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Model for deriving benthic irradiance in the Great Barrier Reef from MODIS satellite imagery: erratum

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Abstract

Corrections for equations in our recently published paper [Opt. Express 27, A1350 (2019)] are presented.

A post-publication review of our methods [1] has indicated that Eq. (8) and Eq. (12) in the original manuscript should read as:

$$bPA{R_n} = \mathop \smallint \limits_{400}^{700} {\bigg (}{{t_g}E_d^{{0^ + }}(\lambda )} {\bigg )}{e^{ - {K_d}(\lambda )z}}d\lambda$$
$$bPA{R_d} = 2\ast \mathop \smallint \limits_{{\phi _{_{rise}}}}^{{\phi _{noon}}} \mathop \smallint \limits_{400}^{700} {\bigg (}{{t_g}E_d^{{0^ + }}(\lambda ,\theta {^{\prime}_{solz}}(\phi )} {\bigg )}{e^{ - {K_d}(\lambda )z}}d\phi d\lambda $$
where $E_d^{{0^ + }} = {F_0} \ast T \ast \cos (\theta {^{\prime}_{solz}}(\phi ))$ following [2]. Here, $E_d^{{0^ + }}$is the above-water downwelling plane solar irradiance, F0 is the extraterrestrial solar irradiance, T is a transmittance parameter that accounts for atmospheric absorption and scattering by gases, clouds, and aerosols [2], and θ’solz$(\phi )$ is the solar zenith angle at a given time between sunrise to noon at each hour angle $\phi $. Note that this correction also implies that all texts pertaining to Es or Es$(\lambda ,{0^ + })$, a nomenclature that could be misinterpreted as scalar irradiance, in the original manuscript should now read as $E_d^{{0^ + }}$or $E_d^{{0^ + }}(\lambda ,\theta {^{\prime}_{solz}}(\phi ))$.

In addition, the term inside the parenthesis in Eq. (13) is missing a negative sign [3] and should read as:

$${\phi _{rise}} = {\cos ^{ - 1}}{\bigg (}{ - \tan (\delta )\tan (lat)} {\bigg )}.$$

We applied these corrections to our original benthic irradiance model and performed matchup and validation exercise as detailed in the original manuscript. The corrected model still shows strong agreement between the satellite-derived and in situ benthic PAR across all four test sites (Fig. 1). Notably, the corrections have led to a more consistent model bias and mean absolute error (MAE) across the test sites. As previously reported, bias and MAE were smaller in clearer offshore waters (Palm Passage and Myrmidon) compared to more optically complex inshore (Yongala) and midshelf (Heron) waters. We note that these corrections did not affect the relevance of our results to understanding benthic light and its effects within the Great Barrier Reef World Heritage Area.

 figure: Fig. 1.

Fig. 1. (a) Scatterplots of concurrent log-transformed satellite-derived instantaneous benthic PAR (bPARi) and in situ bPAR at four test sites (Yongala, Heron, Palm Passage, and Myrmidon). The red-yellow-green-magenta color scale represents month of observation. The scatterplot labelled ‘ALL’ indicates combined observations from all test sites, plotted according to observation site (red to blue color scale). Filled black triangles indicate values considered as outliers due to an extreme weather event experienced in the Yongala study site, which were excluded from the analysis (as previously reported). (b) The same as for (a) except log-log scaled scatterplots are of satellite-derived daily-integrated benthic PAR (bPARd) vs. in situ daily bPAR.

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References

1. M. M. Magno-Canto, L. I. W. McKinna, B. J. Robson, and K. E. Fabricius, “Model for deriving benthic irradiance in the Great Barrier Reef from MODIS satellite imagery,” Opt. Express 27(20), A1350–A1371 (2019). [CrossRef]  

2. R. Frouin, B. A. Franz, and J. P. Werdell, “The SeaWIFS PAR product,” in Algorithm Updates for the Fourth SeaWIFS Data Reprocessing, NASA Technical Memorandum 2003-206892, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Maryland, 2002), pp. 46–50.

3. L. Kumar, A. K. Skidmore, and E. Knowles, “Modelling topographic variation in solar radiation in a GIS environment,” Int. J. Geograph. Inform. Sci. 11(5), 475–497 (1997). [CrossRef]  

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Figures (1)

Fig. 1.
Fig. 1. (a) Scatterplots of concurrent log-transformed satellite-derived instantaneous benthic PAR (bPARi) and in situ bPAR at four test sites (Yongala, Heron, Palm Passage, and Myrmidon). The red-yellow-green-magenta color scale represents month of observation. The scatterplot labelled ‘ALL’ indicates combined observations from all test sites, plotted according to observation site (red to blue color scale). Filled black triangles indicate values considered as outliers due to an extreme weather event experienced in the Yongala study site, which were excluded from the analysis (as previously reported). (b) The same as for (a) except log-log scaled scatterplots are of satellite-derived daily-integrated benthic PAR (bPARd) vs. in situ daily bPAR.

Equations (3)

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b P A R n = 400 700 ( t g E d 0 + ( λ ) ) e K d ( λ ) z d λ
b P A R d = 2 ϕ r i s e ϕ n o o n 400 700 ( t g E d 0 + ( λ , θ s o l z ( ϕ ) ) e K d ( λ ) z d ϕ d λ
ϕ r i s e = cos 1 ( tan ( δ ) tan ( l a t ) ) .
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