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

Abstract

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.

Global Variability of Phytoplankton Carbon and Non‐Algal Particles From Ocean Color Data Based on a Photoacclimation Model

“…The procedure includes three steps: PAR sat was divided by the daytime length (DL, in hours), and multiplied by the transmission coefficient ( α ) which converts radiation from “above sea surface” into “below sea surface” (PAR 0 ): $$${\text{PAR}}_{0}=\alpha \times {\text{PAR}}_{\text{sat}}/\text{DL}$$$ Here, the coefficient α was provided by Mobley and Boss (2012). The PAR profile in the mixed layer (PAR( z )) was estimated from PAR 0 anddiffuse attenuation coefficient K d (490), based on the USRGR model (Xing et al., 2022), which first decomposes PAR 0 into two bands, the Useable Solar Radiation (USR) band (400–560 nm) and Green‐to‐Red (GR) band (560–700 nm), and then attenuates the two‐band radiations (Equation ), based on respective empirical relationships (Equations and ): $$$\text{PAR}(z)=\text{USR}(z)+\text{GR}(z)={\text{PAR}}_{0}\cdot \left[\beta \cdot \mathrm{exp}\left(-{K}_{d}(\text{USR})\cdot z\right)+(1-\beta )\cdot \mathrm{exp}\left(-{K}_{d}(\text{GR},z)\cdot z\right)\right]$$$ $$${K}_{d}(\text{USR})=\left\{\begin{array}{@{}cc@{}}0.91\cdot {K}_{d}{(490)}^{0.89}& \left({K}_{d}(490)\ge 0.1\right)\\ 0.0062+1.16\cdot {K}_{d}(490)-0.00018/{K}_{d}(490)& \left({K}_{d}(490)< 0.1\right)\end{array}\right.$$$ …”

“…The PAR profile in the mixed layer (PAR( z )) was estimated from PAR 0 anddiffuse attenuation coefficient K d (490), based on the USRGR model (Xing et al., 2022), which first decomposes PAR 0 into two bands, the Useable Solar Radiation (USR) band (400–560 nm) and Green‐to‐Red (GR) band (560–700 nm), and then attenuates the two‐band radiations (Equation ), based on respective empirical relationships (Equations and ): $$$\text{PAR}(z)=\text{USR}(z)+\text{GR}(z)={\text{PAR}}_{0}\cdot \left[\beta \cdot \mathrm{exp}\left(-{K}_{d}(\text{USR})\cdot z\right)+(1-\beta )\cdot \mathrm{exp}\left(-{K}_{d}(\text{GR},z)\cdot z\right)\right]$$$ $$${K}_{d}(\text{USR})=\left\{\begin{array}{@{}cc@{}}0.91\cdot {K}_{d}{(490)}^{0.89}& \left({K}_{d}(490)\ge 0.1\right)\\ 0.0062+1.16\cdot {K}_{d}(490)-0.00018/{K}_{d}(490)& \left({K}_{d}(490)< 0.1\right)\end{array}\right.$$$ $$${K}_{d}(\text{GR},z)=\left(0.1+0.79\cdot {K}_{d}(490)\right)+\left(0.21-0.23\cdot {K}_{d}(490)\right)\mathrm{exp}(-0.082\cdot z)$$$...…”

“…(2) The PAR profile in the mixed layer (PAR(z)) was estimated from PAR 0 anddiffuse attenuation coefficient K d (490), based on the USRGR model (Xing et al, 2022), which first decomposes PAR 0 into two bands, the Useable Solar Radiation (USR) band (400-560 nm) and Green-to-Red (GR) band (560-700 nm), and then attenuates the two-band radiations (Equation 7), based on respective empirical relationships (Equations 8 and 9): (3) Finally, the phytoplankton growth light level in the mixed layer (PAR g ) was determined as the PAR at half of MLD (i.e., PAR(MLD/2)).…”

Light‐Driven and Nutrient‐Driven Displacements of Subsurface Chlorophyll Maximum Depth in Subtropical Gyres

“…We estimated the daily PAR profile from the sea‐surface PAR (PAR 0 ) and the quality‐controlled chlorophyll profile by using the USRGR model (Xing et al., 2022), which is a semi‐analytical PAR model that decomposes visible light into two bands, the Useable Solar Radiation band (USR, 400–560 nm) and the Green‐to‐Red band (GR, 560–700 nm). The chlorophyll profiles were used to parametrize the vertical attenuation of USR and GR.…”

Latitudinal-dependent emergence of phytoplankton seasonal blooms in the Kuroshio Extension

“…On the contrary, PAR has a rapid attenuation in the mixed layer. Therefore, we applied the USRGR model of Xing et al (2022) to combine with the monthly diffuse attenuation coefficient at 490nm (Kd490) from MODIS-Aqua sensor and MLD data from BOA-Argo, to calculate the averaged PAR in the MLD (PARg, Figure 3C), aiming at illustrating the effect of PAR in the mixed layer in our model.…”