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Using bottom surface reflectanceto map coastal marine areas: a newapplication method for Lyzenga's modelTatsuyuki Sagawa a , Etienne Boisnier a , Teruhisa Komatsu a ,Karim Ben Mustapha b , Abdalla Hattour b , Naoko Kosaka c &Sanae Miyazaki ca Ocean Research Institute, The University of Tokyo, 1-15-1Minamidai , Nakano-ku , Tokyo , 164-8639 , Japanb Institut National des Sciences et Technologies de la Mer, 2025Salammbo , Tunis , Tunisiec NTT DATA Corporation, 3-3-3, Toyosu , Koutou-ku , Tokyo ,135-6033 , JapanPublished online: 20 Jul 2010.

To cite this article: Tatsuyuki Sagawa , Etienne Boisnier , Teruhisa Komatsu , Karim Ben Mustapha ,Abdalla Hattour , Naoko Kosaka & Sanae Miyazaki (2010) Using bottom surface reflectance to mapcoastal marine areas: a new application method for Lyzenga's model, International Journal ofRemote Sensing, 31:12, 3051-3064, DOI: 10.1080/01431160903154341

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Using bottom surface reflectance to map coastal marine areas:a new application method for Lyzenga’s model

TATSUYUKI SAGAWA*†, ETIENNE BOISNIER†, TERUHISA KOMATSU†,

KARIM BEN MUSTAPHA‡, ABDALLA HATTOUR‡,

NAOKO KOSAKA§ and SANAE MIYAZAKI§

†Ocean Research Institute, The University of Tokyo, 1-15-1 Minamidai,

Nakano-ku, Tokyo, 164-8639 Japan

‡Institut National des Sciences et Technologies de la Mer, 2025 Salammbo, Tunis, Tunisie

§NTT DATA Corporation, 3-3-3, Toyosu, Koutou-ku, Tokyo, 135-6033, Japan

(Received 3 July 2007; in final form 2 September 2008)

Remote sensing is widely used in coastal management. Lyzenga’s model has been

traditionally used to explain the relationship between bottom surface reflectance

and the radiance level measured by satellite. Due to its central assumption, this

model lacks accuracy compared with the other radiative transfer models.

Nonetheless, it enables, with a single and simple equation, representation of the

multiple optical processes taking place in coastal areas. Mapping processes asso-

ciated with this model may include radiometric correction, a technique previously

pointed out as a major driver of mapping accuracy. Radiometric correction is

generally based on a depth-invariant index, efficient for clear waters (Jerlov water

type I to II) but largely unsuitable when transparency decreases (Jerlov water type

II to III). In order to overcome this problem, we developed a new index for

radiometric correction, which combines bathymetry data with attenuation coeffi-

cients. The improved efficiency of our model with regard to the traditional depth

invariant index was demonstrated through two case studies: Funakoshi Bay

(Japan; Jerlov water type II) and the Gabes Gulf part located off Mahares

(Tunisia; Jerlov water type II to III).

1. Introduction

Coastal ecosystem management requirements have emphasized the importance of

accurate mapping (Tortell 1992, Komatsu et al. 2003) and optical remote sensing has

traditionally been presented as one of the most efficient techniques for completing this

task (Pasqualini et al. 2005). In this field, the relationship between bottom surfacereflectance and the radiance level recorded by optical sensors constitutes a funda-

mental issue.

Radiative transfer theory explains how the propagation of radiation is affected by a

medium through absorption, emission and scattering processes, and its mathematical

form was developed by Chandrasekhar (1960). In the field of hydro optics,

Preisendorfer (1976) was amongst the pioneers to refer to the radiative transfer theory

and proposed several analytical tools and procedures. Two years later, Lyzenga

(1978) introduced a radiative transfer model for dealing with shallow coastal areas.

*Corresponding author. Email: sagawa@aori.u-tokyo.ac.jp

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2010 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160903154341

International Journal of Remote Sensing

Vol. 31, No. 12, 20 June 2010, 3051–3064

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Despite the fact that this model neglects the effects of scattering in the water and

internal reflection at the water surface, its simple mathematical form makes it parti-

cularly convenient for remote sensing application. His model is still considered as a

canonical reference for coastal remote sensing (Mumby et al 1998, Karpouzli et al.

2003).In this study, we focus on the application methods specifically developed for

Lyzenga’s model and that imply radiometric correction. Radiometric correction is

defined by the Canada Center for Remote Sensing as the ‘calibration of recorded

variance values reflected from (or emitted by) the ground scene’ (Canada Center for

Remote Sensing 2010). Whilst this step may be ignored in the mapping process,

Mumby and Clark (2000) showed that its use improves significantly the accuracy of

the result. Unlike Mumby and Edwards (2000), we argue that ‘water column correc-

tion’ (i.e. removing the light absorption and scattering effect) is part of the radiometriccorrection, as it deals with recorded value calibration as well. As a radiometric

correction, Lyzenga (1978, 1981) proposed the calculation of a ‘depth-invariant

index’ based on ratios of reflectance values between bands. Mumby et al. (1998)

highlighted the efficiency of such a method for satellite and airborne images but

also mentioned a major limit: this technique is only suitable for high clarity waters

(Jerlov water types I to II). In this study, we developed a bottom reflectance index

capable of not only improving accuracy for Jerlov water types I to II but also dealing

with low transparency waters (Jerlov waters type II to III).In order to test the value of this reflectance index, we compared its efficiency with the

depth invariant index in mapping two different marine areas: the area located off

Mahares, in the Gulf of Gabes (south-east Tunisia) and Funakoshi Bay, located in the

Sanriku coastal area (north-eastern part of Japan). Moreover, in both cases, we selected

IKONOS images, as Mumby and Edwards (2002) pointed out that the high spatial

resolution of this American satellite is particularly adapted to marine environment

mapping.

2. Method

In this study we evaluate the respective efficiency of each correction index through

mapping accuracy. For this purpose, we used a twoep method (see figure 1). First, the

two radiometric correction methods under scrutiny were applied separately to a

similar satellite image. Second, both corrected images were classified via supervised

classification.

2.1 Radiometric correction methods

In the scope of radiometric correction, each pixel value within the image (DN value) is

converted into a radiance value. In the case of IKONOS, the following conversion

equation is generally used (Taylor 2005):

Li ¼Di

Ci

; (1)

where L is the radiance at the sensor aperture (mW cm-2 sr-1), C is the in-band

radiance calibration coefficient (cm2 sr mW-1) and D is the image product value.In the equation the subscript i represents spectral band i. From an optical perspec-

tive, bottom type can be identified by its reflectance. According to Lyzenga (1978), the

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relationship between the radiance level recorded by an optical sensor and bottom

reflectance is expressed by the following equation:

Li ¼ Lsi þ airi expð�KigZÞ (2)

where L is the radiance value calculated by equation (1), Ls is the radiance recorded

over deep water (external reflection from the water surface and scattering in theatmosphere), a is a constant which includes the solar irradiance, the transmittance

of the atmosphere and the water surface, and the reduction of the radiance due to

refraction at the water surface (mW cm-2 sr-1), r is the bottom surface reflectance, K is

the effective attenuation coefficient of the water (m-1), g is a geometric factor to

account for the path length through the water and Z is the water depth (m).

Bottom differences are mirrored by variations in L, as r changes according to the

bottom type. A radiometric correction index is required for estimating r and may be of

two types: depth-invariant index or the one proposed by this study, named reflectanceindex.

2.2 Depth-invariant index

In order to remove light scattering and absorption effects within both the atmosphere

and the water body, Lyzenga (1981) suggested the calculation of a depth-invariantindex. This index is expressed as follows:

Indexij ¼Kj lnðLi � LsiÞ � Ki lnðLj � LsjÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

K2i þ K2

j

q ; (3)

where L, Ls and K are the same as in equation (2), this time with the i and j subscripts

corresponding to two different satellite image bands.

Equation (3) is derived from equation (2) and refers simultaneously to two bands

(bands i and j). For calculating this index, ratios of attenuation coefficients between

bands are necessary. In our case these coefficients were derived from sea truth data

collected with a side scan sonar for a sandy bottom along a depth gradient (Lyzenga

Satellite image (e.g. IKONOS)

Radiometric correction

Image classification

Converted image (e.g. reflectance index)

Bottom habitat map (e.g. seagrass distribution map)

Figure 1. Image analysis process.

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1981). Side scan sonar constitutes a suitable tool for collecting sea truth data, as it is

possible to distinguish clearly a sandy bottom from seagrass beds. Accuracy can even be

compared with aquatic video camera except for boundary areas (Sagawa et al. 2008). In

this study, side scan sonar images were visually interpreted and boundary areas ignored.

Using sea truth data, we plotted satellite data against depth for sandy bottom types. Theregression curve of Lyzenga’s model is then obtained. From this curve –Kg can be

deduced, as g can be geometrically calculated from sun and satellite zenith angles.

2.3 The reflectance index proposed here (reflectance index)

In order to improve mapping accuracy, we propose an alternative radiometric correc-

tion. Our new reflectance index is expressed by the following equation:

Indexi ¼ðLi � LsiÞ

expð�KigZÞ ; (4)

where L, Ls, K, g and Z are similar to equation (2).

To calculate this index, we need to combine depth data with attenuation coeffi-

cients. Each band attenuation coefficient was calculated by using the same sea truthdata as for the depth-invariant index. Concerning depth data, we simply referred to

the bathymetry map supplied by local government institutions. It may be reasonable

to take advantage of these data, as they are easily available and represent generally

accurate input.

Once the numerator in equation (4) was replaced by airi expð�KigZÞ (from equa-

tion (2)) and the equation rearranged, the index becomes the following equation

including bottom reflectance:

Indexi ¼ airi; (5)

where a and r are the same as in equation (2) and i corresponds to a satellite image

band.

Clearly, this index is linearly related to bottom reflectance. As a result, we named it

‘reflectance index’. This index enables us to compare not only the difference in reflec-

tance ratios between bands but also the difference in absolute reflectance for each band.

2.4 Image classification

Once the two radiometric correction types were applied separately, the two different

images obtained were classified by using the supervised classification based on a

maximum likelihood decision rule. At this step of the analysis, sea truth data con-

cerning each bottom type distribution are required. These data were also collectedusing the side scan sonar measurements.

According to Lyzenga (1978), equation (2) should not be applied to very shallow

areas, as the model ignores internal reflection effects occurring at the water surface. As a

result, in this study we applied the above technique exclusively to areas deeper than 2 m.

2.5 Evaluation of the technique

Funakoshi Bay and the marine area off Mahares were selected as test sites to evaluate

the efficiency of the two radiometric correction methods. Mapping accuracy was

calculated by using user accuracy, producer accuracy, overall accuracy (Congalton

1991) and Tau coefficients (Ma and Redmond 1995) derived from error matrices.

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2.6 Case 1 (Funakoshi Bay)

The corresponding IKONOS satellite image was acquired on 17 December 2004.

IKONOS imagery has four bands (blue, green, red and infrared) but only two (blue

and green) were used for the classification, as light present in red and infrared

wavelengths is rapidly absorbed by surface water layers. Zostera oceanica and

Zostera asiatica are dominant species in this bay and both appear on a sandy bottom.

In December, these two species are similar in height (Nakaoka et al. 2003, Watanabe

et al. 2005) and colour, making classification particularly difficult. Field surveys were

carried out between 22 and 28 October 2004.Simultaneously, reflectance values for seagrass species and sand were estimated using

a spectroradiometer (FieldSpec Pro, Analytical Spectral Devices, Inc, Colorado, USA).

More precisely, for each bottom type, a single sample was collected by scuba diving,

randomly, in the mapping area under scrutiny. Samples were put in a circular black

plastic container (diameter 30 cm). The radiance reflected by a white board was used as

a 100% radiance benchmark and we adopted the Lambertian reflectance assumption.

2.7 Case 2 (Mahares)

On 2 October 2005, the corresponding IKONOS image was acquired. In this area,

Posidonia oceanica is the most abundant and common species and, like in FunakoshiBay, it mainly occurs on a sandy bottom. In this case, rather than distinguishing

seagrass species, we tried to distinguish as accurately as possible Posidonia oceanica

from sand. Field surveys, mapping and accuracy evaluation methods were similar to

Funakoshi Bay and were conducted from 3 to 13 October 2005).

3. Results

3.1 Case 1 (Funakoshi Bay)

In Funakoshi Bay, attenuation coefficients estimated from sea truth data were

respectively 0.068 m-1 for the blue band (centre wavelength equals 480 nm) and

0.084 m-1 for the green band (centre wavelength equals 550 nm). Hence, accordingto Jerlov classification (Walker 1994), this bay belongs to water type II. Spectral

reflectance for each bottom type is shown in figure 2. Curves for sand and seagrasses

(Zostera asiatica and Zostera caulescens) display highly distinct shapes. Conversely,

Zostera asiatica and Zostera caulescens curves are pretty similar. Reflectance values

for sand are always higher than seagrass. Figure 3 shows how index choice influences

bottom type distribution results. The related error matrix is displayed in table 1 and

indicates that mapping accuracy based on the reflectance index is superior. Following

Ma and Redmond (1995), a Z-test using the Tau coefficient was conducted andunderlined a significant difference of accuracy between tables 1(a) and 1(b) (p , 0.05).

3.2 Case 2 (Mahares)

In Mahares, attenuation coefficients estimated from sea truth data were respectively

0.088 m-1 for the blue band and 0.093 m-1 for the green band. Hence, according to

Jerlov classification, Mahares belongs to water type II–III. Spectral reflectance for

each bottom type is shown in figure 4. Like in Funakoshi, sand and seagrass curves

(Posidonia oceanica) are significantly different. Figure 5 shows how index choice

influences bottom type distribution results. The related error matrix is displayed in

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table 2 and indicates, as it was already the case for Funakoshi Bay, that mappingaccuracy is increased when the reflectance index is used. A Z-test was conducted and

underlined a significant difference of accuracy between tables 2(a) and 2(b) (p , 0.05).

4. Discussion

Mumby and Edwards (2002) succeeded in getting relatively high user accuracy map-

ping (86–89% for seagrass and 60–72% for sand) by coupling the depth invariantindex and IKONOS imagery. It then becomes interesting to investigate why a similar

method can lead to such variations in accuracy. We argue that differences are

primarily linked with water transparency and turbidity levels.

First, Mumby reported extremely high water transparency (horizontal Secchi depth

deeper than 50 m) in the scope of his study that took place off South Caicos, Turks

and Caicos Islands (British West Indies). In Funakoshi Bay, according to Shibatani

(2004), maximum Secchi depth equals 15 m while in Mahares, attenuation coefficients

indicate that it may be even shallower. With regard to light penetration in water, thesethree sites are then highly different. Broadly speaking, due to sensor resolution limits,

water transparency is an important variable in explaining the radiance level. Hence,

when water transparency is high, radiance level recorded by the satellite sensor is high

as well, as attenuation within the water body is low. Moreover, when the radiance

level is high, distinctions between bottom types are made easier because boundaries

between classes become clearer. Conversely, when the radiance level decreases, these

boundaries become blurred and classification becomes harder.

Second, despite the fact that red and infrared wavelengths may contain useful datafor distinguishing bottom types, light contained in these two bands attenuates quickly

in water, such that they become useless when we have to deal with turbid or deep

waters (see figures 2 and 4). According to McCluney (1974), even in the case of high-

clarity ocean water, penetration depth (i.e. the layer depth for which upwelling

radiance equals 90% of its maximum value) is 3.8 m for the red band covering

600–700 nm. In a separate study, Green et al. (2000) noted that, at such a depth, the

infrared (covering 800–1100 nm) is already completely absorbed.

0.0

0.1

0.2

0.3

350 450 550 650 750 850 950

Ref

lect

ance

Wavelength (nm)

Zostera caulescensZostera asiaticasand

Figure 2. Reflectance level with reference to wavelength for each bottom feature (FunakoshiBay). Values (bold lines) are shown as the mean (� 1 standard deviation represented by brokenlines). For each bottom feature, n ¼ 5.

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Figure 3. Maps derived from satellite image analysis (Funakoshi Bay). Black areas, describedas ‘0–2 metres (unclassified area)’ in the legends, represent the data which were not included inour analysis. The maps are obtained by applying a radiometric correction based on (a) thetraditional depth-invariant index; (b) our new reflectance index.

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What makes our method successful in low transparency conditions? As illustrated

by figures 2 and 4, differences between absolute reflectance values for blue and green

bands are large and the higher these differences are, the easier it is to identify bottomtypes and to increase general mapping accuracy. Our technique takes advantage of the

0.0

0.1

0.2

0.3

Ref

lect

ance

Wavelength (m)

Posidonia oceanica

Sand

350 450 550 650 750 850 950

Figure 4. Reflectance level with reference to wavelength for each bottom feature (Mahares).Values (bold lines) are shown as the mean (� 1 standard deviation represented by broken lines).For each bottom feature, n ¼ 5.

Table 1. Error matrices for satellite image classification (Funakoshi Bay), obtained when using(a) depth-invariant index and (b) reflectance index.

(a)Reference data (sea truth side scan sonar data)

Satellite imageclassification data Seagrass Sand Row total User accuracy

Seagrass 15 8 23 65.2%Sand 15 22 37 59.5%Column total 30 30 60Producer accuracy 50.0% 73.3%Overall accuracy 61.7%Tau coefficient 0.233

(b)Reference data (sea truth side scan sonar data)

Satellite imageclassification data Seagrass Sand Row total User accuracy

Seagrass 25 5 30 83.3%Sand 5 25 30 83.3%Column total 30 30 60Producer accuracy 83.3% 83.3%Overall accuracy 83.3%Tau coefficient 0.667

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sea chart bathymetry data available for almost any coastal area around the globe.

Consequently, and this may appear as a potential drawback, bathymetry data accu-

racy is of primary concern. However, the real influence of mistakes on the finalmapping result remains unclear and will represent the object of a future study.

Figure 5. Maps derived from satellite image analysis (Mahares). Black areas, described as ‘0–2metres (unclassified area)’ in the legends, represent the data which were not included in ouranalysis. The maps are obtained by applying a radiometric correction based on (a) the tradi-tional depth-invariant index; (b) our new reflectance index.

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Pasqualini et al. (1998, 2005) also referred to bathymetry data in order to reduce the

attenuation effect within the water body but the rules driving their depth classification

remain unclear. To be more precise, they divided the image according to three depth

ranges (0 to 5 m, 5 to 10 m and 10 to 20 m) before conducting supervised classification.Pasqualini et al. (1998, 2005) explained this choice of depth ranges with reference to

the map used. Nonetheless, we remain convinced that increasing bathymetry map

accuracy (i.e. more depth gradients) is essential to really benefit from the accuracy

improvement provided by depth data, even if it signifies increasing sampling in situ

as well.

Our method is also dependent on the reliability of Lyzenga’s model itself. The

central assumption of this model is that attenuation coefficients remain constant over

the entire area under scrutiny and are totally independent from bottom type. A plot ofradiance/depth for sand and seagrass using field data is displayed by figures 6

(Funakoshi) and 7 (Mahares). In Mahares, attenuation coefficients are almost similar

while in Funakoshi they are clearly distinct. This result tends to indicate that

Lyzenga’s model does not fit the Funakoshi case well, despite a higher water trans-

parency level. Model limits may hence explain the lower mapping accuracies in

Funakoshi compared with Mahares. As a result, beyond the question of the applica-

tion method selected for the Lyzenga’s model, it appears that the model itself may

require some modifications in order to be used successfully in places like FunakoshiBay. Tassan (1996) was amongst the pioneers questioning the reliability of Lyzenga’s

model by highlighting the need to link water turbidity to water depth. However,

Tassan’s method does not constitute a solution in case of Funakoshi, as attenuation

coefficients do not vary according the depth but according the bottom type. As a

Table 2. Error matrices for satellite image classification (Mahares), obtained when using (a)depth-invariant index and (b) reflectance index.

(a)Reference data (sea truth side scan sonar data)

Satellite imageclassification data Seagrass Sand Row total User accuracy

Seagrass 7 3 10 70.0%Sand 43 47 90 52.2%Column total 50 50 100Producer accuracy 14.0% 94.0%Overall accuracy 54.0%Tau coefficient 0.080

(b)Reference data (sea truth side scan sonar data)

Satellite imageclassification data Seagrass Sand Row total User accuracy

Seagrass 50 10 60 83.3%Sand 0 40 40 100.0%Column total 50 50 100Producer accuracy 100.0% 80.0%Overall accuracy 90.0%Tau coefficient 0.800

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result, we believe that if Lyzenga’s model still constitutes an excellent starting point

for coastal mapping, some major enhancements are required.

In more general models, such as Preisendorfer’s (1976), the attenuation coefficient

is related to absorption and scattering coefficients. As these two coefficients areexpected to fluctuate from place to place, the assumption made by Lyzenga according

to which the attenuation coefficient would be constant can only be considered as

realistic for really small areas (i.e. areas for which the environment can be thought of

as homogeneous). As our method is based on Lyzenga’s model, this limit is also valid

for this study.

In a literature review conducted in 1998, Mumby et al. (1998) reported that only 4%

of the studies involving remote sensing for mapping coastal areas had used radio-

metric correction for the image analysis processing. We hope that the results of thisnew method will create incentives for future studies to apply radiometric correction

more frequently.

Figure 6. Relation between radiance level and depth according to the bottom type for(a) green and (b) blue bands (Funakoshi bay). For both bands, n ¼ 42 for seagrass andn ¼ 49 for sand.

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Acknowledgements

We thank the staff of the International Coastal Research Center, the Ocean Research

Institute, the University of Tokyo, and the Institut National des Sciences et

Technologies de la Mer who helped us in situ and provided useful advice. We are

also grateful to SEA Corporation and Oyo Corporation employees who were very

helpful with sonar measurements. Finally, we would also like to thank Mr Yoshikazu

Ozeki from Japan Space Imaging Corporation for his cooperation. Our study was

partially supported by a Research Fellowship Grant for Young Scientists from the

Japanese Society for the Promotion of Science.

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Figure 7. Relation between radiance level and depth according to the bottom type for (a)green and (b) blue bands (Mahares). For both bands, n ¼ 99 for seagrass and n ¼ 57 for sand.

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