; ⁵University of Florence, Department of Biology, Florence, Italy; ⁶Remote Sensing and Satellite Research Group, School of Earth and Planetary Sciences, Curtin University, Perth, Western Australia, Australia

Abstract

Photosynthetic available radiation (PAR) is the light usable by photosynthetic organisms. Photosynthetic available radiation measurements at depth are required to quantify the light availability for primary production. Direct PAR measurements may be measured with full-spectrum quantum sensors for the range 400 to 700 nm. When spectrally resolved light is measured, as for the downwelling irradiance spectrum E<sub>d</sub>, PAR may be computed by numerically integrating E<sub>d</sub> within those limits. As radiation varies across a spectral continuum, E<sub>d</sub> needs to be resolved at a sufficiently large number of bands, to provide an unbiased PAR estimate. When E<sub>d</sub> is available at a small number of spectral bands, as for multispectral E<sub>d</sub> sensors, it is still possible to numerically integrate E<sub>d</sub>, but the estimation will contain errors. Here, we propose a method that delivers unbiased PAR estimates, based on two-layer neural networks, formulable in a small number of matrix equations, and thus exportable to any software platform. The method was calibrated with a dataset of hyperspectral E<sub>d</sub> acquired by new types of BioGeoChemical (BGC)-Argo floats deployed in a variety of open ocean locations, representative of a wide range of bio-optical properties. This procedure was repeated for several band configurations, including those existing on multispectral radiometers presently the standard for the BGC-Argo fleet. Validation results against independent data were highly satisfactory, displaying minimal uncertainties across a wide PAR range, with the performance varying as a function of each sensor configuration, overall supporting the operational implementation in the Argo program. Model codes are findable at https://github.com/jaipipor/PAR_BGC_Argo.

Since the 1950s, photosynthetically available radiation (PAR; μE m⁻² s⁻¹) has been widely exploited by the oceano- graphic communities worldwide because it helps to identify

the base of the sunlit layer of the upper ocean, namely
the euphotic zone, in which primary production occurs
(Ryther 1956). Photosynthetic available radiation has thus
been widely included as a key variable to modeling net pri-
mary production in the oceans (Behrenfeld and Falkowski
1997; Morel and André 1991) as well as to address and better
reproduce the variability of biological processes (Barbieux
et al. 2019; Lacour et al. 2015; Marra et al. 2014; Mignot
et al. 2014; Ricour et al. 2021; Terzić et al. 2019). In situ PAR is
also useful to validate satellite ocean color products (Begouen
Demeaux and Boss 2022; Laliberté, Bélanger, and Frouin 2016;
Lee et al. 2007; Organelli et al. 2017; Xing et al. 2020).

Photosynthetic available radiation is here quantified
under the assumption that the chemical reactions of

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

**Data Availability Statement:** Argo data were collected and made freely available by the International Argo Program and the national programs that contribute to it. (https://argo.ucsd.edu; https://www.ocean-ops.org). The Argo Programme is part of the Global Ocean Observing System. Boussole data available on request from the authors. MedGOOS data are not shared. Associate editor: Xin Liu

<footnote>*Correspondence: jaime.pitarchportero@artov.ismar.cnr.it</footnote>
photosynthesis are dependent on the number of photons reaching the cell, rather than on their respective energy. In this case, given an incident spectral downwelling sunlight irradiance ($E_d$; W m$^{-2}$ nm$^{-1}$) in the visible electromagnetic range, PAR takes the expression:

$$PAR (\mu E m^{-2} s^{-1}) = \frac{10^{-9} 10^{6}}{hcN_A} \int_{400}^{700} E_d \lambda d\lambda \quad (1)$$

where the factor $10^{-9}$ in Eq. 1 converts the wavelength unit from nm into m, $10^6$ converts mol to $\mu$mol, and h, c and $N_A$ are Plank constant, the speed of light in vacuum and Avogadro's number, all in SI units.

Since 2012, a global array of BGC-Argo floats has been equipped with multi-spectral SeaBird OCR-504 radiometers and acquired depth profiles of PAR plus $E_d$ at three ultraviolet-blue bands: 380, 412 and 490 nm. More than 50,000 multispectral profiles have been acquired so far by such configuration of bands and censed for data quality (Jutard et al. 2021; Organelli et al. 2016; Stoer et al. 2023). However, recently, the Argo community started questioning about the adopted set of the radiometric bands and recommended to replace PAR and the band at 412 nm with the bands in the blue at 443 nm and in the green at 555 nm (Argo Steering Team 2023). This choice is justified by the need to sample the green part of the spectrum in order to more accurately derive optical and biogeochemical variables of interest. Results in this paper will support that choice further in regard to PAR.

When light sensors are multispectral such as those mentioned, $E_d$ is only available at a discrete number of bands. Here, it is still possible to estimate PAR, but simple discrete integration of the spectrum contains intrinsic errors. Alternative approaches may be explored, but they shall deal with challenges due to the large range of spectral shapes and values that are encountered along a profile and across different water types. Therefore, the main goal of this paper is to determine if and to which extent an alternative PAR algorithm from multispectral $E_d$ is suitable for a range of oceanic depths and water types, for four spectral band configurations (Table 1). Configuration 1 represents the configuration currently available on most floats. Configuration 2 represents the newly proposed configuration for floats

<table><caption>**Table 1.** Neural network input band configurations.</caption><thead><tr><th>Wavelength (nm)</th><th>Conf. 1</th><th>Conf. 2</th><th>Conf. 3</th><th>Conf. 4</th></tr></thead><tbody><tr><td>380</td><td>√</td><td>√</td><td>√</td><td>√</td></tr><tr><td>412</td><td>√</td><td>—</td><td>√</td><td>—</td></tr><tr><td>443</td><td>—</td><td>√</td><td>√</td><td>√</td></tr><tr><td>490</td><td>√</td><td>√</td><td>√</td><td>—</td></tr><tr><td>555</td><td>—</td><td>√</td><td>√</td><td>√</td></tr><tr><td>665</td><td>—</td><td>—</td><td>—</td><td>√</td></tr></tbody></table>

equipped with 4-band radiometers (Argo Steering Team 2023). Configuration 3 includes all bands of Configuration 1 and 2. Configuration 4 uses the band 665 nm and has been included to help with the discussion on how the performance of the methods depends on the sampling of spectral regions with significant amount of signal. This configuration list is nevertheless not exhaustive, and there are past and present floats with different ones (Jemai et al. 2021).

To solve such questions, we leverage on newly developed BGC-Argo floats equipped with hyperspectral radiometers (Organelli et al. 2021) to compute exact (or reference) PAR, linked to multispectral $E_d$, which is obtained by down-sampling the hyperspectral $E_d$. Such a dataset, ranging eight orders of magnitude in terms of PAR, and sampled in several distinct oceanic waters, is used to calibrate two-layer neural networks (NN). Unlike other artificial intelligence approaches, this network architecture can be reduced to a small set of matrix equations, readily exportable to other software platforms, and coded in a computationally efficient way. The paper follows with a validation section for several independent data sets and a discussion on the applicability and limitations.

## Materials and procedures

### Neural network description

The neural network ingests input data in matrix form $X_{n_s \times n_s}$, where $n_s$ is the number of $E_d$ spectra to be processed at once and $n_s$ is the number of bands (3, 4, or 5 here). The output PAR ($PAR_{NN}$) is obtained after minimizing the difference respect to the reference, or exact PAR ($PAR_{ex}$). In order to properly accommodate the large dynamic ranges of both input $E_d$ and output PAR and to compensate for their highly statistical skewness toward the lowest values, both variables are $log_{10}$-transformed before ingestion.

The neural network architecture was built with the MATLAB® Neural Network Fitting App (routine *fitnet*). It consists of two layers: a hidden layer made of $n_l$ neurons with a sigmoid transfer function and an output layer with a linear transfer function. Error between output and reference is minimized with a Levenberg-Marquardt backpropagation algorithm (routine *trainlm*). The number of neurons in the hidden layer $n_l$ is a free parameter that was determined by progressively increasing its value while observing the improvement in performance until no substantial fitness increase, in order to prevent overfitting. For this case, it was fixed at $n_l = 10$.

Given all NN calibration data, a 60% split is allocated to *training*, that is, used to find the coefficients according to the error, a 35% for *validation*, or to measure and decide network generalization, and a 5% for *testing*, that is to provide an independent measure of network performance. This internal data split in the neural network “training-validation-testing” refers to the algorithm calibration procedure, and it is made exclusively with the BGC-Argo calibration dataset that is presented in the Data section. The validation datasets presented
thereafter are not used here, but instead they provide independent validation the Assessment section.

The input data undergoes transformation before being fed into the neural network. The log-transformed $E_d$, $\mathbf{X} = \log_{10}E_d$, is normalized into $\bar{\mathbf{X}}$ as:

$$ \bar{X}_{ij} = \frac{(X_{ij} - \mu_j^1)}{\sigma_j^1} - 1, i = 1, \dots, n_s, j = 1, \dots, n_\lambda \quad (2) $$

where $\mu^1$ and $\sigma^1$ are the input data offset and gain, respectively.

The activation of neurons in the hidden layer ($\mathbf{A}^1$) is computed with:

$$ A_{ik}^1 = \tanh\left(b_k^1 + \sum_{j=1}^{n} W_{kj}^1 \bar{X}_{ij}\right), k = 1, \dots, n_l \quad (3) $$

where $\mathbf{b}^1$ is the bias vector and $\mathbf{W}^1$ is the linear coefficient. $n_l$ is the number of neurons in the hidden layer. $\tanh(x)$ is the hyperbolic tangent sigmoid transfer function. It operates element by element and is defined as:

$$ \tanh(x) = \frac{2}{1 + e^{-2x}} - 1 \quad (4) $$

The activation of the output neuron $\mathbf{a}^2$ is calculated as:

$$ a_i^2 = b^2 + \sum_{k=1}^{p} w_k^2 A_{ik}^1 \quad (5) $$

where $p$ is the number of hidden neurons, $b^2$ is the bias and $\mathbf{w}^2$ represents the weights connecting the hidden layer to the output layer.

Finally, the output of the neural network $\mathbf{r}$ is obtained transforming the output of the hidden layer $\mathbf{a}^2$ with a linear operator:

$$ y_i = \frac{\mathbf{a}_i^2 + 1}{\sigma^2} + \mu^2 \quad (6) $$

where $\sigma^2$ and $\mu^2$ are the output data gain and offset, respectively.

Finally, PAR is converted to linear units with $PAR_{est} = 10^\gamma$.

## Data

Hyperspectral $E_d$ data used in this study encompass a large variety of regions (Fig. 1). BGC-Argo float data cover both hemispheres, sub-polar, temperate and tropical areas. Fixed-depth sensor data at the BOUSSOLE location in the Mediterranean Sea have been used for validation and is also marked on this map. Finally, profile data at discrete depths between 5 and 80 m across the Mediterranean Sea (MedGOOS cruises) are also used. Details of all data are given below.

### BGC-Argo data

Hyperspectral $E_d$ profiles were measured with hyperspectral RAMSES radiometers (TriOS GmbH, Rastede, Germany), mounted on eight BGC-Argo floats, distributed across very distinct oceanic regions: sub-polar, temperate, ultraoligotrophic and equatorial. Spectral sampling was slightly different for every float, but essentially from 321 to 780 nm, every ~6 nm for all of them. A dark signal was estimated profile-wise at a deep parking depth (~1000 m), which was subtracted to all data from the same profile. This correction, in addition to the Ramses internal dark current correction, proved to be significant. Hyperspectral $E_d$ were integrated with Eq. 1 following the trapezoidal rule, thereby obtaining $PAR_{ex}$. Then, $E_d$ were

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** A world map of calibration and validation data used in this study. The floats are identified by their World Meteorological Organization (WMO) codes. Four of them (dots) constitute the calibration dataset and the other four (asterisks), the validation dataset. Data at the BOUSSOLE site and from MedGOOS cruises are all for validation only.</figcaption></figure>
down-sampled to each band configuration of Table 1 and integrated similarly, obtaining PAR<sub>sam</sub>.

Float data were filtered prior to use by discarding data with tilt higher than 5°, sun zenith angle higher than 90° and a PAR lower than a threshold of 10<sup>-4</sup>μEm<sup>-2</sup>s<sup>-1</sup>, as this value was agreed to be in correspondence of the RAMSES sensors radiometric sensitivity limit. Data were not screened for clouds as it is considered that PAR under cloudy conditions are still meaningful for ecosystem studies, unlike satellite validation.

Resulting data amounted to what reported in Table 2, providing time span, number of profiles and number of spectra. Data from four floats were used for calibration, and four of them (as well as data in the other sections) for validation. The calibration data spanned eight orders of magnitudes (Fig. 2). Data frequencies strongly drop at the extremes of the range. Data in these zones may suffer from decreased model accuracy as they will have a very low weight in the model calibration. Still, these values are very infrequent, and uncertainties will be bounded within low margins in the vast majority of cases, as documented in the Assessment section.

## Sub-surface fixed-depth data at the BOUSSOLE site

Independent validation benefited from E<sub>d</sub> data at BOUSSOLE (BOUée pour l'acquiSition d'une Série Optique à Long termE, or "buoy for the acquisition of a long-term optical series" in English), collected at average depths of ~3 and ~8 m, every 15 min for 1 min with Satlantic (now SeaBird) HyperOCR hyperspectral irradiance sensors. Spectral sampling was slightly different for the four sensors used in the 305–1150 nm range every ~3.3 nm, and so data were linearly interpolated at 3 nm resolution before use. Dark current values were measured thanks to internal shutters and subtracted from the light signal. The median spectra of the 1-min acquisitions are used. Day values were selected by removing data under a sun zenith angle θ<sub>s</sub> > 85°. Also, data with sensor tilt higher than 5° were discarded. After screening, data amounted to a total of 18,688 observations between June 2016 and February 2019.

## Discrete depth profile data in the Mediterranean Sea

Further validation included 166 spectra from eight oceano-graphic MedGOOS cruises carried out on board of the CNR Urania research vessel between May 2004 and November 2008, at 53 stations, distributed across the open waters of the Mediterranean Sea (Fig. 1). Irradiance data were collected at

discrete depths from 5 until 80 m, with 1 nm resolution between 350 nm and 750 nm by a LI-COR LI1800UW spectroradiometer regularly calibrated and maintained. Measurements were performed with calm sea and uniform sky conditions, around local noon to minimize ship's shading, while simultaneous above water observations provided the required reference. Data were then processed following the standard NASA's radiometric and data analysis protocols (Mueller et al. 2003).

## Assessment

In this section, the performance of the PAR estimated by the neural networks (PAR<sub>NN</sub>) is evaluated against PAR<sub>ex</sub>, calculated from hyperspectral E<sub>d</sub>. Results from numerical integration of the multispectral E<sub>d</sub> (PAR<sub>sam</sub>) are added for comparison. This section is divided in three sections, corresponding to the three different platforms of all independent data in this study: BGC-Argo, fixed-depth data at the BOUSSOLE site and profile cruise data in the Mediterranean Sea.

## BGC-Argo data

Results are presented for data from the four BGC-Argo floats that were not used for calibration (Table 2). Comparisons with respect to the PAR<sub>ex</sub> are presented in percent relative error units to highlight differences that are not very high across a very large dynamic range. The plots display the relative error for each data point (ε = (y - x)/x, where y is the quantity being evaluated and x is the reference value). For an overall assessment of each scenario, general statistics are calculated as the median value of ε, that is, ε<sub>50</sub> and the interquartile range, that is, IQR(ε) = ε<sub>75</sub> - ε<sub>25</sub>.

Figure 3 shows that ε for PAR<sub>sam</sub> varies across the dynamic range, and depending on the band configuration (Table 1). Instead, PAR<sub>NN</sub> succeeds in minimizing the differences respect to PAR<sub>ex</sub> for the whole dynamic range, with a larger spread for Configuration 1 (ε<sub>50</sub> = 6.9%, IQR(ε) = 10%) due to the strong spectral limitations. Performance is much better instead for Configurations 2 and 3 and 4 (Table 1), for most of the PAR range, leading to negligible ε<sub>50</sub> and IQR(ε) at 2.8%, 1.9% and 3.4%, respectively.

These statistics highlight the benefit of adding one band at a green wavelength, as on Configuration 2, compared to Configuration 1. The improvement of adding the 412 nm band, that

<table><caption>**Table 2.** BGC-Argo float data summary. First four columns: calibration data. Last four columns: validation data.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Calibration</th><th colspan="4">Validation</th></tr><tr><th>1,902,578</th><th>4,903,658</th><th>1,902,685</th><th>4,903,660</th><th>6,990,503</th><th>2,903,787</th><th>6,990,514</th><th>1,902,601</th></tr></thead><tbody><tr><th>Float WMO</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Time span</th><td>31 May 2022–31 Mar 2023</td><td>2 Dec 2023–7 May 2024</td><td>23 Sep 2023–7 Jan 2024</td><td>6 Jun 2023–7 Jun 2024</td><td>29 Oct 2022–7 Jun 2024</td><td>2 Jul 2023–7 Jun 2024</td><td>6 Jun 2023–7 Jun 2024</td><td>3 Jul 2023–27 May 2024</td></tr><tr><th>Nr. of profiles</th><td>34</td><td>64</td><td>57</td><td>59</td><td>79</td><td>67</td><td>59</td><td>63</td></tr><tr><th>Nr. of spectra</th><td>6495</td><td>9973</td><td>11,820</td><td>12,256</td><td>16,573</td><td>12,410</td><td>12,269</td><td>15,448</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Left panel: histogram of BGC-Argo $E_d$ used for model calibration for the six spectral bands utilized in this study. Right panel: corresponding histogram of $PAR_{ex}$.</figcaption></figure>

Configuration 3 makes respect to Configuration 2, provides marginal improvement, notwithstanding the potential benefits of such a band for other purposes such as bio-optical modeling.

For values as low as $0.001 \mu E \text{m}^{-2} \text{s}^{-1}$ and lower, given at very deep waters, all light has been attenuated except for a narrow band. Sampling by multispectral sensors may be

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Relative error plots for the validation BGC-Argo dataset of calculated PAR from the integral of the multispectral $E_d$ ($PAR_{sam}$, blue dots) and the neural network approach ($PAR_{NN}$, red dots), respect to the exact PAR (i.e., from integration of hyperspectral $E_d$) for the four band configurations (see Table 1).</figcaption></figure>
insufficient, making PAR estimation very challenging. Still the errors for this part of the range appear well constrained at low values. Moreover, keeping in mind that the sensitivity of Sea-Bird's PAR sensors is given as 0.01 µEm⁻²s⁻¹, that is one order of magnitude higher, this result appears relevant.

For the high end, the error somewhat increases, due to the broad spectra with significant contribution by red wavelengths, in correspondence of shallow depths. Here, still errors remain constrained. To study potential improvements at this part, Configuration 4 was tried as a test case, adding a red band, and it is visible in Fig. 3 how the performance for these highest values is better than the other three. At lower values, the performance of Configuration 4 is slightly worse than of Configurations 2 and 3 due to the coarser spectral sampling of the former in the blue-green spectral parts.

In an attempt to potentially improve results further with the available data, a modification of the methodology was tried, where depth was given as a predictor variable, in addition to $E_d$. Therefore, the NNs were recalibrated again with this additional variable using the calibration dataset and evaluated against the validation dataset. Table 3 gathers the statistics for each band configuration, compared to the statistics of the results obtained without depth as predictor, highlighting that depth only significantly improves results in Configuration 1, where all bands are in the UV or blue region, which clearly makes sense optically, as the depth tends to implicitly account for attenuation at longer wavelengths, where the optical effects of the water constituents are less relevant respect to those of pure water. For Configurations 2–4, the improvement is marginal, if at all. It appears then that a well-calibrated NN using a set of bands that at least reaches green wavelengths does not need the ancillary information provided by the depth to improve the prediction capability. Not including the depth as a predictor is better in view of algorithm exportation to other technologies. Indeed, the used radiometers had a given signal to noise ratio, which limited the maximum depth. Accounting for depth as a predictor would incorporate this limitation as well, but one might think of next generation radiometers able to provide clean data at deeper depths. With this depth-agnostic approach given by the ingestion of the

<table><caption>**Table 3.** Global error metrics for the validation Argo dataset considering depth (z) as a predictor together as the spectra or not considering it. $\epsilon(50)$ and $IQR(\epsilon)$ are the median value and the interquartile range of $\epsilon$, respectively, where $\epsilon = \frac{y-x}{x}$ in percent units. y is the evaluated variable and x the reference value.</caption><thead><tr><th></th><th></th><th>Conf. 1</th><th>Conf. 2</th><th>Conf. 3</th><th>Conf. 4</th></tr></thead><tbody><tr><td rowspan="2">No z</td><td>$\epsilon_{50}$</td><td>6.9</td><td>-0.68</td><td>-0.062</td><td>1.4</td></tr><tr><td>$IQR(\epsilon)$</td><td>10</td><td>2.8</td><td>1.9</td><td>3.4</td></tr><tr><td rowspan="2">With z</td><td>$\epsilon_{50}$</td><td>-0.27</td><td>0.15</td><td>-0.16</td><td>0.35</td></tr><tr><td>$IQR(\epsilon)$</td><td>3.3</td><td>3.1</td><td>2.5</td><td>2.8</td></tr></tbody></table>

spectra only, the NNs are readily exportable. In the remaining of this article, results will be shown for the NNs that ingest $E_d$ data only.

A second validation exercise with the same dataset is made by comparing the calculated $z_{15PAR}$, which is that depth at which $PAR = 15 \mu Em^{-2}s^{-1}$. The upper row panels of Fig. 4 show time series of the exact $z_{15PAR}$ for the four validation BGC-Argo floats, evidencing some variability as the floats move along their respective trajectories and seasons. The panels on the three rows below display the difference $\Delta_{z_{15PAR}}$ with respect to the exact $z_{15PAR}$ made with every method and band configuration. The red dots in the lower panels are much more clustered around the zero value, indicating the better estimation of the neural network approach respect to the integral of the sampled spectra, especially for Configurations 2, 3 and 4. Table 4 presents the mean and standard deviation for each BGC-Argo of the relative difference $\frac{\Delta_{z_{15PAR}}}{z_{15PAR}}$, restricted to Configuration 2 only, to avoid repetition. Results show indeed excellent performance of the neural network approach, that produce errors around half or less respect to the four bands integral.

To show the effect of the correction along depth, one PAR profile for each of the four BGC-Argo floats used for validation was randomly selected and shown in Fig. 5. $PAR_{sam}$ and $PAR_{NN}$ are compared to $PAR_{ex}$, showing a good overlap of $PAR_{NN}$ over $PAR_{ex}$, visually indicating the good performance of the NN approach. The blue line, corresponding to $PAR_{sam}$, instead, keeps the same general profile shape but with noticeable differences, depending on the depth. One must note some missing data points for the neural network approach at deep depths. These are points with negative irradiance at some highly attenuated bands that are needed in the neural network approach. Such a case is unphysical and thus such data were eliminated. Negative spectra can still occur after a dark spectrum subtraction, because the dark spectrum is the average of random fluctuations in both directions, and therefore there are data points where the given spectrum is even lower. This issue depends on the actual radiometer technology and is unimportant for the discussion of this neural network approach. In an operational case, this concern could be easily circumvented by replacing negative values with a very small positive value.

## Sub-surface fixed-depth data at the BOUSSOLE site

Sub-surface $E_d$ fixed sensors at the BOUSSOLE site provide valuable validation data as well, as they sampled during a large time lapse, encompassing daily, seasonal and eventual optical variability. They are also particularly useful to assess the method performance in near-surface observations. Given the fixed location, PAR variability is driven by the diurnal sun cycle and by seasonal variability.

Figure 6 shows the PAR error results for the sensor data at 3 and 8 m. Among the two depths, the deeper one is where
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Upper row: Exact $Z_{PAR15}$ time series for the four BGC-Argo floats used for validation. Lower three panels: differences ($\Delta Z_{PAR15}$) respect to the exact value for each band configuration (Table 1). Blue color: numerical integral estimation of PAR. Red color: neural network estimation of PAR.</figcaption></figure>

results are more satisfactory, as the influence of red wave-lengths is more dampened. Exceptions to this are the results of Configuration 4, that, being the only one that includes a

red band, outperforms the other three, given the shallow depths that do not allow the red part of the spectrum to be much attenuated. Regarding the first three configurations,

<table><caption>**Table 4.** Relative mean and standard deviation of the error in the estimation of $Z_{PAR15}$ for each Argo float in the validation dataset, for Configuration 2.</caption><thead><tr><th>BGC-Argo</th><th>WMO 6990503</th><th>WMO 2903787</th><th>WMO 6990514</th><th>WMO 1902601</th></tr></thead><tbody><tr><td>μ(Z<sub>PAR15</sub>) sam. (%)</td><td>0.7</td><td>-1.5</td><td>-0.7</td><td>0.5</td></tr><tr><td>σ(Z<sub>PAR15</sub>) sam. (%)</td><td>1.7</td><td>3.9</td><td>4.0</td><td>1.1</td></tr><tr><td>μ(Z<sub>PAR15</sub>) NN (%)</td><td>-0.1</td><td>0.1</td><td>-0.3</td><td>-0.1</td></tr><tr><td>σ(Z<sub>PAR15</sub>) NN (%)</td><td>0.1</td><td>2.0</td><td>1.2</td><td>0.5</td></tr></tbody></table>
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Selected PAR profiles for the four validation BGC-Argo floats (WMO 6990503, WMO 29003787, WMO 6990514, WMO 1902601, in sequential rows) and the four band configurations (columns). Black lines: exact PAR. Blue lines: PAR from numerical integration of multispectral radiometry. Red circles: PAR estimated from the neural network approach.</figcaption></figure>

$PAR_{sam}$ contained significant negative biases, from ~ -60% for Configuration 1 and ~ -20% to -40% for Configurations 2 and 3. Compared to that, $PAR_{NN}$ had much lower differences, ~ 0% to -20% for the Configurations 1, 2 and 3, with less spread for the last two. Statistics are shown in Table 5, showing that the NNs deliver negligible or almost negligible $ε_{50}$, even compared to the small spread level given by $IQR(ε)$. These results provide further confidence in the NN approach and confirm its usability for shallow depths and ingesting data that not only come from BGC-Argo platforms.

## Discrete depth profile data in the Mediterranean Sea

Further validation is provided by the $E_d$ profile data at discrete depths collected during the MedGOOS cruises. Figure 7 shows that $PAR_{sam}$ is biased for all configurations, most evident for the Configuration 1, where $ε_{50} = -40\%$ (Table 6). Configurations 2, 3 and 4 have $ε$ values that strongly vary depending on the part of the range. $PAR_{NN}$ compare excellently to $PAR_{ex}$ in all cases, reducing both the mean error and

the spread very much, especially for Configurations 2 and 3, as highlighted both by the error dot clouds in Fig. 7 and by the global statistics of Table 6, once more confirming the benefits of the proposed methodology.

## Discussion

Our assessment showed that integrating a discrete (multispectral) irradiance spectrum $E_d$ to calculate PAR leads to very significant errors. Instead, we have presented a neural network-based methodology that ingests multispectral $E_d$ and derives PAR estimations. The neural networks are fully documented and consist of a reduced number of forward matrix operations, thus being extremely time efficient and exportable to any other programming language or platform.

Obtaining reliable PAR estimations from multispectral data is a challenging problem due to the very large range of shapes and values that an irradiance spectrum displays from the surface to deep waters, which determines varying sampling efficiency by multispectral sensors. This is exemplified in Fig. 8,
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Same as Fig. 3, but for PAR from $E_d$ data at two fixed depths at the BOUSSOLE site.</figcaption></figure>

where three $E_d$ spectra at different depths are shown. In the near-surface case (left plot), there is a very significant amount of red light, implying that Configuration 4 provides a value that is very close to the exact one because it samples the 665 nm band, that significantly contributes to PAR. Surprisingly, Configuration 3 provides a good match too. The worst results are for Configuration 1, that samples only the UV-blue part. In the case of the middle plot, at a middle depth of 30 m, the 665 nm band does not add any information anymore, and the differences between the four configurations are within the dispersion shown in Figs. 3, 6, and 7. Finally, for the deep

spectrum at 90 m (right plot), $E_d$ is very narrow and appears quite well sampled by Configuration 1, but Configurations 2 and 3 also cover the upper decay of the curve, which happens to help in facilitating an almost total agreement respect to the exact value.

The neural networks consistently outperformed the result of the integration according to our validation results, providing estimates with minimal errors with respect to reference (exact) PAR values. Configuration 1 (380, 412, and 490 nm bands) is implemented in a large amount of floats, and was useful to challenge this methodology, showing that, despite

<table><caption>**Table 5.** Global error metrics for the validation fixed-depth dataset at the BOUSSOLE site. $\epsilon(50)$ and $IQR(\epsilon)$ are the median value and the interquartile range of $\epsilon$, respectively, where $\epsilon = \frac{y-x}{x}$, in percent units. $y$ is the evaluated variable ($PAR_{sam}$ or $PAR_{NN}$) and $x$ the reference value ($PAR_{ex}$).</caption><thead><tr><th></th><th></th><th></th><th>Conf. 1</th><th>Conf. 2</th><th>Conf. 3</th><th>Conf. 4</th></tr></thead><tbody><tr><td rowspan="4">Integral of sampled spectra</td><td rowspan="2">3 m</td><td>$\epsilon_{50}$</td><td>-64.9</td><td>-37.1</td><td>-36.3</td><td>-9.2</td></tr><tr><td>$IQR(\epsilon)$</td><td>2.4</td><td>3.3</td><td>3.5</td><td>2.1</td></tr><tr><td rowspan="2">8 m</td><td>$\epsilon_{50}$</td><td>-56.5</td><td>-22.9</td><td>-22.0</td><td>-0.6</td></tr><tr><td>$IQR(\epsilon)$</td><td>2.5</td><td>2.8</td><td>2.8</td><td>3.2</td></tr><tr><td rowspan="4">Neural networks</td><td rowspan="2">3 m</td><td>$\epsilon_{50}$</td><td>-14.5</td><td>-6.5</td><td>-1.9</td><td>4.4</td></tr><tr><td>$IQR(\epsilon)$</td><td>6.6</td><td>2.8</td><td>3.0</td><td>2.0</td></tr><tr><td rowspan="2">8 m</td><td>$\epsilon_{50}$</td><td>-3.2</td><td>3.5</td><td>2.7</td><td>3.5</td></tr><tr><td>$IQR(\epsilon)$</td><td>6.4</td><td>1.4</td><td>1.6</td><td>1.7</td></tr></tbody></table>
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Same as Fig. 3, but for PAR from $E_d$ data from the MedGOOS cruises.</figcaption></figure>

<figure><img src="image_11.png" /></figure>

inherent limitations, PAR can still be estimated with relatively low errors. Configurations 2 and 3 showed much more enhanced performance than the first one, facilitated by the 555 nm band, that covers a distinct band region and extends the range to ~50% of the visible spectrum. Interestingly, improvement of Configuration 3 respect to 2 was not great,

suggesting that adding more bands within a spectral region that is already covered does not suppose a high advantage for these purposes. This may therefore be a result for future designs of band configurations on BGC-Argo floats, where covering distinct regions of the spectrum shall be prioritized when augmenting the band density in some spectral zones is

<table><caption>**Table 6.** Same as Table 5, but for PAR from $E_d$ data from the MedGOOS cruises.</caption><thead><tr><th></th><th></th><th>Conf. 1</th><th>Conf. 2</th><th>Conf. 3</th><th>Conf. 4</th></tr></thead><tbody><tr><td rowspan="2">Integral of sampled spectra</td><td>ε<sub>50</sub></td><td>-42.4</td><td>0.4</td><td>-1.0</td><td>7.6</td></tr><tr><td>IQR(ε)</td><td>8.5</td><td>14.6</td><td>12.0</td><td>20.3</td></tr><tr><td rowspan="2">Neural networks</td><td>ε<sub>50</sub></td><td>-7.5</td><td>0.9</td><td>1.0</td><td>-1.4</td></tr><tr><td>IQR(ε)</td><td>12.0</td><td>2.0</td><td>2.5</td><td>6.1</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Three examples of $E_d$ spectra from the BGC-Argo validation dataset at different depths, and how they are sampled by all the bands used from Configurations 1 to 4 (gray bands). The different PAR estimations by the four band configurations are shown as scale insets in each plot.</figcaption></figure>

not possible. Configuration 4 was tried to study the potential benefits of a red band while keeping the number of bands limited to four, showing effectively that performance near the surface is enhanced, although the benefit disappears at depth.

Statistical parameters $ε_{50}$ and $IQR(ε)$ were overall highly satisfactory against independent validation datasets, but they are global parameters that depend on the data range. In an operational context, where a PAR product delivered accompanied by its uncertainty estimates, $ε_{50}$ and $IQR(ε)$ may be discriminated per small segments of PAR_NN, therefore making this association possible.

In conclusion, this methodology has demonstrated success against independent validation datasets. The MATLAB codes used in this publication have been publicly released at https://github.com/jaipipor/PAR_BGC_Argo. Model equations and coefficients may be revisited in the near future, as soon as more data becomes available for recalibration. Versions for other band configurations not considered here are also possible and straightforward, if requested. In such cases, any model update will be properly documented.

## Acknowledgments

This work has been funded by EU—Next Generation EU Mission 4 “Education and Research”—Component 2: “From research to business”—Investment 3.1: “Fund for the realization of an integrated system of research and innovation infrastructures”—Project IR0000032—ITINERIS—Italian Integrated Environmental Research Infrastructures System—CUP B53C22002150006. The authors acknowledge the Research Infrastructure Euro-Argo ERIC participating in the ITINERIS project with their Italian nodes. We thank the organizers of the MedGOOS campaigns, the crew of the R/V URANIA, and Chiara Melillo and Francesca Polonelli who carried out the spectral measurements. BGC-Argo floats equipped with hyperspectral radiometers were purchased and deployed through

the “REFINE—Robots Explore plankton-drive Fluxes in the marine twilight zone” project, which has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement 834177) and through funding from Centre National d’Etude Spatiale (CNES). This study is a contribution to the BOUSSOLE project, which was funded by the European Space Agency (ESA; grant 4000102992/11/I-NB) and Centre National d’Etudes Spatiales (CNES) and took advantage of the French Oceanographic Fleet (FOF).

## Conflicts of Interest

None declared.

## References

* Argo Steering Team. 2023. 24th Argo Steering Team Meeting (AST-24). Halifax (Canada). https://argo.ucsd.edu/organization/argo-meetings/24th-argo-steering-team-meeting-ast-24/ast-24-agenda-and-related-documents/.

* Barbieux, M., J. Uitz, B. Gentili, et al. 2019. “Bio-Optical Characterization of Subsurface Chlorophyll Maxima in the Mediterranean Sea From a Biogeochemical-Argo Float Database.” *Biogeosciences* 16: 1321–1342. https://doi.org/10.5194/bg-16-1321-2019.

* Begouen Demeaux, C., and E. Boss. 2022. “Validation of Remote-Sensing Algorithms for Diffuse Attenuation of Downward Irradiance Using BGC-Argo Floats.” *Remote Sensing* 14: 4500. https://doi.org/10.3390/rs14184500.

* Behrenfeld, M. J., and P. G. Falkowski. 1997. “A Consumer’s Guide to Phytoplankton Primary Productivity Models.” *Limnology and Oceanography* 42: 1479–1491. https://doi.org/10.4319/lo.1997.42.7.1479.

* Jemai, A., J. Wollschläger, D. Voß, and O. Zielinski. 2021. “Radiometry on Argo Floats: From the Multispectral State-Of-The-Art on the Step to Hyperspectral Technology.”
Frontiers in Marine Science 8: 676537. https://doi.org/10.3389/fmars.2021.676537.

Jutard, Q., E. Organelli, N. Briggs, et al. 2021. "Correction of Biogeochemical-Argo Radiometry for Sensor Temperature-Dependence and Drift: Protocols for a Delayed-Mode Quality Control." *Sensors* 21: 6217. https://doi.org/10.3390/s21186217.

Lacour, L., H. Claustre, L. Prieur, and F. D'Ortenzio. 2015. "Phytoplankton Biomass Cycles in the North Atlantic Subpolar Gyre: A Similar Mechanism for Two Different Blooms in the Labrador Sea." *Geophysical Research Letters* 42: 5403-5410. https://doi.org/10.1002/2015GL064540.

Laliberté, J., S. Bélanger, and R. Frouin. 2016. "Evaluation of Satellite-Based Algorithms to Estimate Photosynthetically Available Radiation (PAR) Reaching the Ocean Surface at High Northern Latitudes." *Remote Sensing of Environment* 184: 199-211. https://doi.org/10.1016/j.rse.2016.06.014.

Lee, Z., A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis. 2007. "Euphotic Zone Depth: Its Derivation and Implication to Ocean-Color Remote Sensing." *Journal of Geophysical Research: Oceans* 112: C03009. https://doi.org/10.1029/2006JC003802.

Marra, J. F., V. P. Lance, R. D. Vaillancourt, and B. R. Hargreaves. 2014. "Resolving the Ocean's Euphotic Zone." *Deep Sea Research Part I: Oceanographic Research Papers* 83: 45-50. https://doi.org/10.1016/j.dsr.2013.09.005.

Mignot, A., H. Claustre, J. Uitz, A. Poteau, F. D'Ortenzio, and X. Xing. 2014. "Understanding the Seasonal Dynamics of Phytoplankton Biomass and the Deep Chlorophyll Maximum in Oligotrophic Environments: A Bio-Argo Float Investigation." *Global Biogeochemical Cycles* 28: 856-876. https://doi.org/10.1002/2013GB004781.

Morel, A., and J.-M. André. 1991. "Pigment Distribution and Primary Production in the Western Mediterranean as Derived and Modeled From Coastal Zone Color Scanner Observations." *Journal of Geophysical Research: Oceans* 96: 12685-12698. https://doi.org/10.1029/91JC00788.

Mueller, J. L., A. Morel, R. Frouin, et al. 2003. Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 4. Volume III: Radiometric Measurements and Data Analysis Protocols, 84. Maryland: National Aeronautical and Space Administration.

Organelli, E., E. Leymarie, O. Zielinski, J. Uitz, F. D'ortenzio, and H. Claustre. 2021. "Hyperspectral Radiometry on Biogeochemical-Argo Floats: A Bright Perspective for Phytoplankton Diversity." *Oceanography* 34: 90-91. https://doi.org/10.5670/oceanog.2021.supplement.02-33.

Organelli, E., H. Claustre, A. Bricaud, et al. 2016. "A Novel Near-Real-Time Quality-Control Procedure for Radiometric Profiles Measured by Bio-Argo Floats: Protocols and Performances." *Journal of Atmospheric and Oceanic Technology* 33: 937-951. https://doi.org/10.1175/JTECH-D-15-0193.1.

Organelli, E., M. Barbieux, H. Claustre, et al. 2017. "Two Databases Derived from BGC-Argo Float Measurements for Marine Biogeochemical and Bio-Optical Applications." *Earth System Science Data* 9: 861-880. https://doi.org/10.5194/essd-9-861-2017.

Ricour, F., A. Capet, F. D'Ortenzio, B. Delille, and M. Grégoire. 2021. "Dynamics of the Deep Chlorophyll Maximum in the Black Sea as Depicted by BGC-Argo Floats." *Biogeosciences* 18: 755-774. https://doi.org/10.5194/bg-18-755-2021.

Ryther, J. H. 1956. "Photosynthesis in the Ocean as a Function of Light Intensity." *Linnology and Oceanography* 1: 61-70. https://doi.org/10.4319/lo.1956.1.1.0061.

Stoer, A. C., Y. Takeshita, T. L. Maurer, et al. 2023. "A Census of Quality-Controlled Biogeochemical-Argo Float Measurements." *Frontiers in Marine Science* 10: 1233289. https://doi.org/10.3389/fmars.2023.1233289.

Terzić, E., P. Lazzari, E. Organelli, et al. 2019. "Merging Bio-Optical Data From Biogeochemical-Argo Floats and Models in Marine Biogeochemistry." *Biogeosciences* 16: 2527-2542. https://doi.org/10.5194/bg-16-2527-2019.

Xing, X., E. Boss, J. Zhang, and F. Chai. 2020. "Evaluation of Ocean Color Remote Sensing Algorithms for Diffuse Attenuation Coefficients and Optical Depths With Data Collected on BGC-Argo Floats." *Remote Sensing* 12: 2367. https://doi.org/10.3390/rs12152367.

Submitted 09 October 2024

Revised 22 January 2025

Accepted 24 January 2025