*4.3. The Implications of VIn Saturation for Detection of Floating and Submerged Kelp*

When the density or biomass of the vegetation increases within a pixel of remote sensing imagery, the VIn for that pixel will asymptotically approach a saturation (i.e., a high VIn value) [39,61]. This happens because when vegetation is dense, the R0+ at band 2 (NIR or RE) is large relative to the R0+ at band 1 (the visible band). Our spectral measurements contained 100% kelp within the field of view, and accordingly, the VIn values calculated from the multispectral simulations were saturated when kelp was at the surface. Therefore, it is critical to understand how saturation affected the VIn values of floating kelp, as well as when kelp was submerged. For example, our WV3 simulations for bulbs at the surface showed that the R0+ at NIR and RE bands were large compared to the red band (21%, 14%, and 1%, respectively). As such, both NIR\_R and RE\_R indices for bulbs at the surface were approaching saturation (0.83 and 0.77 respectively) and either index would perform relatively well for detecting floating kelp if a VIn of zero was used as a threshold to classify kelp and water. When the bulb was submerged, the R0+ in the NIR and RE bands decreased rapidly by 10 cm depth (3.2 and 3.4% respectively) but were still relatively high compared to the red band, which had also decreased (0.6%), and therefore the NIR\_R and RE\_R values (0.66 and 0.68 respectively) were still relatively saturated, despite the large decreases in R0+ at the RE and NIR bands (Figure 5). As the kelp continued to be submerged, the R0+ at the NIR, RE, and red bands all continued to decrease, however, the R0+ at the NIR band decreased at a faster rate and therefore the NIR\_R value dropped below the threshold of zero by 50 cm while the RE\_R value was still above the threshold by 100 cm. Ultimately, this example shows that due to VIn saturation, the choice of RE or NIR will make little to no difference in classification of kelp at or near the surface. However, once submerged, the use of an RE VIn will still detect kelp deeper than an NIR VIn.

#### *4.4. Depth Detection Limits and Separability between Kelp and Water*

While it is important to understand how VIn values change as kelp is submerged, ultimately the accuracy of submerged kelp classification depends on the spectral separability between the submerged kelp and water. Here, we defined the depth at which kelp and water were no longer separable as the depth at where VIn values for submerged kelp decreased below the threshold value. RE VIn values for kelp and water had higher separability at deeper depths than their NIR counterparts (Figure 6), meaning that deeper kelp can be accurately classified when using an RE VIn. Higher separability between kelp and water classes when using RE VIn has been documented using both high spatial-resolution multispectral UAV imagery [13] and with moderate spatial-resolution multispectral satellite imagery of *Macrocystis* [42], indicating that slight submergence of kelp surface-canopy may play a larger role in detection than previously thought.

While the choice between RE and NIR VIn was an important factor in submerged kelp detection, the choice of the visible band can also shift the detection limits of submerged kelp. Our results show that both the water and submerged kelp spectra had higher R0+ in the green and blue wavelength ranges than in the red, and as such, submerged kelp became undetectable at shallower depths when using NIR\_R compared to NIR\_G or NIR\_B. In the visible wavelength ranges, red is absorbed fastest by the water column, and in our experiment, the NIR signal is generally absorbed by around 50 cm depth, making it reasonable for this pairing to consistently have the shallowest detection limits for submerged kelp. At depths where the RE or NIR signal of kelp can no longer be detected, Figure 7 shows that subtle differences between kelp and water in the blue and green bands can still result in the kelp signal remaining above the dynamic threshold. However, these differences are small, and because conditions during the experiment were controlled, the added spectral noise from in situ environmental factors would likely complicate the detection of both surface and submerged kelp in more realistic situations. For example, the blue wavelength ranges can be highly compromised in remote sensing imagery [29,46], with local variation in atmospheric composition reducing the certainty of accuracy for blue band values. Additionally, the optical constituents of coastal water can be highly spatiotemporally variable—affecting all regions of the spectra [28,46]. At high concentrations phytoplankton in the water column may result in changes to reflectance in the visible wavelength ranges as well as high RE or NIR reflectance [62], while changes to optical constituents such as sediment or CDOM may also impede the detection of submerged kelp [47,63].

In this experiment, the optical water conditions (Secchi = 7.5) were typical of the coastal waters of British Columbia [18,28,64]. Considering the Secchi measurement, the local depth (12 m), and the R0+ from water with no kelp (Figure 3), the bottom substrate signal was not part of the measured R0+ in our experiment. Yet kelp on the coast of British Columbia is often found as fringing canopies near the shoreline [18], which can result in a strong contribution of benthic substrate to the R0+ measured by space and air-borne platforms. Reflectance from shallow benthic features can result in highly variable R0+ in both the visible and near-infrared wavelength ranges, resulting in misclassification of submerged vegetation as canopy kelp [47,64]. Therefore, it is important to understand site characteristics (e.g., bathymetry and water turbidity) to define better the use of NIR or RE for kelp classification. For instance, if enough understanding of the local conditions at the time of imagery acquisition is not available, it may be more appropriate to use NIR\_R to reduce the addition of signal of the bottom substrate. Alternately, if imagery or associated ground truth data have a high enough spatial resolution (e.g., from UAV or other aerial platforms), visual interpretation of surface-canopy morphology from expert knowledge may be adequate for manual classification or ground truthing when using an RE VIn.

#### *4.5. Implications for Mixed Pixels*

During the experiment, spectral data were collected using a small footprint to reduce uncertainties associated with having the reflectance signal of multiple targets within the field of view (i.e., mixed pixels). However, remote sensing imagery often contains mixed pixels [16,35]. This becomes especially problematic when sensors have a lower spatial resolution, where erroneous classification of a pixel as kelp may result in the overestimation of total kelp canopy. Multiple end-member spectral mixture analysis (MESMA) is an approach that has been applied to satellite imagery for both *Macrocystis* [11,35] and *Nereocystis* canopy [19,65] to determine what proportion of the pixel is kelp, and what proportion is water. When MESMA is applied to remote sensing imagery for kelp detection, it is assumed that all VIn or band values within a pixel are a linear combination of kelp and water end-members [35]. However, if the kelp fraction within a pixel is low enough, the spectral contribution from water may overwhelm the kelp signal, lowering the overall pixel value and allowing the pixel to be erroneously classified as water [19,27]. Our results suggest that if submerged kelp is present when MESMA is performed, which is most often the case, the

reduced signal from the submerged kelp within the pixel may lead to an underestimation of the kelp fraction within the pixel. Using an RE VIn when performing MESMA may allow the user to detect more submerged kelp, thus contributing to a higher overall pixel value and increasing the accuracy of the classification. This may be especially relevant if attempting to determine relationships between remote sensing imagery and biomass, since *Nereocystis* blades show a higher correlation to the mass of the individual than any other metric tested [10]. Further, *Nereocystis* canopy generally has less dense biomass at the surface than *Macrocystis* [65,66], and, therefore, is more likely to be misclassified in moderate or low spatial resolution imagery.

## **5. Conclusions**

Our experiment contributes new, detailed information on the effects of kelp submersion on the above water reflectance, as well as a comparison of the depth detection limits of kelp when using red-edge and near-infrared indices. We determined that the near-infrared region of kelp spectra is strongly absorbed upon submersion, however, there is a narrow spectral peak in the red-edge region that can be used to enhance the remote sensor's ability to detect submerged kelp due to lower water absorption. Detection limits varied based on kelp tissue, the thresholding method, and the visible band used in the vegetation index calculation, but overall, red-edge vegetation indices detected deeper than their counterpart NIR indices, which may allow the remote sensor to improve accuracy when mapping sparse and partially submerged kelp canopy or attempting to derive biomass from canopy reflectance values. Kelp forests may be mapped using remote sensing for various reasons, ranging from estimation of biomass for kelp harvesting to multi-year temporal analyses to assess the impacts of environmental drivers on kelp ecosystems. Yet kelp systems can be highly variable in abundance between years, and our study shows that the spectral variables used to detect kelp canopy in remote sensing imagery play an important role in the amount of submerged kelp canopy detected. Therefore, it is critical for a remote sensing user to understand how the physical interaction between light and water may affect the depth at which kelp can be detected. For example, RE VIn might be especially useful if resource managers are attempting to set quotas for harvestable biomass of *Nereocystis* and wish to detect as much blade biomass as possible for specific beds. However, if one wishes to reduce detection of subsurface kelp canopy or other shallow benthic vegetation, we recommend the use of the NIR\_R (NDVI), which consistently had the shallowest detection limits of the indices tested.

**Author Contributions:** B.T., M.C. and L.Y.R. designed the study. B.T. and L.Y.R. carried out the experiment. B.T. conducted the analysis and wrote the manuscript with input and guidance from M.C., L.Y.R., F.J. and M.H.-L. All authors have read and agreed to the published version of the manuscript.

**Funding:** During this research BT was supported through a MITACS Accelerate internship with the Hakai Institute, as well as an NSERC CGS-M award and Costa's NSERC-DG.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are available for research purposes upon request to the authors' institutions.

**Acknowledgments:** We thank the Hakai Institute and the Canada NSERC-DG for providing funding for this research as well as Robert Atwood for letting us use his slip at the Oak Bay marina to test this experiment. Also, thank you to Lianna Gendall for helping with the kelp in the graphical abstract.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Appendix A**

**Figure A1.** Differences between R0+ values of each shared band of the Micasense RedEdge-MX (MSRE) and WorldView-3 sensors, as simulated from the bulb (**a**) and blade (**b**) spectral measurements.

#### **References**

