**9. Results and discussion**

#### **9.1 Image processing**

A Landsat 7-ETM+ image from March 29, 2000 was processed. Before conducting the quantitative analysis of the data, a post-calibration was performed of the constant gain and offset to convert the image ND to spectral radiance. The spectral radiance was also corrected for atmospheric effects to obtain the surface reflectance values. A geometric correction was not performed because the level of the processing of the Landsat images includes this correction. Only 3 of the 8 bands contained by Landsat were used (blue, green and red). The depth correction was developed with the Lyzenga (1981) method, which has been used and described by other authors (Mumby et al., 1997, 1998; Mumby and Edwards 2002; Andréfouët et al., 2003).

#### **9.2 Water column correction**

Lyzenga (1981) shows that when drawing a scatterplot of 2 of the logarithmically transformed bands in the visible spectrum (one on each axis), the pixels for the same type of bottom (i.e. sand at different depths) follow a linear trend. Repeating this process for different types of bottoms produces a series of parallel lines and the intersection of those lines generate a unique depth-invariant index which is independent of the type of bottom; all the pixels for a particular bottom have the same value as the index regardless of the depth at which they are found (Andréfouët et al., 2003). A group of pixels representative of the depth of the water column was selected for this study, therefore pixels very close to the surface (< 1m) were eliminated. Sand was the only substrate used since it is the most homogenous bottom in coral environments, and is the one most used by various authors (Mumby and Edwards 2002; Lyzenga, 1981) and the most easily recognizable for interpretation purposes. For the specific case of the Chinchorro Bank, 100 points of sand between 1 and 10m of depth were used to determine the attenuation coefficient (quotient) for the band pair ½, 99 points were used for bands 1/3 and 96 for bands 2/3. The data for point radiance to a type of bottom were extracted from the image and transferred to a spreadsheet. Figure 6a shows the graphic spectral radiance of bands 1 and 2 (atmospherically corrected) with respect to the depth for one specific type of bottom (sand) and variable depth.

Figure 6b shows the linearization of the exponential attenuation of the radiance for bands 1 and 2 using natural logarithms, since in practice it is virtually impossible for the points to adhere to a perfect line given the natural heterogeneity of the different types of bottoms, variations in the water quality, surface roughness of the water, etc. Figure 6c shows the biplot of bands 1 and 2 for a single substrate (sand) at different depths. To this end, the variance of band 1 and the covariance of bands 1 and 2 are evaluated (Table 2 and 3). Table 3 shows the different values for obtaining the attenuation coefficient, according to spectral band.


Table 2. Variance of the radiance of each band

A Landsat 7-ETM+ image from March 29, 2000 was processed. Before conducting the quantitative analysis of the data, a post-calibration was performed of the constant gain and offset to convert the image ND to spectral radiance. The spectral radiance was also corrected for atmospheric effects to obtain the surface reflectance values. A geometric correction was not performed because the level of the processing of the Landsat images includes this correction. Only 3 of the 8 bands contained by Landsat were used (blue, green and red). The depth correction was developed with the Lyzenga (1981) method, which has been used and described by other authors (Mumby et al., 1997, 1998; Mumby and Edwards 2002;

Lyzenga (1981) shows that when drawing a scatterplot of 2 of the logarithmically transformed bands in the visible spectrum (one on each axis), the pixels for the same type of bottom (i.e. sand at different depths) follow a linear trend. Repeating this process for different types of bottoms produces a series of parallel lines and the intersection of those lines generate a unique depth-invariant index which is independent of the type of bottom; all the pixels for a particular bottom have the same value as the index regardless of the depth at which they are found (Andréfouët et al., 2003). A group of pixels representative of the depth of the water column was selected for this study, therefore pixels very close to the surface (< 1m) were eliminated. Sand was the only substrate used since it is the most homogenous bottom in coral environments, and is the one most used by various authors (Mumby and Edwards 2002; Lyzenga, 1981) and the most easily recognizable for interpretation purposes. For the specific case of the Chinchorro Bank, 100 points of sand between 1 and 10m of depth were used to determine the attenuation coefficient (quotient) for the band pair ½, 99 points were used for bands 1/3 and 96 for bands 2/3. The data for point radiance to a type of bottom were extracted from the image and transferred to a spreadsheet. Figure 6a shows the graphic spectral radiance of bands 1 and 2 (atmospherically corrected) with respect to the depth for one specific type of bottom (sand)

Figure 6b shows the linearization of the exponential attenuation of the radiance for bands 1 and 2 using natural logarithms, since in practice it is virtually impossible for the points to adhere to a perfect line given the natural heterogeneity of the different types of bottoms, variations in the water quality, surface roughness of the water, etc. Figure 6c shows the biplot of bands 1 and 2 for a single substrate (sand) at different depths. To this end, the variance of band 1 and the covariance of bands 1 and 2 are evaluated (Table 2 and 3). Table 3 shows the different values for obtaining the attenuation coefficient, according to spectral

Band 1 Band 2 Band 3

*ii* ) 0.2628 0.6334 0.2761

**9. Results and discussion** 

**9.1 Image processing** 

Andréfouët et al., 2003).

and variable depth.

Variance (

Table 2. Variance of the radiance of each band

band.

**9.2 Water column correction** 

Fig. 6. Steps for water column correction: (a) spectral radiance of bands 1 and 2 (atmospherically corrected), (b) exponential decay of the radiance for bands 1 and 2 using natural logarithms and (c) biplot of bands 1 and 2 for a single bottom (sand) at different depths.


Table 3. Calculation of ratio of attenuation coefficients

Figure 6c shows the biplot of the logarithmically transformed bands 1 and 2, representing the attenuation coefficient (ki/kj) for bands 1 and 2. It is important to mention that if different types of bottoms are represented in a biplot, they would theoretically represent a line with a similar behavior, varying in position only due to differences in spectral reflectance. The gradient of the line would be identical since ki/kj does not depend on the type of bottom. The intersection of the line with the y-axis represents the depth-invariant index, since each type of bottom has a unique y-intersect regardless of depth. Each pixel is assigned an index depending on the type of bottom, which is obtained using the natural logarithm transformation for each band and the connection of the coordinate to the origin of the y-axis through gradient line ki/kj. The pixels are thus classified for different types of bottoms.

Satellite Remote Sensing of Coral Reef Habitats Mapping in

zones with greater depths.

**9.3 ISODATA classification** 

without correction (Figure 8c).

the ecology of the corals, as explained next.

Shallow Waters at Banco Chinchorro Reefs, México: A Classification Approach 347

resulting from the depth-invariant index was significantly different than the image without correction, since it reveals more details of the structures of the benthic bottom, especially in

As an initial approach to the classification of submerged benthic ecosystems in the Chinchorro Bank, ISODATA was used as a classification method, since not much needs to be known about that data beforehand. A little user effort is required to identify spectral clusters in data. The results of the benthic classification in the Chinchorro Bank were visually evaluated according to the quality of the segmentation using the classification by Aguilar-Perera & Aguilar-Dávila (1993), and with bathymetric data that greatly determine

Figure 8a shows the Landsat image with atmospheric correction for the RGB (1,2,3) combination and Figure 8b shows the image resulting from the depth-invariant index by bottom type. At the bottom of the figure, two images classified using ISODATA are included, both with the same type and number of classes. Figure 8c presents the classification performed without water column correction; that is, using the image from 8a as input. Figure 8d includes the classification performed based on the depth-invariant index (shown in 8b); that is, taking into account water column correction. To identify the categories resulting from the ISODATA process, benthic bottoms in the Chinchorro Bank as defined by Aguilar-Perera & Aguilar Dávila (1993) were used as a basis. It can be seen (8c) that the classification without water column correction produced a substantial mix of classes throughout the image, unlike the classification obtained by applying water column correction (8d). According to authors such as Aguilar-Perera & Aguilar Dávila (1993), Chávez and Hidalgo (1984) and Jordán (1979), the periphery of the Chinchorro Bank is surrounded by abundant coral growth on the eastern margin. A barrier reef is thereby formed that disappears along the western margin where the coral growth is semicontinuous and diffuse. This spatial distribution of the corals can be clearly seen in the results of the classification with water column correction (Figure 8d), unlike classification

One known ecological characteristic of reef systems is that the zonation of the reef bottom and its ecological dynamics are strongly influenced by the depth (Huston, 1985; Loya, 1972; Gonzáles et al., 2003). The seagrasses constitute a type of benthic bottom normally present in shallower zones. These observations and the use of bathymetry enable corroboration of the validity of the spatial distribution of seagrasses obtained by classification with water column correction. The shallower zones are located in the northern (1-2m) and central (3 and 4 m) portions; these two zones best correspond to the zone with seagrass generated in the image shown in 8d, as opposed to the image in 8c where it can be seen that the seagrass class is distributed throughout the bank. In addition, 8c shows a mix between seagrass and corals, a result that is not justifiable since the corals normally develop at depths between 5 and 30m. Using the depth criterion again in order to define the zonation, it is possible to state that the classification with water column correction produces good results for identifying coral patches, since they are found at depths between 7 and 12 m, as can be seen in Figure 8d. As a general observation, we can state that the results of the classification with water column correction generate data that are consistent with the theory regarding the

As mentioned before, the depth-invariant index is generated according to band pairs—1/2, 1/3 and 2/3, correponding to bands 1 (blue), 2 (green) and 3 (red) (Figure 7). The image

Fig. 7. Visualization of the Landsat 7-ETM+ image before and after water column correction. a) image of band 1 (blue, 450-520 nm), b) band 2 (green, 530-610 nm), c) band 3 (red, 630-655 nm), d) depth-invariant index combination of bands 1/2, e) 2/3 and f) 1/3.

resulting from the depth-invariant index was significantly different than the image without correction, since it reveals more details of the structures of the benthic bottom, especially in zones with greater depths.

#### **9.3 ISODATA classification**

346 Remote Sensing – Applications

As mentioned before, the depth-invariant index is generated according to band pairs—1/2, 1/3 and 2/3, correponding to bands 1 (blue), 2 (green) and 3 (red) (Figure 7). The image

Fig. 7. Visualization of the Landsat 7-ETM+ image before and after water column correction. a) image of band 1 (blue, 450-520 nm), b) band 2 (green, 530-610 nm), c) band 3 (red, 630-655

nm), d) depth-invariant index combination of bands 1/2, e) 2/3 and f) 1/3.

As an initial approach to the classification of submerged benthic ecosystems in the Chinchorro Bank, ISODATA was used as a classification method, since not much needs to be known about that data beforehand. A little user effort is required to identify spectral clusters in data. The results of the benthic classification in the Chinchorro Bank were visually evaluated according to the quality of the segmentation using the classification by Aguilar-Perera & Aguilar-Dávila (1993), and with bathymetric data that greatly determine the ecology of the corals, as explained next.

Figure 8a shows the Landsat image with atmospheric correction for the RGB (1,2,3) combination and Figure 8b shows the image resulting from the depth-invariant index by bottom type. At the bottom of the figure, two images classified using ISODATA are included, both with the same type and number of classes. Figure 8c presents the classification performed without water column correction; that is, using the image from 8a as input. Figure 8d includes the classification performed based on the depth-invariant index (shown in 8b); that is, taking into account water column correction. To identify the categories resulting from the ISODATA process, benthic bottoms in the Chinchorro Bank as defined by Aguilar-Perera & Aguilar Dávila (1993) were used as a basis. It can be seen (8c) that the classification without water column correction produced a substantial mix of classes throughout the image, unlike the classification obtained by applying water column correction (8d). According to authors such as Aguilar-Perera & Aguilar Dávila (1993), Chávez and Hidalgo (1984) and Jordán (1979), the periphery of the Chinchorro Bank is surrounded by abundant coral growth on the eastern margin. A barrier reef is thereby formed that disappears along the western margin where the coral growth is semicontinuous and diffuse. This spatial distribution of the corals can be clearly seen in the results of the classification with water column correction (Figure 8d), unlike classification without correction (Figure 8c).

One known ecological characteristic of reef systems is that the zonation of the reef bottom and its ecological dynamics are strongly influenced by the depth (Huston, 1985; Loya, 1972; Gonzáles et al., 2003). The seagrasses constitute a type of benthic bottom normally present in shallower zones. These observations and the use of bathymetry enable corroboration of the validity of the spatial distribution of seagrasses obtained by classification with water column correction. The shallower zones are located in the northern (1-2m) and central (3 and 4 m) portions; these two zones best correspond to the zone with seagrass generated in the image shown in 8d, as opposed to the image in 8c where it can be seen that the seagrass class is distributed throughout the bank. In addition, 8c shows a mix between seagrass and corals, a result that is not justifiable since the corals normally develop at depths between 5 and 30m. Using the depth criterion again in order to define the zonation, it is possible to state that the classification with water column correction produces good results for identifying coral patches, since they are found at depths between 7 and 12 m, as can be seen in Figure 8d. As a general observation, we can state that the results of the classification with water column correction generate data that are consistent with the theory regarding the

Satellite Remote Sensing of Coral Reef Habitats Mapping in

other authors regarding the spatial distribution of sea-bottoms.

Shallow Waters at Banco Chinchorro Reefs, México: A Classification Approach 349

influence of depth in defining the zonation of benthic bottoms, as well as observation of

Figure 9 shows a close-up to facilitate the visual analysis of the differences between the classes obtained using ISODATA, implemented with and without water column correction.

Fig. 9. Comparison among a) Landsat 7-ETM+ image, RGB (1, 2, 3), b) depth-invariant index

by bottom type for bands 1/2, c) ISODATA without water column correction and c)

ISODATA with water column correction.

Fig. 8. a) Landsat 7-ETM+ image, RGB (1, 2, 3), b) image resulting from the depth-invariant index by bottom type using bands 1 and 2, and classification of the benthic bottom in the Chinchorro Bank using ISODATA, c)without water column correction and d) with water column correction.

Fig. 8. a) Landsat 7-ETM+ image, RGB (1, 2, 3), b) image resulting from the depth-invariant index by bottom type using bands 1 and 2, and classification of the benthic bottom in the Chinchorro Bank using ISODATA, c)without water column correction and d) with water

column correction.

influence of depth in defining the zonation of benthic bottoms, as well as observation of other authors regarding the spatial distribution of sea-bottoms.

Figure 9 shows a close-up to facilitate the visual analysis of the differences between the classes obtained using ISODATA, implemented with and without water column correction.

Fig. 9. Comparison among a) Landsat 7-ETM+ image, RGB (1, 2, 3), b) depth-invariant index by bottom type for bands 1/2, c) ISODATA without water column correction and c) ISODATA with water column correction.

Satellite Remote Sensing of Coral Reef Habitats Mapping in

structure.

changes.

**11. Acknowledgments** 

**12. References** 

4028

geomorphologic characterization of the reef.

Shallow Waters at Banco Chinchorro Reefs, México: A Classification Approach 351

can contribute to maintaining biodiversity. On the other hand, the human impacts—which may seem to be less intense because they are not as perceivable to the eye—are chronic and can unleash a chain of negative effects. This sequence of negative effects normally does not give ecosystems the opportunity to recover and maintain their characteristic function and

The search for new methodologies to process satellite images is indispensable to identifying the current trend in the degradation of marine habitats; methodologies that generate new and improved classifications that are highly reliable and with a level of detail that is adequate for mapping these ecosystems. Through this type of study, it is possible to organize, relate and manage information from satellite images in order to propose agreedupon strategies to conserve natural resources, as part of comprehensive environmental policies to properly solve the problems. Thus, these data can be used as a basis to plan the monitoring of reefs in order to create scientific methods to generate knowledge and environmental awareness in the society and to contribute to the mitigation of the loss of reefs due to impacts from current global warming and other anthropogenic and global

The authors would like to thank the Mexican Navy (SEMAR), Deputy Department of Oceanography, Hydrography and Meteorology (Dirección General Adjunta de Oceanografía, Hidrografía y Meteorología) for the information provided regarding bathymetry and the field sampling of sand data. We also thank Dr. Juan Pablo Carricart Ganivet and Janneth Padilla Saldívar for the information and geographic basis from the Comprehensive Management of the Chinchorro Bank: Geographic survey and

Aguilar-Perera A. & Aguilar-Dávila W., (1993). Banco Chinchorro: Arrecife Coralino en el

Andréfouët, S. ; Kramer, P. ; Torres-Pulliza, D. ; Joyce, K. ; Hochberg, E. ; Garza-Perez, R. ;

*environment*, Vol. 88, No. 1-2. (November 2003), pp. 128-143, ISSN 0034-4257 Benfield, S., H. Guzman, J. Mair & A. Young (2007). Mapping the distribution of coral reefs

*sensing*, Vol. 28, No. 22, (November), pp. 5047-5070, ISSN 5047 5070

& González, N.E. pp. 1-35 Com. Nal. Biodiversidad y CIQRO, México Andréfouët, S. y Riegl, B. (2004). Remote sensing: a key tool for interdisciplinary assessment

Caribe. Pp. 807-816. In: *Biodiversidad Marina y Costera de México,* Salazar-Vallejo, S.I.

of coral reef precesses. *Coral reef,* Vol. 23, No. 1, (April 2004), pp 1-4, ISSN: 0722-

Mumby, P. ; Riegl, B. ; Yamano, H. ; White, W. ; Zubia, M. ; Brock, J. ; Phinn, S. ; Naseer, A. ; Hatcher, B. & Muller-Karger, F. (2003). Multi-site evaluation of IKONOS data for classification of tropical coral reef environments. *Remote sensing of* 

and associated sublittoral habitats in Pacific Panama: a comparison of optical satellite sensors and classification methodologies. *Internatinal joural of remote* 

In this figure, it can be seen that thanks to the water column correction, the classes are better defined, with mixing among them—caused by interference by the depth of the water column—avoided to whatever extent possible. The ISODATA algorithm more accurately selects and groups clusters, eliminating this problem. This visualization again confirms the advantage of performing water column corrections to obtain better results for the processes to classify benthic bottoms.
