**4. Mapping coral reefs using remote sensors**

334 Remote Sensing – Applications

Spectral reflectance (ρ) is a key parameter for conducting studies of coral reefs using RS (Hochberg et al., 2004). Two factors clearly and concisely explain this. First, ρ represents the boundary of radiative transference in the water surface optics. Therefore, taking into account ρ can resolve the problem of inverse radiative transference presented by passive remote sensors when applied in this field. Second, ρ is the function that denotes the object, the composition of the material and its structure. Therefore, it serves as a bridge between the

In the process of classifying images and generating thematic maps, large differences have been noted in spectral reflectance among the coral reefs' benthic communities (Brock et al., 2006). Variability in the vertical relief, or rugosity, is a significant aspect of the complexity of a habitat, a factor that both reflects and governs the spatial distribution and density of many reef organisms (McCormick 1994). These factors, which respond to these evaluations, vary according to the differences among sediments, the presence of different algae species and the coverage of atypical algae in surface water in some reef zones. Thus, Hochberg et al. (2004) mention the importance of creating a specific approach using RS to study the surface water mass presented by atypical algae, since it has been shown that the mere presence of these organisms indicates classes that are spectrally distinct from other reef communities,

Differences among the spectral signatures of corals provide a high likelihood of satisfactorily delineating and defining their different features in a satellite image. The problem with the above process is that the ρ of the corals is a function of pigmentation, structure, the orientation of their branches and their internal characteristics (Newman et al., 2006). In addition, though the interactions between light and the atmosphere are wellstudied, the challenge is to establish controls for the effects of the water column in which the coral is found that influence these factors. Taking into account the curvatures in order to correct the acquired data provides more valuable information about the conditions and health of the living communities sheltered by the coral. Newman et al. (2006) indicate that two categories have been defined by recent studies which were conducted to measure in situ

i. The spectral signatures are examined according to the variation in the pigment density, which characterizes the sensorial color of the different coral species (Newman et al., 2006). Some studies have analyzed the contribution of color to the measurement of radiance (R), in particular, by comparisons with unpigmented coral structures. These observations resulted in the spectrum of coral whitening and structures saturated with zooxanthellae (Newman et al., 2006), which provide a measure of the health status of the complex reef system. Color has been used as a comparison measurement among three coral species, five algae species and three benthic communities (Hochberg and Atkinson, 2000), and as a means to differentiate between dead coral in different stages

ii. Spectral signatures were examined according to morphological characteristics

Corals exhibit distinct and complex structural morphologies, partially due to environmental conditions such as light availability, water motion and suspended sediment (Joyce & Phinn, 2002). Reflectance values measured over varying angles and azimuths were examined to determine the bidirectional reflectance distribution

optics of the object and the shape of the sea bottom (Hochberg et al., 2004).

even when they represent the same species.

the spectral signatures of the coral environment:

and algae colonization (Clark et al., 2000).

(Newman et al., 2006).

The worldwide importance of coral reefs in light of current threats has generated interest in developing methods to study this type of ecosystems at global scales (Kuhn 2006). The use of remote sensing to map underwater habitats is increasing substantially. This enables using the derived information to determine the status of these natural resources as a basis for planning, management, monitoring, conservation and evaluating their potential.

Fig. 1. Components of Remote Sensing in mapping coral reefs.

As was mentioned previously, high resolution spectral sensors exist that have elements that enable specific analysis with an excellent capacity for modelling environmental and structural variables in the coral reefs (Holden and LeDrew, 1998). The data produced by this type of sensors provide products that can be combined with models to photosynthetically calculate the radiation available through the photic zone and the surface of benthic substrates. Established models for calculating incident solar radiation are developed and evaluated based on routine satellite and meteorological observations (Brock et al., 2006). The spectral differences among corals, seagrass and algae are nearly imperceptible and not easy to detect with the three bands (blue, green and red) of the sensors that can penetrate the

Satellite Remote Sensing of Coral Reef Habitats Mapping in

seen as a function of the atmospheric parameters. ¶(6pt)

and scattered in different (adjacent) directions.

**5.1.2 Atmospheric correction** 

**5.1.3 Geometric correction** 

**5.2 Water column correction** 

other sources.

is shown in Figure 2.

Shallow Waters at Banco Chinchorro Reefs, México: A Classification Approach 337

The total signal captured by the sensor consists of three parts: atmospheric scattering of radiation, radiation reflected by the pixel and radiation reflected by the vicinity of the pixel

The atmospheric conditions (water vapor, aerosols and visibility) in a scene can be calculated using algorithms that are performed using a database based on atmospheric functions. The surface spectral reflectance of an interaction target in a scene can thereby be

The geometric correction consists of distinguishing the other types of radiation and only considering that which is reflected by the pixel. The objective is to remove geometric distortion; that is, to locate each pixel in its corresponding planimetric position. This enables associating the information obtained from a satellite image with thematic information from

The coral reefs generally develop in transparent or clear water, which facilitates study and analysis with passive optic, multispectral or hyperspectral sensors (Mumby et al., 1999). When light penetrates the water column, its intensity exponentially decreases as the depth increases. This process is known as attenuation, and it has an important effect on data obtained by remote sensors in aquatic environments (Green, 2000). The attenuation process

Fig. 2. Processes of light attenuation in the water column (SERC, 2011).

water column (Holden and LeDrew 1998; Hedley and Mumby 2002; Karpouzli et al., 2004). This is why RS studies applied to the mapping of submerged benthic ecosystems requires the generation of new processing methodologies. In addition, coral habitats present a heterogeneity that is inherent of their complexity, and therefore the task of discerning among the different spectral signatures is more complicated. That is, the pre-processing of images applied to this type of environments should not only incorporate the elimination of noise in the atmospheric and batimetric portions, but should also take into account the components of the water column, as shown in Figure 1.

#### **5. Pre-processing of satellite images**

All satellite images must undergo an initial processing of crude data to correct radiometric and geometric distortions of the image and eliminate noise. It must be taken into account that the energy captured by the sensor goes through a series of interactions with the atmosphere before reaching the sensor. As a result, the radiance registered by the sensor is not an exact representation of the actual radiance emitted by the covering. This means that the image acquired in a numerical form presents a series of anomalies with respect to the real scene being detected. These anomalies are located in the pixels and digital levels of the pixels that make up the data matrix. The purpose of correction operations is to minimize these alterations. The corrections are made during pre-processing operations, since they are carried out before performing the procedures to extract quantitative information. The product obtained is a corrected image that is as close as possible, geometrically and radiometrically, to the true radiant energy and spatial characteristics of the study area at the time the data are collected. Atmospheric correction is a process used to reduce or eliminate the effects of the atmosphere and allow for more precisely seeing the reflectance values of the surface being studied or analyzed.

Nevertheless, when attempting to map or derive quantitative information from subaquatic habitats, the depth of the water significantly affects the measurements taken by remote sensors, making it possible to generate confusion about spectral signatures. Therefore, atmospheric and geometric corrections are not sufficient when the objective is to extract features of the covering of the bottom of the water. That could be considered a characteristic and, in some cases, a limitation of passive sensors in remote sensor applications in marine environments. Thus, in this type of studies, a water column correction is performed to improve reliability when analyzing the results of the image and to eliminate the noise resulting from the variation in the ground's reflectance (Holden 2002; Holden and LeDrew, 1998; Mumby, 1998).

#### **5.1 Correction of remotely sensed imagery**

#### **5.1.1 Radiometric correction**

The radiance from the sensor (L) is calculated as:

$$\text{L} \Leftarrow \text{c0} \text{+c1} \text{\*} \text{ND} \tag{1}$$

Where c0 and c1 are the offset and gain, respectively, of the radiometric calibration and ND is the digital number recorded in a particular spectral band. The process of obtaining L is called radiometric correction.

The total signal captured by the sensor consists of three parts: atmospheric scattering of radiation, radiation reflected by the pixel and radiation reflected by the vicinity of the pixel and scattered in different (adjacent) directions.

#### **5.1.2 Atmospheric correction**

336 Remote Sensing – Applications

water column (Holden and LeDrew 1998; Hedley and Mumby 2002; Karpouzli et al., 2004). This is why RS studies applied to the mapping of submerged benthic ecosystems requires the generation of new processing methodologies. In addition, coral habitats present a heterogeneity that is inherent of their complexity, and therefore the task of discerning among the different spectral signatures is more complicated. That is, the pre-processing of images applied to this type of environments should not only incorporate the elimination of noise in the atmospheric and batimetric portions, but should also take into account the

All satellite images must undergo an initial processing of crude data to correct radiometric and geometric distortions of the image and eliminate noise. It must be taken into account that the energy captured by the sensor goes through a series of interactions with the atmosphere before reaching the sensor. As a result, the radiance registered by the sensor is not an exact representation of the actual radiance emitted by the covering. This means that the image acquired in a numerical form presents a series of anomalies with respect to the real scene being detected. These anomalies are located in the pixels and digital levels of the pixels that make up the data matrix. The purpose of correction operations is to minimize these alterations. The corrections are made during pre-processing operations, since they are carried out before performing the procedures to extract quantitative information. The product obtained is a corrected image that is as close as possible, geometrically and radiometrically, to the true radiant energy and spatial characteristics of the study area at the time the data are collected. Atmospheric correction is a process used to reduce or eliminate the effects of the atmosphere and allow for more precisely seeing the reflectance values of

Nevertheless, when attempting to map or derive quantitative information from subaquatic habitats, the depth of the water significantly affects the measurements taken by remote sensors, making it possible to generate confusion about spectral signatures. Therefore, atmospheric and geometric corrections are not sufficient when the objective is to extract features of the covering of the bottom of the water. That could be considered a characteristic and, in some cases, a limitation of passive sensors in remote sensor applications in marine environments. Thus, in this type of studies, a water column correction is performed to improve reliability when analyzing the results of the image and to eliminate the noise resulting from the variation in the ground's reflectance (Holden 2002; Holden and LeDrew,

 L=c0+c1\*ND (1) Where c0 and c1 are the offset and gain, respectively, of the radiometric calibration and ND is the digital number recorded in a particular spectral band. The process of obtaining L is

components of the water column, as shown in Figure 1.

**5. Pre-processing of satellite images** 

the surface being studied or analyzed.

**5.1 Correction of remotely sensed imagery** 

The radiance from the sensor (L) is calculated as:

1998; Mumby, 1998).

**5.1.1 Radiometric correction** 

called radiometric correction.

The atmospheric conditions (water vapor, aerosols and visibility) in a scene can be calculated using algorithms that are performed using a database based on atmospheric functions. The surface spectral reflectance of an interaction target in a scene can thereby be seen as a function of the atmospheric parameters. ¶(6pt)

#### **5.1.3 Geometric correction**

The geometric correction consists of distinguishing the other types of radiation and only considering that which is reflected by the pixel. The objective is to remove geometric distortion; that is, to locate each pixel in its corresponding planimetric position. This enables associating the information obtained from a satellite image with thematic information from other sources.

#### **5.2 Water column correction**

The coral reefs generally develop in transparent or clear water, which facilitates study and analysis with passive optic, multispectral or hyperspectral sensors (Mumby et al., 1999). When light penetrates the water column, its intensity exponentially decreases as the depth increases. This process is known as attenuation, and it has an important effect on data obtained by remote sensors in aquatic environments (Green, 2000). The attenuation process is shown in Figure 2.

Fig. 2. Processes of light attenuation in the water column (SERC, 2011).

Satellite Remote Sensing of Coral Reef Habitats Mapping in

The procedure is divided into various steps:

this requirement.

measurements.

where 

Shallow Waters at Banco Chinchorro Reefs, México: A Classification Approach 339

used and described by other authors, such as Mumby et al., 1997, 1998, Mumby and Edwards 2002, Andréfouët et al., 2003, etc. This approach has the advantage of taking into account the majority of the spectral information and not requiring data for the components of the water surrounding the reef. Instead of deriving the spectra of the different types of sea bottoms and water properties, this method transforms the spectral values into "depth-invariant indices." The primary limitation of this method, among others, is that it must be applied to clear water (i.e. type 1 or type 2); the study area meets

To eliminate the influence of depth on sea bottom reflectance, the following need to be taken into account: the identification of the characteristics of attenuation of the water column and having digital models of the depth; although these are not very common, particularly for coral reef systems (Clark et al., 2000). This work used a bathymetric model provided by SEMAR (2008) that makes possible a good deal of reliability and precision to the

1. Elimination of the atmospheric scattering and the external reflection from the water surface (atmospheric correction). This can be carried out using a variety of methods, such as dark pixel subtraction (Maritorena, 1996) and ATCOR (Richter, 1996, 1998).

3. Selection of a spectral band pair, with good penetration of the water column (that is, bands found in the visible light spectrum—Landsat TM and ETM+ 1/2, 2/3 and 1/3). 4. Linearization of the relationship between depth and radiance, Xi = ln (Li), where Xi is the transformed radiance of the pixel in band i (band 1) and Li is the radiance of the pixel in band j (band 2). When the intensity of the light (radiance) is transformed using the natural logarithm (ln), this relationship becomes linear with the depth. Therefore,

5. Determination of the attenuation coefficient (quotient) using a biplot of the transformed radiance of the 2 bands (Li and Lj). The biplot contains data for one type of uniform

6. Lastly, the depth-invariant index is generated using the equation by Lyzenga (1981):

*<sup>k</sup> IIP L <sup>L</sup>*

*ii* is the variance in band i and a is the covariance between bands i and j.

ln ln *<sup>i</sup> ij i j j*

*k* 

bottom (sand) and variable depth. It is created using the following equations:

2 *jj ii ij*

and

*a*  *X Ln L i i* (2)

<sup>2</sup> 1 *KK a a i j* (3)

*ij XX XX <sup>i</sup> <sup>j</sup> <sup>i</sup> <sup>j</sup>* (4)

(5)

2. Selection of pixel samples with the same substrate and different depths.

the transformed radiance values will decrease linearly as depth increases:

There are two reasons for this phenomenon:


The attenuation varies according to the wavelength of the electromagnetic radiation (EMR). For example, in the region of visible light, the red portion of the spectrum attenuates more quickly than the short wavelength, such as blue.

Figure 3 shows, for 4 spectral bands (blue, green, red and infrared), how the spectrum in a particular habitat (seagrass or macroalgae) can change as the depth increases. The spectral radiance registered by a sensor is dependent on the reflectance of the substrates and the depth. As the depth increases, the possibility to discriminate spectrums or spectral signatures of the habitats decreases. In practice, the spectrum of sand at a depth of 2 meters is very different than that at 20 meters. According to Mumby and Edwards (2000), the spectral signature of sand at 20 meters could be similar to that of seagrass at 3 meters. All these factors influence the signal and can create a good deal of confusion when using visual inspection or spectral classification to classify these habitats. Therefore, the influence of the variability in depth must be eliminated, which is known as water column correction or depth correction (Mumby and Edwards 2000).

Fig. 3. Spectral differences for a habitat (seagrass or macroalgae) at different depths (Mumby and Edwards, 2000).

A variety of models exist that can be used to compensate for the effect of the water column. Nevertheless, many require optical measurements of the optical properties of the water itself, as well as information about the depth of water per pixel (Gordon, 1978; Philpot, 1989; Mobley et al., 1993; Lee et al., 1999; Maritorena et al., 1994; Maritorena 1996; Lee et al., 1999). Thus, the method proposed by Lyzenga (1981) is applied, which has been used and described by other authors, such as Mumby et al., 1997, 1998, Mumby and Edwards 2002, Andréfouët et al., 2003, etc. This approach has the advantage of taking into account the majority of the spectral information and not requiring data for the components of the water surrounding the reef. Instead of deriving the spectra of the different types of sea bottoms and water properties, this method transforms the spectral values into "depth-invariant indices." The primary limitation of this method, among others, is that it must be applied to clear water (i.e. type 1 or type 2); the study area meets this requirement.

To eliminate the influence of depth on sea bottom reflectance, the following need to be taken into account: the identification of the characteristics of attenuation of the water column and having digital models of the depth; although these are not very common, particularly for coral reef systems (Clark et al., 2000). This work used a bathymetric model provided by SEMAR (2008) that makes possible a good deal of reliability and precision to the measurements.

The procedure is divided into various steps:

338 Remote Sensing – Applications

 Absorption: light energy is converted into another type of energy, generally heat or chemical energy. This absorption is produced by the algae, which utilize the light as a source of energy, by suspended organic and inorganic particulate matter (OPM and

 Scattering: This phenomenon results from the collision of light rays and suspended particles, causing multiple reflections. The more turbid the water (more suspended particles) the greater the scattering effect, making it difficult for light to penetrate. The attenuation varies according to the wavelength of the electromagnetic radiation (EMR). For example, in the region of visible light, the red portion of the spectrum attenuates more

Figure 3 shows, for 4 spectral bands (blue, green, red and infrared), how the spectrum in a particular habitat (seagrass or macroalgae) can change as the depth increases. The spectral radiance registered by a sensor is dependent on the reflectance of the substrates and the depth. As the depth increases, the possibility to discriminate spectrums or spectral signatures of the habitats decreases. In practice, the spectrum of sand at a depth of 2 meters is very different than that at 20 meters. According to Mumby and Edwards (2000), the spectral signature of sand at 20 meters could be similar to that of seagrass at 3 meters. All these factors influence the signal and can create a good deal of confusion when using visual inspection or spectral classification to classify these habitats. Therefore, the influence of the variability in depth must be eliminated, which is known as water column correction or

Fig. 3. Spectral differences for a habitat (seagrass or macroalgae) at different depths (Mumby

A variety of models exist that can be used to compensate for the effect of the water column. Nevertheless, many require optical measurements of the optical properties of the water itself, as well as information about the depth of water per pixel (Gordon, 1978; Philpot, 1989; Mobley et al., 1993; Lee et al., 1999; Maritorena et al., 1994; Maritorena 1996; Lee et al., 1999). Thus, the method proposed by Lyzenga (1981) is applied, which has been

IPM), dissolved inorganic compounds and the water itself.

There are two reasons for this phenomenon:

quickly than the short wavelength, such as blue.

depth correction (Mumby and Edwards 2000).

and Edwards, 2000).


$$X\_i = \operatorname{Ln}(L\_i) \tag{2}$$

5. Determination of the attenuation coefficient (quotient) using a biplot of the transformed radiance of the 2 bands (Li and Lj). The biplot contains data for one type of uniform bottom (sand) and variable depth. It is created using the following equations:

$$K\_i \not\gets K\_j = a + \sqrt{\left(a^2 + 1\right)} \tag{3}$$

$$a = \frac{\sigma\_{\vec{\boldsymbol{\eta}}} - \sigma\_{\vec{\boldsymbol{\alpha}}}}{2\sigma\_{\vec{\boldsymbol{\eta}}}} \text{ and } \sigma\_{\vec{\boldsymbol{\eta}}} = \overline{X\_i X\_j} - \overline{X\_i}\overline{X\_j} \tag{4}$$

where *ii* is the variance in band i and a is the covariance between bands i and j.

6. Lastly, the depth-invariant index is generated using the equation by Lyzenga (1981):

$$IIP\_{ij} = \ln\left(L\_i\right) - \left[ \left(\frac{k\_i}{k\_j}\right) \ln\left[\left(L\_j\right)\right] \tag{5}$$

Satellite Remote Sensing of Coral Reef Habitats Mapping in

the zones with the highest reflectance. c. The pixels are assigned to the closest cluster.

iterations. Both parameters can be specified

Fig. 4. Study Area: Chinchorro Bank, Mexico.

**7. Case study** 

Shallow Waters at Banco Chinchorro Reefs, México: A Classification Approach 341

a. The user decides on the number N of clusters to be used. For the first calculation, it is recommended to use a high number, which is then reduced by interpreting the image. b. A set of N clusters in the space between the bands is selected. The initial location is in

d. The clusters are associated, dispersed or eliminated depending on the maximum

e. The grouping of pixels in the image is repeated until the maximum number of iterations has been reached, or a maximum percentage of pixels are left unchanged after two

The Chinchorro Biosphere Reserve (Fig. 4) is located in the open Caribbean Sea, 30.8 km east of the coastal city of Mahahual, which is the closest continental point. The coral reef of Chinchorro Bank, Mexico, is part of the great reef belt in the western Atlantic, the second largest in the world, and is the biggest oceanic reef in Mexico. With a reef lagoon area of 864 km2, it is considered a pseudo-atoll or reef platform (Camarena, 2003). Chinchorro Bank is a reef complex that contains an extensive coral formation with a vast wealth and diversity of species and high ecological, social and cultural value. It inherently provides certain services, including the protection of the coast from battering by storms and hurricanes. The area has been exploited by fishing and tourist-related scuba diving over the past decades. The Chinchorro Bank supports pristine reefs, coral patches, extensive areas of seagrass, microalgae beds and sand beds. The reserve's ecosystems are marked by mangroves and reef zones. The composition of the taxocenosis of coral is known to contain hexacorals,

distance of the class or the minimum number of pixels in a class.

The result of this operation generates a new band—the image with water column correction for a band pair (depth-invariant index). Since the values of this band are whole numbers with decimals and can be negative, in order to visualize them they need to be converted into an 8-bit format, that is, gray values between 0 and 255. To this end, minimum and maximum values for the resulting image must be found and linearly distributed between the values 1 and 255 (0 is not included because it is assigned to the masked surface area). The depthinvariant index is essential when the objective of the study is to extract spectral data for submerged aquatic environments.
