# Towards Deeper Measurements of Tropical Reefscape Structure Using the WorldView-2 Spaceborne Sensor

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Study Area

^{2}, the study area encompassed a great variety of geomorphic features, ranging from consolidated habitats, including outer reefs, reef crest, barrier and fringing reefs, to clastic sediments found in the pass and the channel. These latter banks were composed of gravel-sand from coral erosion. Areas with fine grain-size, appear to have stronger visual reflectance (e.g., the bank located in the southeastern region of the study area in Figure 1). The outer reef was significantly impacted by two major events, namely the 2006–2009 crown-of-thorns seastar (Acanthaster planci) outbreak [17] and Cyclone Oli in February 2010 [10], resulting in grayish pavement and coral rubble colonized by very sparse Pocillopora sp.-dominated coral communities. The reef crest is typically covered with brown macro-algae (Turbinaria sp.). Sheltered in the lagoon, massive stony corals, mainly represented by brown/yellow Porites sp. and brown/yellow branching corals such as Synarea rus. The larger coral colonies can be topped by red coralline algae and Turbinaria sp., green algae (Halimeda sp.), or filamentous turf algae when the entire colony was dead. While the seaward slope of the fringing reef was primarily populated by S. rus, the middle part was pavement, colonized by red encrusting algae and tufts of brown algae (Padina sp.).

#### 2.2. Image Acquisition and Processing

#### 2.2.1. WorldView-2 Spaceborne Multispectral Data

^{−2}·sr

^{−1}) using the band-related coefficients (contained in the .imd file).

#### 2.2.2. Pansharpening

#### 2.2.3. Atmospheric Correction

^{−2}.

#### 2.2.4. Bathymetry Retrieval

_{b}is the benthic albedo, R

_{∞}is the radiance over a hypothetical optically deep water column (typically >60 m depth in the study area’s waters) to avert the skew due to the benthic-associated albedo, k is the diffuse attenuation coefficient, and z is the height of the water column. The wavelength terms inherent to R, A

_{b}, R

_{∞}, and k parameters are omitted for clarity.

_{b}. However, an empirical approach avoids solving for the latter parameter and estimates the bathymetry by correcting for albedo using a ratio of two wavelengths (or wavebands in our study) [24]. Although this method demonstrated satisfactory results for localized areas, Stumpf et al. [15] stressed that the constraint on this method is that five parameters need to be empirically determined, which either turns out to be time-consuming or demands potentially unrealistically strong assumptions of spatial homogeneity. Because the purpose of this work was to define an optimal combination of spectral bands for the bathymetry retrieval, we sought an algorithm providing an optimal trade-off between proficiency and simplicity. The ratio transform proposed by Stumpf et al. [15] adequately responded to the selection criteria. Endowed with capabilities of retrieving bathymetry over variable benthic types, even the darker ones relative to R

_{∞}, and requiring a unique parameter to adjust, the ratio transform was solved for bathymetry as follows:

_{i}and R

_{j}refer to radiances of wavebands i and j, respectively, m

_{1}is an adjustable function allowing the ratio to be depth-scaled, n is a fixed constant ensuring the natural logarithm to be positive, and m

_{0}is the offset. Since the tidal level in Moorea varies within the bathymetric accuracy (<0.2 m), m

_{0}was fixed at 0.

#### 2.3. Spectral Combinations

#### 2.4. Acoustic Ground-Truthing

_{1}within Equation (2)) the DRDM and ultimately convert them into Digital Absolute Depths Models (DADM). The water depths surveyed ranged from 0 to 67.09 m (mean = 14.12, variance = 104.25, skewness = 0.75, and kurtosis = 0.54). The 8,489 floating points were linearly interpolated to build two Digital Ground-truth Depth Models (DGDM, one at 2 m and one at 0.5 m resolution), suitable to be stacked as a layer into the DRDM datasets (Figure 7). However, this rasterization was undertaken only to gain time in rapidly extracting the monitored 8,489 points of interest, and not to employ it where pixel values were interpolated. The consistency between DGDM and DRDM was quantified with a Pearson product-moment correlation coefficient (r) and attendant p-value (i.e., the observed significance probability of obtaining a greater F-value by chance alone if the linear model fitted no better than the overall response mean). After sorting the matrix of 8,489 instances × 163 attributes by DGDM values, we computed r across the water depth. We got thereafter 66 r: the first computed corresponding to all ground-truth values (until 67 m), the second computed corresponding to ground-truth values topped at 65 m, the third computed corresponding to ground-truth values topped at 64 m, etc. While gradually reducing the dataset, this approach enabled the most efficient spectral combinations, regarding the bathymetry retrieval, to be discriminated and furthermore the depth range where they are the most robust. This “downscaling” analysis provided an optimal combination of spectral combinations, each of these specific to retrieving the bathymetry in a delineated depth window at 1 m resolution. The spectral combinations providing the three best correlations with the DGDM were further examined in searching for the best statistical relationships using various fitting models and associated Root Mean Square Error and R

^{2}adjusted. While R

^{2}measures the proportion of the variation around the mean explained by the fitting model, R

^{2}adjusted adjusts the R

^{2}value to make it more comparable over models with different numbers of parameters by using the degrees of freedom in its computation. Root Mean Square Error estimates the standard deviation of the remaining variation which is not explained by the fitting.

## 3. Results

#### 3.1. Performance of the Spectral Band Combinations

^{−16}, NS). Regarding the average performance across the water depth gradient, the best correlation was reached by the purple, green, yellow and NIR3 combination (1348, |r| = 0.63), while the worst correlation was obtained from the purple, green, NIR1 and NIR3 combination (1368, |r| = 0.08). This overall description necessitated a refinement in the analysis, taking into account the influence of the spatial resolution and atmospheric correction.

#### 3.1.1. Influence of Spatial Resolution on Bathymetry Retrieval

#### 3.1.2. Influence of the Atmospheric Correction on Bathymetry Retrieval

#### 3.2. Mapping the Bathymetry Using the Best Spectral Band Combinations

_{aod}modality, i.e., the original 2 m with a dark object subtraction by way of atmospheric correction. Topping the correlation curves, three spectral combinations succeeded one another across the water depth gradient (Figure 8(B)).

^{2}adj. = 0.51, Figure 9(A)). While the model reproduced actual depths up to approximately 20 m, a threshold around 25 m indicated the failure of the prediction. However, from 25 to 40 m, the same linear regression retrieved again meaningful water depths. The spatialized DRDM was calibrated with such an equation to build a DADM. The 1267-DADM, deemed the deep DADM, showed that spurs-and-grooves, visually revealed by two consecutive levels, and even the outer sandy spread (darkest feature off-shore) could be unraveled. Conversely, reefscape elements just above and under the water surface such as emerged and very shallow reefs with active wave breaking (seen as white zones inside the water body) were not elucidated by the model.

^{2}adj. = 0.61, Figure 9(B)). Although the model adequately followed the crescent-like patterns of the data cloud, the scattering around it gradually increased with water depth, and especially from 15 m. Compared to the previous DADM, the 1348-DADM, called the intermediate DADM, substantially refined shallower reefscape features such as the furrowed platform, the reef crest, surge channels, the barrier and fringing reef flats. Water surface discrepancies noticed in the previous DADM were circumvented by this model. However, the improvements emerged at the expense of rendering spur-and-groove features and the outer sandy spread.

^{2}adj. = 0.71, Figure 9(C)), based on 61 points. In this respect, the scatterplot showed two clouds, one lying on the ordinate axis and the other one more erratic between 0.5 and 1 m, which were linked by the linear model. Despite the negative model, the color ramp of the DADM matched those of both previous DADMs for the sake of readability. Bound by 0 and 1.5 m, the DADM, called the shallow DADM, put the emphasis on the extremely shallow reefscape elements, such as the reef crest, the barrier and fringing reef flats punctuated with micro-atolls. Since the model was selected for its performance between 0 and 1 m, modeled water depths seaward the reef crest and within the channel (both globally rendered in darker tones) did not retrieve actual bathymetry.

## 4. Discussion

#### 4.1. Differential Contributions of the Pansharpening and Atmospheric Corrections

#### 4.2. Spectral Enhancement Implied a Refinement of the Bathymetry Retrieval

_{ao}). From the 67 to 34 m, the plateau slightly increased from 0.11 to 0.15, then rapidly grew to 9 m, meeting 0.55, momentarily fluctuating between 0.54 and 0.37 to 3 m, and finally topped at 0.84 (in absolute values) at 1 m. An inflection point visible at 20 m may concur with both above-cited works. However, using the four novel WV2 bands (purple, yellow, NIR1 and NIR3), the bathymetry retrieval was strongly refined relative to the pseudo QB2 results: from 67 to 30 m, the WV2 1267 combination varied between 0.67 and 0.71, from 30 to 3 through 14 m, the WV2 1348 combination met 0.67, 0.77 and 0.44, respectively, and finally the WV2 1357 combination reached 0.85 (in absolute values) at 1 m. Those results stemmed from the 2 m/dark object correction modality (R

_{aod}). We thereafter compared L

_{ao}2357 (pseudo QB2) and R

_{aod}1267/1348/1357 spectral combinations so that the gain conveyed by the WV2 four novel bands can be accurately quantified (Figure 10). Except for 3 and 4 m, the best WV2 combination systematically outperformed the pseudo QB2 results, gaining a high increase in correlation values from 4 to 34 m (from 0 to 0.54, respectively) and a more moderate growth from 34 to 67 m (from 0.54 to 0.6). The overall accuracy, close to 1 m, might be assumed as the effect of the noise integrated into the EMR measurement, detectable as random variance within 1 pixel lag. Since we found the two most sharply contrasted average performances to within one spectral band of difference (1348, |r| = 0.63 and 1368, |r| = 0.08), we suggest that the selection of bands played a crucial role in subsequent retrievals.

#### 4.3. Towards an Improved Solution for Benthic Albedo

## 5. Conclusions

## Acknowledgments

## References

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**Figure 1.**Location of study area on the north shore of Moorea, Society Island archipelago, French Polynesia, and color image of study area. The study area encompassed Irahonu Pass, outer, barrier and fringing reefs and a sand bank.

**Figure 2.**Visible spectral capabilities of the two Very High Resolution Sensors, Quickbird-2 (QB2) and WorldView-2 (WV2), related to the diffuse attenuation coefficient estimated for Moorea’s tropical waters (modified from [18]).

**Figure 3.**Representative example of the Gram-Schmidt spectral pansharpening method, supported by the spectral response function of the WorldView-2 (WV2). This method transformed the (

**A**) 2-m initial multispectral dataset into a (

**B**) 0.5-m multispectral dataset based on the 0.5-m initial panchromatic dataset, while preserving spectral patterns. Solid, dashed and dotted lines represent the mean, the standard deviations and the extremes of the spectral signatures of the subset area, respectively.

**Figure 4.**Three modalities regarding the atmospheric correction have been retained: (

**A**) none; (

**B**) empirical Dark object Subtraction (DS); and (

**C**) analytical FLAASH correction. Lower plots represent spectral signatures of five features (golden stars over images) against the three modalities.

**Figure 5.**Conceptual flowchart of the experimental approach aiming at optimizing the bathymetry retrieval with respect to two spatial resolutions (no pansharpening and with pansharpening) and three atmospheric corrections (none, empirical dark object subtraction and analytical FLAASH procedure).

**Figure 6.**Flowchart of the spectral band combinations tested. The six test modalities (spatial resolution and atmospheric correction) encompassed 27 spectral combinations composed of four different bands.

**Figure 7.**Digital Ground-truth Depth Model (DGDM) linearly interpolated from the 8,489 acoustic soundings, represented in red points.

**Figure 8.**Scatterplots of Pearson product-moment correlation coefficients (r) computed between models of bathymetry retrieval and acoustic ground-truth measurements as a function of the maximal water depth. The 27 spectral combinations (series) used as bathymetric model inputs were analyzed with respect to spatial resolution and atmospheric correction. In the measured mode (2 m resolution): (

**A**) no atmospheric correction for L

_{ao}; (

**B**) empirical dark object subtraction for R

_{aod}; (

**C**) analytical FLAASH correction for R

_{aof}. In the pansharpened mode (0.5 m resolution); (

**D**) no atmospheric correction for L

_{aop}; (

**E**) empirical dark object subtraction for R

_{aopd}; (

**F**) analytical FLAASH correction for R

_{aopf}.

**Figure 9.**Digital Absolute Depth Models (DADM) and scatterplots of the ground truth acoustic measurements expressed as a function of the modeled water depths (R

_{aod}: 2 m and dark object subtraction), resulting from (

**A**) the 1267 (purple, blue, NIR1 and NIR2) spectral combination; (

**B**) the 1348 (purple, green, yellow and NIR3) spectral combination; and (

**C**) the 1357 (purple, green, red and NIR2) spectral combination.

**Figure 10.**Absolute Pearson product-moment correlation coefficients (r) as a function of water depth as computed between the best WV2 R

_{aod}model (composed of the 1267 (purple, blue, NIR1 and NIR2), the 1348 (purple, green, yellow and NIR3) and the 1357 (purple, green, red and NIR2) spectral combinations); the pseudo QB2 L

_{ao}model (2357 (blue, green, red and NIR2) spectral combination); and their difference.

**Figure 11.**Data points per 1 m-depth class (×10) involved to compute correlation coefficients across the water depth gradient.

**Table 1.**Spectral characteristics of the two best Very High Resolution spaceborne sensors, Worldview-2 (WV2) and QuickBird-2 (QB2).

Waveband Colours | Waveband Numbers | Waveband Names | WV2 Wavelength Range (nm) | QB2 Wavelength Range (nm) |
---|---|---|---|---|

Purple | 1 | “Coastal blue” | 400–450 | |

Blue | 2 | Blue | 450–510 | 450–520 |

Green | 3 | Green | 510–580 | 520–600 |

Yellow | 4 | Yellow | 585–625 | |

Red | 5 | Red | 630–690 | 630–690 |

NIR1 | 6 | “Red edge” | 705–745 | |

NIR2 | 7 | Near InfraRed 1 | 770–895 | 760–890 |

NIR3 | 8 | Near InfraRed 2 | 860–1040 | |

Panchromatic | 450–800 | 450–900 |

**Table 2.**Parameter values for the MODerate resolution TRANsmittance (MODTRAN)4-driven Fast Line-of-site Atmospheric Analysis of Spectral Hypercubes (FLAASH) module.

Altitude (km) | 770 |

Ground Elevation (km) | 0 |

Pixel size (m) | 2/0.5 |

Flight Date | 17 March 2010 |

Flight Time (GMT) | 20 h 13 min 3 s |

Atmospheric model | Tropical |

Aerosol Model | Maritime |

Aerosol Retrieval | None |

Initial Visibility (km) | 40 |

Aerosol Scale Height (km) | 1.5 |

CO2 Mixing Ratio (ppm) | 390 |

Square Slit Function | None |

Adjacency Correction | Yes |

MODTRAN Resolution (cm^{−1}) | 15 |

MODTRAN Multiscatter Model | Scaled DISORT |

Number of DISORT Streams | 8 |

**Table 3.**Pearson product-moment correlation coefficients (r) of the best and worst averaged and performance of the bathymetry retrievals against spatial resolution and atmospheric correction.

No Correction | Dark Object Subtraction | FLAASH | |||||
---|---|---|---|---|---|---|---|

2 m | 0.5 m | 2 m | 0.5 m | 2 m | 0.5 m | ||

Averaged | Maximum | 0.63 | 0.5 | 0.63 | 0.53 | 0.46 | 0.46 |

Minimum | 0.16 | 0.13 | 0.13 | 0.08 | 0.08 | 0.16 | |

Punctual | Maximum | 0.84 *** | 0.58 *** | 0.85 *** | 0.63 *** | 0.81 *** | 0.73 *** |

Minimum | 5.78 × 10^{−4} (NS, p = 0.95) | 1.89 × 10^{−3} (NS, p = 0.92) | 4.81 × 10^{−4} (NS, p = 0.97) | 1.38 × 10^{−3} (NS, p = 0.94) | 1.25 × 10^{−16} (NaN) | 2.21 × 10^{−4} (NS, p = 0.99) |

^{***}means p-value < 0.0001, NS means No Significance (p-value >0.01), and NaN means Not a Number owing to the constant value of one the two variables to be correlated.

## Share and Cite

**MDPI and ACS Style**

Collin, A.; Hench, J.L. Towards Deeper Measurements of Tropical Reefscape Structure Using the WorldView-2 Spaceborne Sensor. *Remote Sens.* **2012**, *4*, 1425-1447.
https://doi.org/10.3390/rs4051425

**AMA Style**

Collin A, Hench JL. Towards Deeper Measurements of Tropical Reefscape Structure Using the WorldView-2 Spaceborne Sensor. *Remote Sensing*. 2012; 4(5):1425-1447.
https://doi.org/10.3390/rs4051425

**Chicago/Turabian Style**

Collin, Antoine, and James L. Hench. 2012. "Towards Deeper Measurements of Tropical Reefscape Structure Using the WorldView-2 Spaceborne Sensor" *Remote Sensing* 4, no. 5: 1425-1447.
https://doi.org/10.3390/rs4051425