*2.4. Threshold Selection and Depth Limits for Kelp Detection*

Once a VIn has been selected for classifying kelp in remote sensing imagery, a VIn value is then chosen as a threshold to classify the kelp and water within the imagery. For example, Cavanaugh et al. (2010) selected a threshold based on the 99.98th percentile highest NIR\_R value from a histogram of known 'deep water' pixels, and Nijland et al. (2019) determined a NIR\_R value of 0.05 to be a reasonable threshold by comparing pixel values of sparse kelp and open water. Since the R0+ values of water vary spatially and temporally according to optical constituents and inherent optical properties of water, as well as the characteristics of local substrate and bathymetry [28,46,47], these thresholds are often 'dynamic', and are therefore determined on an image-by-image basis. For satellite or airborne imagery covering a large regional scale, it may even be appropriate to select multiple thresholds across different regions within an image.

We determined a dynamic threshold for each VIn based on the maximum VIn value measured for water during the experiment following Cavanaugh et al. (2010). The depth where the mean VIn value of submerged kelp dropped below the dynamic threshold value was considered the depth where kelp was spectrally indistinguishable from water. Since our experiment was conducted under ideal conditions (flat calm water, full sun, etc.) the dynamic thresholds were all negative values and the maximum depth of detection using these thresholds likely overstate the potential depths for kelp detection in actual remote sensing imagery. Therefore, we also used a second VIn threshold of zero, based on the theoretical spectral properties of kelp within an individual pixel that contains 100% kelp. For example, within a pixel, if the R0+ value of band 2 (RE or NIR) equals the R0+ value as band 1 (the visible band), the numerator in the VIn equation (Equation (2)), and therefore the overall VIn value for that pixel, equals zero. This conservative threshold is closer to the values of 0.05 and 0.003 determined from remote sensing imagery by Nijland et al. (2019) and Mora-Soto et al. (2020), respectively.

Depth detection limits were reported to the nearest 10 cm depth on the shallow side of the threshold because the kelp was submerged in 10 cm intervals. To determine whether the detectable kelp (values above the threshold) and non-detectable kelp (values below the threshold) were statistically separable, the means for kelp measurements immediately above and below the threshold were compared for significant differences using Welch's *t*-test [48].

#### **3. Results**

Here, we present the spectral characteristics of *Nereocystis* bulbs and blades as they are each submerged from the surface to 100 cm, as well as the changes seen in the hyperspectral data when they are simulated into multispectral sensor bandwidths. Next, we show VIn comparisons for kelp, focusing on comparing the RE and NIR counterpart indices (e.g., NIR\_R & RE\_R, or NIR\_B & RE\_B) at each depth, and finally, we present the depth detection limits for each VIn as determined by both dynamic and conservative thresholds.

#### *3.1. Spectral Characteristics of Surface and Submerged Kelp*

Overall, the R0+ of both *Nereocystis* bulbs and blades showed similar placement of spectral features, however, the magnitude of reflectance at these features was different (Figure 3a,b). For *Nereocystis*, spectral features in the visible wavelength ranges are largely due to absorption by a combination of chlorophyll-a, chlorophyll-c, and fucoxanthin pigments, which are characteristic pigments of bull kelp, as well as other kelp species [49,50]. Accordingly, here we saw a broad absorption feature in the 400–550 nm range and narrower absorption features around 633 and 675 nm for both bulbs and blades at the surface. These absorption features resulted in reflectance peaks at 575, 600, and 645 nm for both bulbs and blades (Figure 3a,b, insets). In the NIR region, broad reflectance peaks were detected from 690 nm (RE) to 900 nm (NIR) (Figure 3a,b, insets) and small, narrow peaks centered at 761 nm were observed (Figure 4a,b).

**Figure 3.** Reflectance values (R0+) between 400–900 nm (mean +/− sd) of water with (**a**) *Nereocystis* bulbs, and (**b**) *Nereocystis* blades, at incremental depths below water surface. The inset plots contain spectra of bulbs and blades on the surface compared to the same spectra of submerged bulb and blades as in the main plots, for the purpose of showing the difference in magnitude.

**Figure 4.** Zoomed in plot showing solar-induced chlorophyll fluorescence (SICF) peaks centered at 761 nm for above-water R0+ for *Nereocystis* bulbs (**a**) and blades (**b**) at incremental depths below the water surface. Spectra are normalized at 770 nm to show relative changes to the shape of the SICF peak with submergence.

When kelp structures were submerged, the influence of the water and its constituents on the R0+ signal increased with submersion for both bulb and blades. The decreases in R0+ in the RE and NIR region were far greater than decreases in R0+ observed across the visible region of the spectra (Figure 3a,b, insets). With initial submersion below the water's surface, the largest declines in the visible wavelength ranges were seen at 600 nm and 645 nm, although all peaks in the visible region continued to decrease with submersion (Figure 3a,b). While the R0+ at the absorption feature between 400–550 nm initially decreased with submersion, the reflectance then rose as the depth of submersion increased. In the NIR region of spectra for both structures, once kelp was submerged, the broad NIR peaks were

replaced by two peaks centered around 715 nm and 815 nm (Figure 3a,b), hereafter referred to as the RE peak and the NIR peak, respectively. At each depth, the R0+ at the RE peak was higher than the NIR peak. As submergence increased, the position of the RE peak shifted toward lower wavelengths within the RE wavelength ranges while the position of the NIR peaks remained relatively stable. The small peaks at 761 nm remained stable, but decreased in magnitude with submersion, becoming difficult to visibly distinguish around 50 cm depth (Figure 4a,b).

R0+WV and R0+MSRE showed the same general patterns as the hyperspectral data (Figure 5a–d). However, some spectral information was lost with the reduction of spectral resolution, such as the location and magnitude of different peaks. Overall, the differences in width and placement of bands resulted in only small differences in R0+WV3 and R0+MSRE band values (Figure A1a,b). For both bulbs and blades at the surface, differences in the visible wavelength ranges between R0+WV and R0+MSRE were less than 0.8% for the red, blue, and green bands, and these differences became even smaller as kelp was submerged. In the RE and NIR bands, differences between R0+WV and R0+MSRE were less than 0.3% on the surface. Once submerged to 10 cm, differences between R0+WV and R0+MSRE increased to 1.8% in the NIR bands and 0.5% in the RE bands, although similar to the visible bands, the differences between R0+WV and R0+MSRE also became smaller as the kelp was submerged deeper.

**Figure 5.** Reflectance values (R0+) for bulbs (**a**,**c**) and blades (**b**,**d**) of simulated bands (mean +/− sd) shared by the Micasense RedEdge-MX (MSRE; **a**,**b**) and WorldView-3 (WV3; **c**,**d**), derived from the hyperspectral data (Figure 3) using Gaussian response functions (Figure 2).

#### *3.2. Vegetation Indices: Signal Strength and Depth-Detection Limits of Submerged Kelp*

Generally, RE VIn values were higher than NIR VIn values at a given depth as kelp was submerged (Figure 6). For bulbs, RE VIn values decreased linearly from the surface to 100 cm, while NIR VIn showed a steeper linear decrease over the first 50 cm, followed by an inflection point and a lesser decline towards 100 cm. For blades, trendlines of both NIR

and RE VIn resemble exponential functions, with the NIR VIn displaying a steeper decrease of values than the RE VIn.

**Figure 6.** Mean +/− sd of vegetation index (VIn) values for Nereocystis bulbs (**a**,**c**) and blades (**b**,**d**), submerged from the surface to 100 cm and water; derived from simulated Micasense RedEdge-MX (MSRE; **a**,**b**) and WorldView-3 (WV3; **c**,**d**) bandwidths. Paired letters above each column represent no significant differences (*p* ≥ 0.05) between mean index values at that depth.

Specifically, the Games–Howell post hoc tests showed that for kelp at the surface, RE VIn values were either smaller than or not significantly different from their counterpart NIR indices (Figure 6), depending on the visible band used. Once kelp was submerged, RE VIn values were significantly greater than their NIR counterparts at each depth with the MSRE sensor. However, with the WV3 sensor, RE VIn values were not significantly greater than their NIR counterparts until 10 cm and 20 cm depth for blades and bulbs, respectively. All VIn values for water were negative, meaning that the R0+ at the visible band used in the VIn was higher than the R0+ at the RE or NIR band used in the VIn, regardless of sensor simulation or index combination. RE\_R consistently showed the highest values for water, followed by NIR\_R, and there were no significant differences between RE\_B and RE\_G water values, nor for NIR\_B and NIR\_G water values. Here, we focused on the statistical results comparing the RE and NIR counterpart indices only (e.g., NIR\_R & RE\_R, or NIR\_B & RE\_B) at each depth, however, Figure 6 displays paired letters to indicate all pairs of VIn where no significant difference between VIn pairs was detected.

The depth detection limits varied based on sensor type, kelp structure, and thresholding method (Table 5; Figure 7). Overall, when using the conservative (more realistic) threshold of zero, RE VIn showed detection of kelp at least twice as deep as NIR VIn, and bulbs were detectable at greater depths than blades. Detection limits for the same VIn between sensors were generally within a range of 0–20 cm apart, although in a few cases (e.g., RE\_R) these differences were larger. In addition, the choice of different visible bands for a VIn only resulted in detection limit differences up to 20 cm, with RE\_R once again proving the exception. No RE indices crossed below the dynamic thresholds at 100 cm

depth, meaning RE indices could detect kelp to at least 100 cm depth with these thresholds, while NIR indices could generally detect kelp to around 100 cm depth or less. In all cases, the RE indices at 100 cm depth were more separable from water than the NIR indices at the same depth. The use of different visible bands in the VIn combination generally resulted in detection limit differences of 0–30 cm for bulbs. For all measured depth detection limits, the index values measured at the increments 10 cm above and below the threshold remained divergent (*p* < 0.05), suggesting that all the measured results for conservative and dynamic thresholds are accurate to at least 10 cm increments.

**Table 5.** Depth detection limits (cm) based on conservative threshold of 0.0 and the dynamic thresholds (maximum water value) for Nereocystis bulbs and blades, as simulated to Micasense RedEdge-MX (MSRE) and WorldView-3 (WV3) bandwidths.


**Figure 7.** Mean +/− sd of vegetation index (VIn) values for Nereocystis bulbs (**a**,**c**) and blades (**b**,**d**) submerged from the surface to 100 cm. derived from simulated Micasense RedEdge-MX (MSRE; **a**,**b**) and WorldView-3 (WV3; **c**,**d**) bandwidths. The black dashed lines at 0 represent the more conservative and realistic threshold, and the blue bars represent the full range of water values for each respective index, with the adjacent dashed lines representing the dynamic threshold.

#### **4. Discussion**

Overall, we found that submersion of kelp in water changes the shape and magnitude of R0+ in the RE and NIR region of kelp spectra (Figure 3), and *Nereocystis* bulbs had a higher magnitude R0+ in the RE and NIR region than blades (Figure 3). We also observed that RE VIn values for submerged kelp had higher separability from water than their NIR counterparts (Figure 6), meaning that kelp can be positively classified at deeper depths when using an RE VIn (Table 3; Figure 7). Our results also showed that VIn that used a visible band with high R0+ (e.g., green or blue) had worse detectability for submerged kelp than a VIn that used a visible band with low R0+ (e.g., red). Together, these findings have important implications for the application of kelp remote sensing to the applied monitoring of kelp forests.
