A Dual-Band Model for the Vertical Distribution of Photosynthetically Available Radiation (PAR) in Stratified Waters

Based on the optical properties of water constituents, the vertical variation of photosynthetically available radiation (PAR) can be well modeled with hyperspectral resolution; the intensive computing load, however, demands simplified modeling that can be easily embedded in marine physical and biogeochemical models. While the vertical PAR profile in homogeneous waters can now be accurately modeled with simple parameterization, it is still a big challenge to model the PAR profile in stratified waters with limited variables. In this study, based on empirical equations and simulations, we propose a dual-band model to characterize the vertical distribution of PAR using the chlorophyll concentration (Chl). With an inclusive dataset including cruise data collected in the Southeast Pacific and BGC-Argo data in the global ocean, the model was thoroughly evaluated for its general applicability in three aspects: 1) estimating the entire PAR profile from sea-surface PAR and the Chl profile, 2) estimating the euphotic layer depth from the Chl profile, and 3) estimating PAR just below the sea surface from in situ radiometry measurements. It is demonstrated that the proposed dual-band model is capable of generating similar estimates as that from a hyperspectral model, thus offering an effective module that can be incorporated in large-scale ecosystem and/or circulation models for efficient calculations.

Introduction

The diurnal and seasonal cycles of solar radiation and its underwater vertical distribution play an important role in ocean heat uptake (Lewis et al., 1990), which impacts sea-surface temperature and upper-ocean stratification (Liang and Wu, 2013; Pimentel et al., 2019; Liu et al., 2020) and in turn acts on ocean circulation (Liang and Wu, 2015) and air–sea interaction (Liu et al., 2021). Moreover, solar radiation also supports primary production and the entire marine ecosystem (Evans and Parslow, 1985; Bryant et al., 2016; Skákala et al., 2020). The visible light part of solar radiation, i.e., photosynthetically available radiation (PAR), is defined as the downwelling photon flux integrated from 400 to 700 nm. The accuracy of both marine net primary production (NPP) algorithms (Westberry et al., 2008; Fox et al., 2020) and ecosystem models (Skákala et al., 2020) highly depends on the vertical distribution of PAR. Skákala et al. (2020) demonstrated that different PAR attenuation models may result in vastly discrepant phytoplankton seasonal bloom patterns and community structures. Recently, Xing and Boss (2021) illustrated that the use of PAR attenuation models with large uncertainties could lead to an error of 100% of estimated PAR at the half mixed layer depth, which would significantly impact the NPP estimates. PAR attenuation also highly affects the physical oceanography modeling of seawater temperature and mixing (Rochford et al., 2001; Liu et al., 2020; Liu et al., 2021), the diurnal cycles of sea-surface temperature (Pimentel et al., 2019), and even the atmospheric and ocean circulation (Gnanadesikan and Anderson, 2009). For example, Liu et al. (2020) found that the uses of different PAR models would lead to differences up to 1.5°C–2°C in sea surface temperature. An accurate estimate of the PAR profile is the prerequisite to determine the euphotic layer, which is typically used as a proxy for the compensation depth of the phytoplankton ecosystem (Ryther, 1956; Wu et al., 2021). The model-estimated euphotic layer depth is critical not only in carbon export assessment of the ocean biological carbon pump (Carlson et al., 1994; Siegel et al., 2014; Buesseler et al., 2020) but also in marine ecosystem modeling (e.g., Chai et al., 2002; Aumont et al., 2015), as well as in studies on the mechanisms of seasonal phytoplankton blooms (e.g., Behrenfeld, 2010; Mignot et al., 2018).

Accurate estimation of the PAR profile with concise parameterizations has been a serious challenge in the past 50 years (e.g., Lorenzen, 1972; Paulson and Simpson, 1977; Zaneveld and Spinrad, 1980; Byun et al., 2014). Most of the difficulty lies in the combined effects of two characteristics of the propagation of solar radiation in water: the strong and spectrally selective attenuation near the sea surface and the quasi-inherent optical property (IOP) characteristics of the blue-green band in open oceanic waters. The former is related to the faster attenuation in the longer wavelengths due to the strong absorption by water molecules (Paulson and Simpson, 1977; Lee, 2009), while the latter behaves as a correlation of the PAR attenuation to chlorophyll concentration (Chl; Morel, 1988). Therefore, for highly stratified waters where a deep chlorophyll maximum (DCM) exists at the subsurface, the vertical distribution of PAR in the ocean is characterized by two fast-attenuation layers: the first one is near the sea surface related to the fast loss of red light (Paulson and Simpson, 1977; Lee, 2009), and the second one is around the DCM, as a result of enhanced absorption and backscattering by phytoplankton (Xing and Boss, 2021). It is not surprising that the parameterization scheme of PAR based on homogeneous IOPs (Lee et al., 2005) cannot accurately estimate the attenuation around DCM (Xing and Boss, 2021), as the IOPs vary with depth (Bricaud et al., 2010). The entire profile of IOPs or Chl, therefore, is required for the simulation of PAR profiles in stratified waters. Recently, Xing and Boss (2021) proposed a chlorophyll-profile-based parameterization scheme, termed “GCMM.” This scheme combines the clear-sky spectral irradiance model of Gregg and Carder (1990) (GC90) and the empirical spectral relationships between Chl and the spectral diffuse attenuation coefficients (K_d) developed by Morel and Maritorena (2001) (MM01). With the Chl profile as input and a hyperspectral resolution, the scheme solves well the combined effects of spectral selectivity and quasi-IOP characteristics.

Although the GCMM model showed good performance in estimating PAR profiles in stratified waters (Xing and Boss, 2021), it needs hyperspectral processing, i.e., decomposing PAR to spectral irradiance with a wavelength resolution of 1 nm. As a result, the computing load is very high, particularly when implementing in ecosystem models or global gridded datasets. Recently, Lee et al. (2014) have proposed the concept of usable solar radiation (USR), which focused on the irradiance or photon flux in the 400–560-nm domain. The merits of USR are that it is not influenced by the fast attenuation at longer wavelengths, and the attenuation of USR is highly sensitive to phytoplankton. Therefore, based on the characteristics of USR attenuation, in this study, we propose a dual-band PAR parameterization model that decomposes PAR into two wide bands, USR (400–560 nm) and Green-to-Red (GR, 560–700 nm). Such a processing of splitting the whole PAR domain to two or three bands has been used before in some regional models (e.g., Fasham et al., 1983; Zielinski et al., 2002; Wollschläger et al., 2020). Our proposed model, termed USRGR, has a simplified parameterization compared to the hyperspectral GCMM scheme but delivers equivalent performances in estimating the PAR profile in stratified waters. This model is applicable not only to estimate the euphotic layer depth and daily PAR profile from in situ Chl measurements, and sea-surface PAR from underwater PAR observations, but also to ecosystem or general circulation models that require daily or hourly PAR profiles to drive the phytoplankton growth or upper-layer water temperature change.

Materials and Methods

Model Structure

To model a PAR profile with a Chl profile as the input, the procedures and components of USRGR (Figure 1) include the following:

FIGURE 1

Figure 1 Structure of the USRGR model.

1) The sea-surface PAR(0-) is decomposed into two bands (Eq. 1), USR and GR, via the relative measure (represented as β) of USR(0-) out of PAR(0-), which can be determined from the latitude and day of year (see the look-up table made through the GC90 model¹). β is around 0.48 for the quanta unit (e.g., μmol photons m^-2 s^-1) and around 0.55 for the irradiance unit (e.g., W m^-2), with a slight dependence on the solar zenith angle.

$\begin{array}{ll}USR\left(0-\right)=\beta •PAR\left(0-\right)& \text{(1a)}\end{array}$

$\begin{array}{ll}GR\left(0-\right)=\left(1-\beta \right)•PAR\left(0-\right)& \text{(1b)}\end{array}$

2) A given Chl profile is interpolated into a fine resolution at an interval of 1 m (1 m, 2 m, 3 m, etc.);

3) K_d(USR,z) is modeled as a function of K_d(490,z) (Eq. 2; Lin et al., 2016), with K_d(490,z) at each depth z determined with the Chl–K_d empirical relationship of MM01 (Eq. 3);

$\begin{array}{ll}{K}_d\left(USR,z\right)=\{\begin{array}{cc}0.91•K_d{\left(490,z\right)}^{0.89}& \left(K_d\left(490,z\right)\ge 0.1\right)\\ 0.0062+1.16•K_d\left(490,z\right)-0.00018/K_d\left(490,z\right)& (K_d\left(490,z\right)<0.1)\end{array}& (2)\end{array}$

$\begin{array}{ll}{K}_d\left(490,z\right)=0.0166+0.072•Chl{\left(z\right)}^{0.69}& (3)\end{array}$

Here this Chl–K_d relationship represents a nominal solar-zenith angle ~40°. For situations of extremely high or low sun angles, an adjustment is necessary if higher accuracy is desired.

4) USR is vertically attenuated with K_d(USR,z) layer by layer (Eq. 4):

For z = 1 m, (z-1) represents the sea surface (0-);

$\begin{array}{ll}USR\left(z\right)=USR\left(z-1\right)•exp\left[-K_d\left(USR,z\right)•1\right]& (4)\end{array}$

5) A layer-averaged diffuse attenuation coefficient (κ_d) is used for the propagation of the GR band from the surface to any depth (Eq. 5):

$\begin{array}{ll}GR\left(z\right)=GR\left(0-\right)•exp\left[-{\kappa }_d\left(GR,z\right)•z\right]& (5)\end{array}$

Note that κ_d here represents the averaged diffuse attenuation coefficient from the surface (0-) to any given depth (z), while K_d of Eq. 4 represents the diffuse attenuation coefficient at the given depth (z). We use the layer-averaged one here because the light attenuation of GR mainly depends on the pure-water absorption For Chl in a range of 0.02 to 2.0 mg/m³ (100 data points, ~4% increase rate), through numerical simulations of Hydrolight (Mobley, 1995), it is found that κ_d(GR) can be approximated as:

$\begin{array}{ll}\begin{array}{l}{\kappa }_d\left(GR,z\right)=\left(0.1+0.79•K_d{\left(490\right)}_{surf}\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+\left(0.21-0.23•K_d{\left(490\right)}_{surf}\right)exp\left(-0.082•z\right)\end{array}& (6)\end{array}$

Here, K_d(490)_surf is derived from Eq. 3 using averaged Chl within z ≤ 10 m.

6) Finally, PAR at each depth (PAR(z)) is obtained as a sum of USR(z) and GR(z):

$\begin{array}{ll}PAR\left(z\right)=USR\left(z\right)+GR\left(z\right)& (7)\end{array}$

Applications of the USRGR Model

Figure 2 illustrates three applications of the USRGR model, with the first one to estimate daily PAR profiles. Its required inputs include the observed or modeled Chl profile and sea-surface daily PAR(0-) from ocean-color satellites (e.g., MODIS-Aqua) or reanalysis products (e.g., ECMWF-ERA). It is applicable with vertical Chl observations obtained from in situ platforms (e.g., research vessel, BGC-Argo, and underwater glider), global gridded Chl profile datasets (e.g., Sauzède et al., 2016), and ecosystem models with the Chl profile as a product (e.g., Fennel et al., 2006; Fujii et al., 2007). The corresponding Matlab function can be found in GitHub². For observation data, the derived PAR profile can be further employed to estimate net primary production, through the Carbon-based Production Model (CbPM; Westberry et al., 2008), Photoacclimation-based Production Model (PbPM; Fox et al., 2020), or Absorption-based Model (AbPM; Lee et al., 1996; Lee et al., 2015); for ecosystem models, the derived PAR profile can be used to initiate the process of photosynthesis and then drive the phytoplankton growth and Chl change. The dynamics of phytoplankton biomass would in turn adjust the light penetration via bio-optical feedbacks (Manizza et al., 2005).

FIGURE 2

Figure 2 Applications of the USRGR model. z_x% represents the depth where PAR is attenuated to 1% (z_1%; Ryther, 1956) or 0.5% of sea-surface value (z_0.5%; Wu et al., 2021).

Second, the euphotic layer depth, defined as the depth where PAR is attenuated to 1% (z_1%; Ryther, 1956) or 0.5% of sea-surface value (z_0.5%; Wu et al., 2021), can be derived directly through the USRGR model from a Chl profile (Figure 2). In this case, the sea-surface PAR is not required, as the euphotic layer depth refers to the relative change of PAR in the water column, which actually represents the transmittance of PAR. From the model structure of the USRGR (Eqs. 1, 4, 5, and 6), it is clear that the transmittance of PAR mainly relies on K_d(490,z), which is further expressed as a function of Chl. As such, the percentage PAR profile (i.e., a relative PAR profile normalized by sea-surface PAR) can be directly calculated from the corresponding Chl profile, and then the euphotic layer depth would be determined.Third, the USRGR model can also be used to obtain sea-surface PAR(0-) from underwater radiometry observations (e.g., a radiometry profiler conducted on a research vessel or a BGC-Argo float with downwelling PAR observation). It should be clarified, although the PAR profile can be measured in situ, that it is rarely possible to measure PAR close to z = 0-, owing to surface waves. As such, PAR(0-) has to be estimated from downwelling irradiance observed above the sea surface or by upward extrapolation from downwelling irradiance within the water column. However, the above-surface observation is not always available, e.g., from the BGC-Argo floats. The USRGR model can be employed to extrapolate PAR(0-) from the underwater PAR profile based on the bio-optical relationships. In natural waters, it is reasonable to assume a homogeneous distribution of IOPs and Chl within the surface layer (like ≤10 m) due to the surface mixing effect. Within this layer, therefore, Chl can be regarded as a depth-independent variable. Then the USRGR model could express the PAR profile within the 10-m layer with only two variables: PAR(0-) and Chl. As such, it would be straightforward to derive PAR(0-) via an optimization analysis on the PAR profile (Figure 2). The derived PAR(0-) can be further employed to calculate the layer-averaged diffuse attenuation coefficient from the surface to any depth (Xing et al., 2020).It should be noted that all three applications (estimation of the PAR profile, euphotic depth, and sea-surface PAR) are not exclusive to the USRGR model but can also be achieved by some other PAR attenuation models. In this study, we evaluate the USRGR model through these applications, to demonstrate that the USRGR model can tackle these questions with similar quality (i.e., performance) as the previous models (e.g., hyperspectral), but with efficient computation.

Data

In this study, we evaluate the performance of the USRGR model against two in situ datasets: the first one is the ship-borne measurements collected from the Biogeochemistry and Optics South Pacific Experiment (BIOSOPE) cruise (Claustre et al., 2008). The cruise was conducted in the Southeast Pacific between October and December 2004 (Supplementary Figure 1). A total of 39 spectral-irradiance profiles were recorded by a Satlantic profiler, and the corresponding surface irradiance measurements were obtained by a Satlantic TSRB (Tethered Spectral Radiometer Buoy). The radiometry data covered various trophic conditions, from eutrophic (west of Marquesas Island, and the Chile upwelling) to ultra-oligotrophic (center of South Pacific subtropical gyre). We first conducted a quality-control procedure following Organelli et al. (2016) for all radiometry data to get rid of noisy profiles and data spikes, and 35 profiles remained. The measured irradiance values above the sea surface at each wavelength [E_s(λ)] were converted to the ones just below sea surface E_d(0-,λ), by multiplying the air–sea transmission factor α (Mobley and Boss, 2012). Following the MODIS Algorithm Theoretical Basis Document (Carder et al., 2003), the PAR(z) profile and sea-surface PAR(0-) were defined as the integration of photons from 400 to 700 nm (Eq. 8).

$\begin{array}{ll}PAR\left(z\right)=\underset{400}{\overset{700}{\int }}\frac{\lambda }{hc}{E}_d\left(\lambda ,z\right)d\lambda & \text{(8a)}\end{array}$

$\begin{array}{ll}PAR\left(0-\right)=\underset{400}{\overset{700}{\int }}\frac{\lambda }{hc}{E}_d\left(\lambda ,0-\right)d\lambda & \text{(8b)}\end{array}$

where h is Plank’s constant and c is the speed of light in a vacuum. Correspondingly, the observed USR and GR profiles are calculated as:

$\begin{array}{ll}USR\left(z\right)=\underset{400}{\overset{560}{\int }}\frac{\lambda }{hc}{E}_d\left(\lambda ,z\right)d\lambda & (9)\end{array}$

$\begin{array}{ll}GR\left(z\right)=\underset{560}{\overset{700}{\int }}\frac{\lambda }{hc}{E}_d\left(\lambda ,z\right)d\lambda & (10)\end{array}$

Chl profile data were measured through collecting discrete water samples quasi-simultaneously to the radiometry and then submitted to the laboratory analysis with high-performance liquid chromatography (HPLC; see Supplementary Text 1).

Despite the accurate Chl measurement and above-water PAR observation, the BIOSOPE cruise only covered a limited area and data samples are not adequate. The second dataset we use is a global BGC-Argo dataset (Supplementary Figure 2), the same as Xing and Boss (2021), to validate the PAR profiles derived from the USRGR model, and to compare the results from the GCMM model. The dataset encompasses 193 BGC-Argo floats in the global open oceans collected from October 2012 to March 2020. All these floats were equipped with Satlantic OCR504 radiometers and Wet Labs ECO in vivo chlorophyll-a fluorometers. The quality control of radiometry followed Organelli et al. (2016), and the correction of Chl fluorometry data were described in Supplementary Text 2.

Besides, as a case application, the monthly climatological Chl profile data, termed SOCA2021 (Sauzède et al., 2021), with a 0.25° horizontal resolution and 36 vertical levels from the surface to 1,000-m depth, provided by the Copernicus Marine Environment Monitoring Service (CMEMS), were used to estimate the euphotic layer depth. This depth-resolved Chl dataset was derived from a neural network model (Sauzède et al., 2016), with inputs including remote-sensing reflectance, daily PAR, and sea-level anomaly from satellites, along with the mixed-layer depth (MLD) product from a reanalysis gridded temperature and salinity dataset (Guinehut et al., 2012).

Statistical Metrics

The statistical metrics used in this study include the root mean square difference (RMSD), mean difference (MD), and mean percentage difference (MPD), defined as:

$\begin{array}{ll}RMSD=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n}{\left(E_i-M_i\right)}^2}& (11)\end{array}$

$\begin{array}{ll}MD=\frac{1}{n}{\displaystyle \sum _{i=1}^n}\left(E_i-M_i\right)& (12)\end{array}$

$\begin{array}{ll}MPD=\frac{1}{n}{\displaystyle \sum _{i=1}^n}\frac{\left(E_i-M_i\right)}{M_i}•100\%& (13)\end{array}$

Here, M_i and E_i are the in situ measured and corresponding model-estimated values, respectively, and n is the number of observations. RMSD represents the total deviations between the measured and estimated values, while MD and MPD represent the absolute and relative system biases of estimated values, respectively.

Results and Discussion

Estimate of the PAR Profile From Sea-Surface PAR and Chl Profile

We first examined the performance of the USRGR model in estimating the PAR profile based on the BIOSOPE cruise data. Figure 3 shows example profiles of observed Chl, PAR, USR, and GR, collected at Station GYR5, in the ultra-oligotrophic center of the Southeast Pacific subtropical gyre (Claustre et al., 2008). At this station, the sea-surface Chl was extremely low (~0.015 mg m^-3), and the DCM appeared at 180 m (Figure 3A). The observed USR profile showed a constant attenuation [i.e., close to a straight line in the semi-log coordinate (x-axis as log scale)] near the sea surface but attenuated faster below the depth of ~80 m (Figure 3B), where the corresponding Chl was enhanced (Figure 3A); in contrast, the observed GR profile attenuated very fast near the sea surface and slowed down below ~30 m (Figure 3C), as a result of the fact that all red photons were lost near the surface. Combining USR and GR, we obtained the total PAR profile (Figure 3D). It is clearly observed that there were two fast attenuation layers of the vertical PAR, with the first layer mainly caused by the attenuation in the GR band and the second layer mostly attributed to the enhanced attenuation in the USR band. Overall, the USRGR model performed well to estimate the USR, GR, and total PAR profile, respectively (Figures 3B–D), except for some underestimation of GR below 50 m (Figure 3C), where GR had attenuated to a very low value (<3 μmol photons m^-2 s^-1). Such an underestimation did not significantly affect the estimation of the PAR profile (Figure 3D). More importantly, compared to the performance of the hyperspectral GCMM model, the dual-band USRGR model resolved similar PAR profiles from the surface to 200 m (Figure 3D).

FIGURE 3

Figure 3 An example of the observed and model-estimated USR, GR, and PAR profiles at Station GYR 5 (26.07°S, 114.02°W) on November 15, 2004 in the Southeast Pacific. (A) Observed Chl based on the HPLC method. (B) Observed USR (black) and estimated one from the USRGR model (red). (C) Observed GR (black) and estimated one from the USRGR model (red). (D) Observed PAR (black) and estimated ones from the USRGR (red) and GCMM model (green), respectively.

Figure 4 shows the statistical results for all the 35 quality-controlled downwelling radiometry profiles observed in the BIOSOPE cruise. All profiles were described using the normalized depth ζ, which was defined as z/z_1%. MPD was calculated at each ζ. We found that the estimated USR profiles had quite low MPD values from 0- to 1.5-fold z_1% (Figure 4A), except for some slight underestimation around z_1%, and the averaged absolute MPD (AMPD) from 0- to 1.5-fold z_1% was 8%. The estimated GR profile had a low MPD near the sea surface, and underestimation appeared below ~0.2-fold z_1% (Figure 4B), similar to the example profile shown in Figure 3C. Such an underestimation reached maximum around z_1%, with MPD close to -100%. However, again, it should be noted that, at such a depth, GR had attenuated to a very low level as mentioned above. As a consequence, the estimated PAR was not affected by the GR underestimation at depth, and its MPD profile displayed a similar vertical pattern to that of the USR (Figures 4A, C), with an AMPD of 9.5%. Compared with the performance of GCMM (AMPD = 12.5%), the USRGR model demonstrated similar and even better performance in estimating the PAR profile.

FIGURE 4

Figure 4 Validation statistics of the estimated USR (A), GR (B), and PAR (C) profiles based on the BIOSOPE cruise dataset. The mean percentage difference (MPD) at each depth was normalized by z_1% for the Chl-based USRGR (red) and Chl-based GCMM model (green). The numbers in the legend represent the averaged absolute MPD (AMPD) from the surface to the 1.5-fold z_1%.

Besides, the global BGC-Argo dataset compiled by Xing and Boss (2021) was also used here to evaluate the USRGR model in estimating the PAR profile. Here we compared its performance with the Chl-profile-based GCMM model and IOP-based Lee05 model (Lee et al., 2005). The results are shown in Figure 5. For a better evaluation, we characterized all the BGC-Argo Chl profiles into two types, the Mixed Type (maximal Chl locates within the mixed layer) and the DCM Type (maximal Chl locates below the mixed layer). Note that such a classification is only used for the evaluation here and is not required in the general application of the USRGR model. Within the 1.5-fold z_1% layer, the USRGR model worked well for both types, with AMPD of 12.5% in Mixed-Type and 9.3% in DCM-Type waters, similar to the performance of GCMM. As discussed in Xing and Boss (2021), Surface-IOP-based Lee05 performed well in the Mixed-Type waters but overestimated the PAR profile in the DCM-Type ones from 0.5-fold to 1.5-fold z_1%, reflecting the strong impact of DCM in regulating the attenuation of PAR in the water column.

FIGURE 5

Figure 5 Validation statistics of the estimated PAR profiles based on the global BGC-Argo dataset. The mean percentage difference (MPD) at each depth was normalized by z_1% for the estimated PAR by the satellite IOP-based Lee05 (blue), Chl-based USRGR (red), and Chl-based GCMM model (green), for Mixed-Type (maximal Chl locates within the mixed layer) (A) and DCM-Type (maximal Chl locates below the mixed layer) (B) waters, respectively. The numbers in the legend represent the averaged absolute MPD (AMPD) from the surface to the 1.5-fold z_1%.

In addition, the USRGR model consumes much shorter computing time than GCMM. A test was conducted to derive the PAR profiles from the global climatological Chl profile data in January; the USRGR model took only 260 s, significantly faster than the GCMM (4195 s) by 93.8%. This is because GCMM decomposes the visible light into 300 wavebands, but USRGR has only two; GCMM frequently calls the GC90 model function, but USRGR only accesses a look-up table of β (Eq. 1).

Estimate of Euphotic Layer Depth From the Chl Profile

It is very common that only Chl observation is available on some in situ observation platforms (e.g., BGC-Argo, glider, as well as the research vehicles) but without radiometry. For example, 53% of the present alive BGC-Argo floats are equipped with Chl fluorometers, but only about 15% with radiometers. The USRGR model, therefore, could be employed to estimate the euphotic layer depth directly from in situ observed Chl profiles; e.g., Xing et al. (2021) estimated z_1% based on the GCMM model using BGC-Argo-observed Chl.

Here we adopted the conventional definition of 1% surface PAR (z_1%) to represent the euphotic layer depth, although a depth of 0.5% of surface PAR better matches the compensation depth of phytoplankton photosynthesis (Wu et al., 2021). To evaluate the performance of the USRGR model in estimating z_1%, the BIOSOPE cruise data were employed (Figure 6). The radiometer-observed z_1% showed a wide range from 26 m (in the eutrophic upwelling zone) to 163 m (in the ultra-oligotrophic waters). The USRGR model had a good estimate of z_1% with an RMSD of 7.9 m and a little system bias (MPD = -1.5%). In contrast, the surface-Chl-based empirical model of Morel et al. (2007) displayed higher errors (RMSD = 12.9 m), particularly with an obvious underestimation in the ultra-oligotrophic waters (z_1% > 140 m), as reported in Xing et al. (2020). In addition, we found that the USRGR model also showed good performance for z_0.5%, with RMSD of 7.6 m and MPD of 0% (figure not shown here). It should be noted, similarly, that the USRGR model also admits to estimate euphotic layer depths by other definitions: e.g., z_0.1% and z_0.9%USR (the depth where USR decreases to 0.9% of sea-surface USR; Wu et al., 2021).

To demonstrate its application, here we applied the USRGR model to the global Chl profile data (Sauzède et al., 2021) to estimate monthly climatological z_1%, with the results of January and July shown in Figures 7A and B. Spatially, z_1% was deeper in the subtropical gyres and shallower at high latitudes (Southern Ocean and North Atlantic Subpolar region), in the upwelling zones, as well as the summer Oyashio Extension. In the five oligotrophic subtropical gyres, z_1% was deeper than 100 m, and the deepest values were found in the Southeast Pacific subtropical gyre (>170 m in summer), consistent with the BIOSOPE data (shown in Figure 6). Moreover, the derived z_1% values in other oligotrophic gyres were also in good agreement with previous in situ observations, e.g., with the deepest value of ~140 m in both North and South Atlantic gyres as reported by Poulton et al. (2017) and ~120 m in the Northeast Pacific gyre as recorded by Letelier et al. (2004). On the seasonal scale (comparing Figures 7A, B), for all the five subtropical gyres, z_1% was deeper in summer (January in the Southern Hemisphere and July in the Northern Hemisphere) than in winter (July in the Southern Hemisphere and January in the Northern Hemisphere), due to less sea-surface Chl and deeper DCM in summer (Letelier et al., 2004; Mignot et al., 2014). In contrast, z_1% at mid-latitudes (30°–60°) was deeper in winter than in summer, due to the characteristics of seasonal stratification, i.e., deep mixing in winter and strong stratification in summer (Xing et al., 2021). The deep mixing in winter eroded DCM and brought some subsurface particles into the mixed layer; such a particle-entrainment process enhanced sea surface Chl, and therefore shoaled z_1%; in contrast, the strong stratification in summer obstructed nutrient supply into the mixed layer, and thus the lower Chl at the sea surface and deeper DCM co-determined z_1% to be deeper (Xing et al., 2021). Figures 7C, D shows the difference between USRGR-derived z_1% and Morel07-derived ones based on MODIS Aqua monthly climatological Chl. Most of the disparity were in subtropical gyres, where USRGR showed deeper z_1% than Morel07 in both January and July by 10–40 m (with a maximum relative difference larger than 50%), and their differences were larger in summer, corresponding to less sea-surface Chl and deeper DCM. Besides, USRGR derived shallower z_1% than Morel07 in the Southern Ocean and Tropical Eastern Pacific by 20–30 m.

FIGURE 6

Figure 6 Comparison between the observed and estimated z_1% based on the BIOSOPE dataset. Morel07 (blue) represents the surface-Chl-based empirical model proposed by Morel et al. (2007).

FIGURE 7

Figure 7 Global monthly climatological z_1% in January (A) and July (B), estimated by the USRGR model based on the neural-network-based monthly climatological Chl profile dataset (Sauzède et al., 2021); the difference in z_1% between the USRGR model and the Morel07 model (z_1% was based on the monthly climatology of MODIS-Aqua Chl) in January (C) and July (D).

Estimate of PAR(0-) for the Underwater PAR Profile

Third, the USRGR model can be employed to estimate the PAR just below the sea surface [i.e., PAR(0-)] from the underwater PAR profile. As mentioned in Section 2.2, the estimation of PAR(0-) generally relies on upward extrapolation from underwater downwelling radiometry. For downwelling irradiance (E_d(λ,z)) at a certain wavelength, the extrapolation based on a linear regression between ln(E_d) and depth is usually adequate with the assumption of vertically uniform IOPs and K_d(λ) within the surface mixed layer. However, this assumption is not valid for downwelling PAR, where K_d(PAR) may vary threefold (much higher K_d(PAR) near the surface for oceanic waters) within the surface 10-m layer (Lee, 2009). Xing et al. (2020) tried to solve the problem by developing a second-degree polynomial function regression between observed ln(PAR) and z, from which PAR(0-) could be estimated through an extrapolation of the regressed equation to z = 0. However, such a regression method is purely empirical. Different from the regression method, here the optimization analysis of the USRGR model (See Applications of the USRGR Model) is based on the bio-optical relationships, despite some empirical equations used. Figure 8 shows the comparison between observed PAR(0-) from the BIOSOPE cruise data and the estimated ones from the USRGR model. All the PAR(0-) were measured around local noon, with a dynamic variation range from 402 μmol photons m^-2 s^-1 (overcast) to 2,178 μmol photons m^-2 s^-1 (clear sky). Clearly, the USRGR achieved more accurate estimates than the regression method, with an RMSD of 189 μmol photons m^-2 s^-1 and a slight bias (MPD = 7.5%).

FIGURE 8

Figure 8 Comparison between the observed and estimated PAR(0-) based on the BIOSOPE dataset. The regression method (blue) represents the regression of second-degree polynomial function (Xing et al., 2020).

Error Source Analysis

The main error sources of the USRGR model stem from three empirical equations (Eqs. 2, 3, and 6), particularly the Chl-K_d(490) bio-optical relationship (Eq. 3). This relationship was established by Morel and Maritorena (2001) based on a global near-surface observation dataset with Chl varying from 0.02 mg m^-3 (ultra-oligotrophic) to 40 mg m^-3 (eutrophic). However, it is well known that K_d mainly represents the total absorption coefficient (Gordon, 1989; Lee et al., 2005), including the contributions not only from phytoplankton and pure water (both are considered in Eq. 3) but also from chromophoric dissolved organic matter (CDOM) and detritus (also called non-algal particles), which are to some degree correlated with Chl in the open oceans (Bricaud et al., 1998; Morel, 2009). Therefore, the empirical Chl–K_d relationship represents a global near-surface “mean state” of co-varying relationship between phytoplankton and other organic matters. However, the bio-optical anomaly around the mean state exists and some are quite large, particularly for the CDOM–Chl relationship, among different regions (Morel and Gentili, 2009). Besides, as reported by Bricaud et al. (2010), the chlorophyll-specific CDOM generally decreases with depth. That is to say, the near-surface-based Chl–K_d relationship could overestimate deep-water K_d(490) and in turn underestimate USR and PAR to some extent. Therefore, it is not surprising that our BIOSOPE-based analysis results show that the USRGR model slightly underestimated USR and PAR at depth, with the negative maximum of MPD reaching ~-20% (Figures 3 and 4). Since PAR is underestimated to some extent (i.e., PAR is attenuated faster than expected), so is the euphotic layer depth z_1% (i.e., shallower than expected) in the ultra-oligotrophic waters, as shown in Figure 6. Nevertheless, the USRGR model still provides a relatively accurate approach to estimate the PAR profile and euphotic layer depth. It is noteworthy that the same error source also exists in the Chl-based GCMM model. At the current stage, there is neither parameterization method nor empirical equation available to correct the CDOM (and/or detritus, suspended particles) anomaly in deep waters; therefore, the USRGR model could be further improved once the contributions from other constituents are better quantified/parameterized in the future.

In addition to the error from the empirical Chl–K_d relationship, the Chl observation/estimation error is also noteworthy. For example, on autonomous mobile platforms (e.g., BGC-Argo, gliders), Chl is estimated by in vivo fluorometers; the Chl-fluorescence variability can introduce additional errors due to the fluorescence efficiency’s uncertainty (Proctor and Roesler, 2010). In some cases, Chl profiling is not available either spatially or temporally; the use of alternative model-estimated Chl profile products (e.g., Uitz et al., 2006; Sauzède et al., 2021; Chen et al., 2022) would also introduce some errors, mainly from the estimated DCM depth, magnitude, and thickness. As analyzed by Xing and Boss (2021), the use of a model-estimated Chl profile (from Uitz et al. (2006)) showed an obvious improvement in estimating the PAR profile in stratified waters, yet with large errors around the euphotic layer depth (MPD of ∼25% at z_1%). Although the SOCA-modeled Chl were well evaluated with the global BGC-Argo Chl dataset and a global HPLC Chl database (Sauzède et al., 2021), the averaged absolute percentage error from the Chl profile was reported to be ~40%. We tested the sensitiveness of the USRGR-derived z_1% to the Chl uncertainty using the BIOSOPE cruise data, and it is found that the error of +40% and -40% in the Chl profiles would lead to an MPD of 11% and 21% in z_1%, respectively (results not shown).

Summary

By decomposing the entire PAR into two wavebands (USR and GR), and then parameterizing their respective attenuation characteristics, here we propose a simplified PAR parameterization model, named USRGR. From a practical point of view, the USRGR model expresses a simple but high-performance approach to model the vertical profiles of PAR for stratified waters. The attenuation of USR maintains the quasi-IOP characteristics, highly related to K_d(490) (Lee et al., 2014; Lin et al., 2016). Taking advantage of the global Chl–K_d empirical relationship (Morel and Maritorena, 2001), the depth-resolved quasi-IOP characteristics can be expressed as a function of the Chl profile. Although some vertical and regional anomalies may affect the accuracy of the Chl–K_d relationship as mentioned in Section 3.4, Chl is still the most common proxy and index of phytoplankton biomass and optical characteristics, in both in situ observations and ecosystem models. Particularly, the fast attenuation of PAR around DCM can be well expressed by the Chl profile, although underestimation may still exist in the estimated PAR profile around z_1%. On the other hand, the attenuation of the GR band mainly displays the strong spectral filtering of PAR, with fastest attenuation near the surface and a gradual decrease with depth. Therefore, in this study, the diffuse attenuation coefficient of the GR waveband is parameterized as the function of depth (z) and sea-surface K_d(490).

The new USRGR model is a simplified version of the hyperspectral GCMM model, following the same processing approach: spectral decomposition and vertical IOP variability. Based on the validation results and analyses using the BIOSOPE cruise data and global BGC-Argo dataset, it is well demonstrated that the USRGR model could effectively estimate the PAR profile in both stratified and mixed waters, particularly with a satisfactory performance the same as GCMM in stratified waters. Besides, USRGR is more much efficient, with much less computing time than GCMM (saving more than 90% of time). Third, USRGR is also widely applicable, not only to the in situ observation but also to the marine ecosystem models for estimating the entire PAR profile and euphotic layer depth.

It is also noteworthy that the USRGR-estimated PAR profile is of significance to studies of marine ecosystem dynamics. For example, the median PAR in the mixed layer derived from the PAR profile represents the light condition of mixed-layer phytoplankton growth, which is a key parameter in the photoacclimation models (Behrenfeld et al., 2005; Behrenfeld et al., 2016); z_0.415, the isolume depth where the daily PAR value reaches 0.415 mol photons m^-2 day^-1, is another proxy of compensation depth (Letelier et al., 2004) and can be easily determined from the PAR profile. It has been used in the studies of seasonal algal bloom (e.g., Boss and Behrenfeld, 2010; Cetinić et al., 2015). Recently, some depth-resolved NPP models have been proposed (e.g., Westberry et al., 2008; Fox et al., 2020) for better NPP estimates than the surface-based NPP model (e.g., VGPM); the daily PAR profile, therefore, becomes indispensable in calculating the depth-resolved and vertically-integrated NPP. Especially the neural network model SOCA2021 (Sauzède et al., 2021) provides not only the monthly climatological Chl and backscattering profiles [a proxy for phytoplankton carbon (Graff et al., 2015)] but also the 22-year consecutive weekly Chl and backscattering profiles (1998–2019). The global weekly depth-resolved NPP can be well determined based on the PAR profile estimated from the USRGR model.

Data Availability Statement

The original contributions presented in the study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding author.

Author Contributions

ZL designed the concept. PX and FC coordinated the overall research project. SC contributed to the remote sensing data analysis. XX was responsible for data processing and drafting the manuscript. All authors revised the manuscript. All authors contributed to the article and approved the submitted version.

Funding

This work is supported by the National Natural Science Foundation of China (41890805, 41876032).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

The authors are grateful to Prof. Hervé Claustre (Laboratoire d’Océanographie de Villefranche, Sorbonne Université, Villefranche-sur-Mer, France) for providing the BIOSOPE cruise data, the Copernicus Marine Environment Monitoring Service (CMEMS) for distributing the monthly climatological Chl profile data, and all the BGC-Argo data providers and the principal investigators of related BGC-Argo float missions and projects. The BGC-Argo data were collected and made freely available by the International Argo Program (https://doi.org/10.17882/42182), and the BGC-Argo data processing and quality control in this study was conducted in the China Argo Real-time Data Center (http://www.argo.org.cn).

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmars.2022.928807/full#supplementary-material

Footnotes

1. ^ https://github.com/BGC-Argo/USRGR/blob/main/Beta1.txt
2. ^ https://github.com/BGC-Argo/USRGR/blob/main/USRGREstPARProfile.m

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