SPOT shallow water bathymetry of a moderately turbid tidal inlet based on field measurements

Remote Sensing of Environment 81 (2002) 136 – 148 www.elsevier.com/locate/rse

SPOT shallow water bathymetry of a moderately turbid tidal inlet based on field measurements V. Lafona,*, J.M. Froidefonda, F. Lahetb, P. Castainga a

b

DGO, CNRS-UMR 5805 ‘‘EPOC,’’ Universite´ Bordeaux I, Avenue des Faculte´s, Talence Cedex 33405, France Laboratoire Re´gional de Te´le´de´tection, Institut de Recherche pour le De´veloppement (IRD), Cayenne Cedex BP 165-97323, France Received 9 October 2000; received in revised form 30 July 2001; accepted 30 November 2001

Abstract The determination of shallow water depth in high-energy tidal inlets is essential to model and to forecast the navigation channel position or the short-term topographic evolution of beaches. Colour satellite imagery provides, at low cost, complete maps of areas that are difficult to map by traditional hydrographic means due to their size and their rough underwater morphology. In order to calibrate SPOT images to derive bathymetric maps, a simple method applied to shallow waters of a moderately turbid tidal inlet has been carried out. Its development is based on a set of field measurements, including the reflectance of the water and of the bottom sediment, the vertically averaged diffuse attenuation coefficient, and the concentrations of inorganic particles in suspension, of chlorophyll a and pheopigments and of dissolved organic carbon (DOC). From these data, it appears, first, that the water reflectance is directly linked to the depth, and second, that the water reflectance varies slowly with the turbidity in this area for total suspended matter (SM) concentrations lower than 9 mg l
1. The extinction of light with depth has been characterized in the inlet. The relationship obtained is slightly different from that observed in clear waters. The bathymetric models established for the clearest waters do not calculate the depth accurately. In the contrary, reflectance code adapted to Case II water type, calibrated with in situ measurements, allows us to retrieve depth down to 6 m and for total SM concentrations ranging from 0.2 to 9 mg l
1. This relationship has been applied to five SPOT images of the mouth of Arcachon lagoon. The accuracy of the derived map has been assessed by in situ depth measurements. The mean difference between measured depths and computed depths is about 20%. This accuracy is adequate to assess the inlet morphodynamics quantitatively, which is necessary for middle-term to short-term mathematical modeling of the 3D inlet evolution. D 2002 Elsevier Science Inc. All rights reserved. Keywords: Ocean colour; Coastal zone; Bathymetry; Tidal inlet; SPOT

1. Introduction The coastal zone and, particularly, the tidal inlets that link harbors to the sea are attractive economic areas where the building timelessness depends on the coast stability. The morphology of tidal inlets is related to the transport capacities of the swell and of the tidal currents (Davis & Hayes, 1984). When both waves and currents are of high energy, the morphologic evolution of inlets is fast (Oertel, 1972). The lagoon of Arcachon, situated on the southwest coast of France (Fig. 1), is linked to the Atlantic ocean by a large inlet (15  7 km) composed of several channels and sand-

* Corresponding author. Fax: +33-5-56-84-08-48. E-mail addresses: [email protected] (V. Lafon), [email protected] (J.M. Froidefond).

banks emerging at low tide. In a mesotidal context, the strong littoral drift moves southwards these channels and sandbanks by several tens of meters each year and influences the morphology of the coastline (Michel, 1997). To model inlet morphodynamics, in order to forecast the position of the navigation channel, or to plan beach replenishment, it is necessary to obtain accurate topographic maps. Fast evolutions of the coastal zone are generally studied by comparing hydrographic measurements at several time steps (Hicks & Hume, 1997; Michel, 1997). However, hydrographic maps of Arcachon inlet are rare, expensive, incomplete, particularly in the rough shallow waters, and composed of data recorded for several months. Therefore, submarine topographic maps were generated from satellite data. This technique provides instantaneously complete coverage of the study area. Furthermore, spatial maps are adapted to study both the coastline evolution (Chen, Chen,

0034-4257/01/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved. PII: S 0 0 3 4 - 4 2 5 7 ( 0 1 ) 0 0 3 4 0 - 6

V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

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SPOT remotely sensed water reflectances and in situ depth measurements (Lafon et al., 1998). However, this method still requires hydrographic measurements for calibration purposes. Furthermore, as hydrographic data are scarce in the shallow waters, calibration is not valid in the first meter of water. Therefore, this calibration equation has been determined in the field, which allowed us to measure the reflectance of the shallowest waters. Moreover, we evaluated the range of water turbidity in the inlet of Arcachon, and the influence of the water turbidity changes on both reflectance and diffuse attenuation coefficient. This data set was used to run usual optical models and to test the calibration equation obtained in the field. Then, inlet depths are carried out from SPOT images. Hereafter, hydrographic data are used with the aim to validate the model results only.

2. Method

Fig. 1. Location and description of the tidal inlet of Arcachon.

& Chen, 1995) and the shallow water morphology (Irish & Lillycrop, 1997; Lafon, Froidefond, & Castaing, 1998). Airborne photos were soon used as the surface water colour depends on water depth (Duntley, 1963), and photogrammetry still provides morphologic maps where bottom colour and water quality are homogeneous (Stojic, Chandler, Ashmore, & Luce, 1998). Polcyn, Brown, and Sattinger (1970) introduced first the utilization of colour satellite imagery. They determine the water depth as a function of the bottom colour, the deep water radiance, and the diffuse attenuation coefficient of light in the water mass to include the effect of turbidity variations. Based on the single- or quasi-single scattering theory (Gordon, Brown, & Jacobs, 1975), numerous authors developed relationships to determine depth from spatial reflectance (Benny & Dawson, 1993; Bierwirth, Lee, & Burne, 1993; Garlan, 1989; Lee, Carder, Mobley, Steward, & Patch, 1998; Loubersac, Burbam, Lemaire, Chenon, & Varet, 1989; Lyzenga, 1978; Maritorena, 1996). These models are routinely used in the clear Pacific waters. However, they are less adequate in areas where the turbidity is high and variable, but the one proposed by Lee et al. (1998). Furthermore, they are often calibrated with hydrographic measurements (Garlan, 1989) and they become useless when bottom colour, turbidity, and depth change simultaneously (Philpot, 1989). Several years ago, two methods of bathymetry determination have been successfully tested in Arcachon lagoon. The first one is based on the 2D cartography of the water surface on XS3 SPOT images (Prud’homme, Froidefond, & Castaing, 1994). Several coastlines drawn during flood or ebb are necessary to carry out a 3D map. The second method, less expensive, is based on a statistical adjustment between XS1

This work is divided into two parts. From field data, a model of depth determination has been established. Then, this method is applied to five SPOT images. Spatial depths are finally compared to hydrographic measurements to assess the accuracy of spatial maps. Fig. 2 summarizes both measurements and calibration procedures. 2.1. Field measurements Remote sensing reflectance (Rrs) above the seawater is defined as the ratio of the water leaving radiance (Lw) at a given wavelength (l) to the downwelling irradiance (Ed) at (l) (Eq. (1)): Rrs ðlÞ ¼

Lw ðlÞ Ed ðlÞ

ð1Þ

Water leaving radiance, and henceforth water reflectance, varies with depth (Gordon & Brown, 1973), bottom colour (Lyzenga, 1978; Spitzer & Dirks, 1987), and water content (Morel & Prieur, 1977; Sathyendranath & Morel, 1983). This triple dependence is summarized on the following relationship (Lee et al., 1998), dropping wavelength for brevity: h i 1 D B rrs ¼ rrsD 1
e
ðKd þKu Þz þ RBrs e
ðKd þKu Þz p

ð2Þ

where rrs represents the marine reflectance with subscript D for deep water, z is the depth, and RrsB is the reflectance of the bottom that is assumed to be Lambertian. Kd is the vertically averaged diffuse attenuation coefficient for downwelling irradiance. KuD and KuB are the vertically averaged diffuse attenuation coefficients for upwelling radiance measured, respectively, in deep and shallow water according to the following relationship (Eq. (3)): Ku ðlÞ ¼

lnLu1 ðlÞ
lnLu2 ðlÞ z1
z2

ð3Þ

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V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

Fig. 2. Field measurement procedure and depth determination model calibration and validation.

where Lu1 and Lu2 are the upwelling radiances at depth z1 and z2, respectively. As the sandbanks of the inlet and beaches close to the mouth are composed of yellow quartz homogeneous sands (Bouchet, 1994), whose grain size is included between 200 and 400 mm (Pedreros, Howa, & Michel, 1996), the contribution of the bottom to the water reflectance is constant for the whole area. Therefore, we studied in the field (1) the variability of turbidity in the inlet, and (2) the influence of the variations of both depth and turbidity on the resultant reflectance and on vertically averaged diffuse attenuation coefficients. Measurements have been made during spring 1997 and the summer 1998. Optical measurements have been made with a high-resolution spectroradiometer (Spectron SE-590) that records visible (VIS) and near infrared (NIR) light. The spectrometer views in a specific direction and has a field of view of 6. It provides radiance values. Ed and Lw are both necessary to calculate Rrs. To carry out Ed, the downwelling radiance (Ld) has been measured on a standard spectralon plate that has a defined backscattering coefficient (Rsp). As the spectralon plate is Lambertian, we must consider that Ld does not change with the viewing angle, which can be expressed as (Eq. (4)): Ed ¼ p Ld

ð4Þ

Lw is carried out by measuring the radiance a few centimeters above the water surface. However, upwelling light integrates the water leaving radiance and the amount of

skylight reflected by the water surface. Therefore, a few centimeters above the water surface, upwelling radiance is an apparent radiance (Lz), which needs to be corrected as proposed by Whitlock et al. (1981) to obtain in situ reflectance (Ris): Ris ðlÞ ¼ Rsp ðlÞ

Lz ðlÞ
0:02 Lsky ðlÞ Ldsp ðlÞ

ð5Þ

Apparent radiance is measured about 50 cm above the water surface. Lsky is the sky radiance. Measurements have been made following a vertical axis. Lsky is multiplied by 0.02 that is the Fresnel reflection factor for quite nadir view. Ldsp is the measure of the downwelling radiance realized on the spectralon plate. Considering that water leaving radiance is the difference between Lz and the term in Lsky, and that Rsp is a calibration factor, which only takes into account the amount of downwelling light reflected by the spectralon plate, Ris can be expressed by the following equation (Eq. (6)): Ris ðlÞ ¼

Lw ðlÞ Ld ðlÞ

ð6Þ

As Ld is proportional to Ed, in situ reflectance is proportional to remote sensing reflectance (Eq. (7)): Rrs ðlÞ ¼

Ris ðlÞ p

ð7Þ

V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

Finally, Rrs is related to the marine reflectance by the following relationship (Lee et al., 1998) (Eq. (8)): Rrs ðlÞ ¼

0:518rrs ðlÞ 1
1:562rrs ðlÞ

ð8Þ

In situ reflectance is measured from emerged sands (RBis) to deep waters (RD is ). In a first time, the value of Kd was approached by the vertically averaged diffuse attenuation coefficient for radiance, KL. Indeed, media rich in inorganic particulate matter are mainly diffusive between 500 and 600 nm. Therefore, it can be assumed that radiance distribution is nearly uniform, which means that the irradiance attenuation is approximately the same as the radiance attenuation. To compute Ku and KL, Lu and Ld have been measured, respectively, inside the water mass with an optical fiber connected to the sensor (Fig. 2). To estimate water clarity, a Secchi disc was plunged in the water. Simultaneously, water samples were taken in the North Channel, in the South Channel, and close to the Banc d’Arguin, 50 cm below the water surface. Two subsamples were filtered (Whatman GF/F filters). The first one has been used to determine the total amount of particulate matter in the water (weighting the dried filter before and after filtration), and the second one to measure the concentration of chlorophyll a and pheopigments by HPLC (Turner Designed Fluorimeter). A second sample has been taken to obtain DOC concentration. For this purpose, the water has been filtered, then after catalytic oxidation of organic matter, the DOC amount has been obtained by an infrared spectrophotometer (Shimatzu TOC 5000A). 2.2. SPOT data and image processing SPOT scenes are composed of three bands: XS1 (500 – 590 nm), XS2 (610 – 680 nm), and XS3 (790 – 890 nm). Their spatial resolution is 20 m. The scenes were recorded in 1986 (9/02), 1989 (10/04), 1991 (9/08), 1995 (6/28), and 1997 (8/23). These images are characterized by calm swell conditions. Wave breaking never appears in the inlet. Furthermore, in 1986, 1989, 1991, and 1995, images have been recorded nearly at low tide. In these cases, tidal current does not exceed 40 –50 cm s
1 (Cayocca, 1996), and henceforth does not allow suspended load transportation for grain size included between 200 and 400 mm (Reineck & Singh, 1980). Last image (1997) has been recorded 2 1/2 h before high tide. Considering a tidal range of about 3.4 m, flood current speed reaches 1 m s
1 in the inlet. In this case, suspended load transportation over sand banks and in tidal channels can occur, which increases suspended matter concentration. Therefore, depths computations must be checked with greatest cares in this specific case. To apply optical models or empirical relationships to SPOT images, the pixel numerical counts (NC) were transformed into reflectance values comparable to those recorded on the Earth’s surface, according to a two-step method

139

proposed by Viollier, Tanre´, and Deschamp (1980). Reflectance values at the top of the atmosphere (r*) were computed first: r* ¼

pLwi ms Esi

ð9Þ

where i represents SPOT waveband. Lw is obtained by dividing NC by SPOT absolute calibration gain. ms, the cosine of the solar zenith angle, is provided with the image and Es, the solar irradiance at the top of the atmosphere, has been computed with 6S atmospheric correction code (Vermote, Tanre´, Deuze´, Herman, & Morcrette, 1994). From Eq. (9), it appears that reflectance at the top of the atmosphere is proportional to both remote sensing and in situ reflectances. Then, from r*, the target reflectances (r) were derived, according to: r¼

1 ðr*
ratm Þ t

ð10Þ

where t represents the atmospheric transmittance and ratm, the atmospheric reflectance, is obtained by summing aerosol or Mie reflectance (rr), Rayleigh reflectance (rr), and reflectance due to coupling between aerosol and Rayleigh scattering (rar) (Eq. (11)): ratm ¼ ra þ rr þ rar

ð11Þ

On XS2 and XS3 SPOT images, weak reflectance pixels (for instance, deep water pixels) represent the atmospheric reflectance. Rayleigh scattering is computed by 6S, taking into account ozone concentration and air pressure on the Earth’s surface. Then, the magnitude of aerosol contribution is computed using deep water reflectance and Rayleigh reflectance values, assuming the coupling between aerosol and Rayleigh scattering is negligible in XS2 and XS3. Determining aerosol contribution from several wavebands enables to assess the spectral dependence of aerosol scattering, and then to chose an aerosol model appropriate to the image. From XS2 and XS3 SPOT images, it is therefore possible to calculate, respectively, ra2 and ra3. Then, Angstro¨m number (n), which governs the spectral variation of ra, is derived (Gordon & Clark, 1980) (Eq. (12)): n¼


lnðra2 =ra3 Þ lnðl2 =l3 Þ

ð12Þ

Finally, the oceanic version of 6S code has been run with varying atmospheric compositions with aim to obtain realistic values of n, ra2, and ra3. Once the aerosol model has been selected, 6S is run to carry out the transmittance and the atmospheric reflectance from which water remote sensing reflectance is determined using Eq. (10). Considering each image, computed Angstro¨m number and selected aerosol model are indicated in Table 1. Also, Table 1 provides humid sand and deep water reflectances in XS1, XS2, and XS3 wavebands, measured in the field during the campaigns of 1997 and 1998, and deduced from the SPOT

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V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

Table 1 Atmospheric correction of images: computed Angstro¨m number and percentage of aerosol used (O: oceanic, D: dust-like, W: water-soluble) Sand reflectance (%)

Water reflectance (%)

Date

Angstro¨m number

Aerosol model

XS1

XS2

XS3

XS1

XS2

XS3

In situ September 2, 1986 October 4, 1989 September 8, 1991 June 28, 1995 August 23, 1997


1.116
0.23 0.13 0.25 0.99

100% O 100% O 100% O 100% O 20% W, 40% O, 40% D

20.9 ± 6 14.8 14.9 19.3 16.9 17.7

28.5 ± 5.7 20.2 19.3 24.4 19.3 22.8

32.7 ± 5.9 24.3 30.5 25 25.5 25

1.61 ± 0.29 1.2 1.22 1.34 1.69 1.98

0.38 ± 0.04 0.3 0.15 0.3 0.39 0.16

0.09 ± 0.04 0.2
0.02
0.1 0.16
0.01

Humid sand and deep water reflectance are added to demonstrate the validity of the atmospheric correction.

scenes. This comparison validates 6S computations as in situ and computed reflectance values are of the same range. To validate the developed bathymetric method, hydrographic data recorded by the Port Authorities have been used. Regarding the images, hydrographic surveys carried out from February to June 1986, from May to October 1989, from March to May 1991, from March to July 1995, and from February to April 1997 have been used. Hydrographic data representing large flat areas have been selected. Therefore, sand bank sides have not been considered for validation purposes. A geometric correction performed with Idrisi Software (Clarks Laboratories: Worcester, MA) allows us to superimpose the hydrographic chart to the image. The geometric rectification accuracy is about two pixels (40 m).

3. Results 3.1. Water content Total suspended matter (SM), chlorophyll a and pheopigments ( P), and DOC concentrations measured in the field are presented in Table 2. P and DOC variations with time and Table 2 Concentrations in SM, in chlorophyll a + pheopigments ( P), and in DOC measured at various places of the tidal inlet in 1997 and 1998 Date

Location

SM (mg l
1)

June 5, 1997

North Channel North Channel South Channel Banc des Chiens Banc des Chiens South Channel North Channel Banc d’Arguin Banc des Chiens South Channel Banc d’Arguin Banc des Chiens South Channel Banc d’Arguin South Channel South Channel Banc d’Arguin South Channel

7 8.2 7.2 9 1.45 1.15 0.8 0.7 0.9 1.3 0.75 0.9 0.95 0.6 1.35 0.55 0.2 0.5

June 6, 1997 July 27, 1998

July 28, 1998

July 29, 1998

July 30, 1998

July 31, 1998

P (mg l
1)

location are small. Previous DOC concentration measurements showed variations from 0.7 to 5.0 mg l
1 in the inlet (Bonjour & Carruesco, 1986). On the contrary, SM concentrations were 10 times higher during 1997 field trip, regardless of location. Consecutively, the Secchi disc disappeared at a depth of 5 m in 1997 and at 6 m in 1998. SM concentrations measured during the field trips are representative of usual SM concentrations. This classic range has been obtained by compiling the monthly samplings carried out by IFREMER (Institut Franc˛ais de Recherche pour l’Exploitation de la MER) in the inlet between 1989 and 1997 (Lafon, 1999). 3.2. Variations for KL and Ku with water content and depth The vertically averaged diffuse attenuation coefficient for downwelling radiance spectra (KLD) recorded in the South Channel (15 m of depth) in 1997 and 1998 is represented in Fig. 3 by dashed lines. SM concentrations were 8.2 mg l
1 (thick line) and 1.3 mg l
1, respectively. The spectra shape is representative of moderately to fairly turbid waters, according to Jerlov’s (1976) classification. The variation of KLD due to the increase of SM concentration reaches 10% at the wavelengths corresponding to XS1 SPOT waveband, and 17% at the wavelengths corresponding to XS2. The vertically averaged diffuse attenuation coefficient for upwelling radiance measured in deep water KuD varies with SM concentrations also. At low SM concentrations, KuD is, respectively,

DOC (mg l
1)

2.1 1.1 1.4 2.18 1.77

1.1 1.2 1.55

2.95 2.40 2.40 2.41 2.18 3.5 3.17 2.52 2.62 2.59

1.55 1.3

Fig. 3. In situ reflectance (Ris, continuous) and vertically averaged attenuation coefficient for downward radiance (KDL , dashed) spectra recorded, respectively, above and inside North Channel waters. SM concentrations of 8.2 mg l
1 (bold) and 1.3 mg l
1, respectively, have been considered.

V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

0.16 m
1 and 0.28 m
1 at wavelengths corresponding, respectively, to XS1 and XS2. At SM concentrations around 9 mg l
1, KuD, respectively, is 0.2 m
1 and 0.34 m
1 at wavelengths corresponding to XS1 and XS2. The vertically averaged diffuse attenuation coefficient for downwelling radiance spectra has been measured close to the Banc d’Arguin also (KLB) for water depths varying between 2.5 and 5 m and for SM concentration ranging from 0.6 to 9 mg l
1. The results show that KLB is nearly constant and equal to 0.21 m
1 for wavelengths equivalent to XS1 and 0.43 m
1 for wavelengths equivalent to XS2. Considering the same concentration range, KBu is 0.27 m
1 at wavelengths corresponding to XS1 and 0.45 m
1 at wavelengths corresponding to XS2. Vertically averaged diffuse attenuation coefficient values are summarized in Table 3. The sum of Ku and KL typical of shallow and deep waters is written, respectively, as KB and KD. It seems that KB is, respectively, 0.48 m
1 and 0.88 m
1 at wavelengths corresponding to XS1 and XS2 wavebands regardless of SM concentration. On the contrary, K D increases with SM concentration from 0.47 m
1 to 0.52 m
1 at wavelengths corresponding to XS1, and from 0.73 m
1 to 0.97 m
1 at wavelengths corresponding to XS2. Therefore, mean values of KD (respectively, 0.5 m
1 and 0.85 m
1 at wavelengths corresponding to XS1 and XS2 wavebands) are close to KB values. In Eq. (2), the sum B B of KLD and KD u and the sum of KL and Ku can be replaced by the value of an effective attenuation coefficient (K), which is 0.49 m
1 in XS1 and 0.87 m
1 in XS2. From this approximation, Eq. (2) is simplified to the following relation:   1 B Rrs
rrsD e
ðKÞz ð13Þ rrs
rrsD ¼ p Relation (13) can be written for each waveband. Taking the logarithm on both sides of Eq. (13) gives (i specifying waveband number):   1 B D D ð14Þ lnðrrs
rrs Þi ¼ ln Rrs
rrs
Ki z p i As proposed by Bierwirth et al. (1993), Eq. (14) can be summed over N wavebands to obtain an equation useful to determine the depth:   N N X ln p1 RBrs
rrsD i lnðrrs
rrsD Þi X z¼
ð15Þ
N Ki
N Ki i¼1 i¼1 Table 3 Vertically averaged diffuse measured atttenuation coefficient for upwelling (Ku) and downwelling (KL) radiance in shallow water (index B) and in deep water (index D), according to SM concentration and wavelength KB = KBu + KLB (m
1)


1 D KD = KD ) u + KL (m

Variable SM concentration

Low SM concentration

High SM concentration

XS1

XS2

XS1

XS2

XS1

XS2

0.48

0.88

0.47

0.73

0.52

0.97

141

3.3. Variation of Ris with water content and depth 3.3.1. Deep water Reflectance spectra recorded above the South Channel deep waters are compared to KL spectra measured simultaneously (Fig. 3). Ris (l) (continuous line) is obviously linked to KL (l). The shape of the reflectance spectra is typical of a Case II water dominated by organic matter (Sathyendranath & Morel, 1983). The highest reflectances are situated around 560 nm. In the clear shallow waters, the reflectance maximum is included between 500 and 570 nm (Spitzer & Dirks, 1987). The presence of chlorophyll causes a slight reflectance minimum at 670 nm and a minor peak at 685 nm (Morel & Prieur, 1977). Ris increases by 35% with SM concentration at the wavelengths corresponding to XS1, and by 26% in the red wavelengths. The increase of Ris with SM concentration is relatively weak in comparison to the one generally observed (Doxaran, 1999; Han, 1997; Lahet, Ouillon, & Forget, 2000). In the Gironde estuary, where the same reflectance measurement proceeding has been applied (Eq. (5)), Ris (550) reaches, respectively, 1.1% and 6.8% for SM concentrations of 1 and 9.1 mg l
1 (Doxaran, 1999). In the inlet of Arcachon, Ris (550) does not exceed 2% for SM concentration equal to 8.2 mg l
1. Sediments are mostly responsible for diffusion of light in the water and particularly for backscattering of light towards the water surface. The reflectance increases with diffusion in the yellow-green and red wavelengths (Morel & Prieur, 1977). A mathematical relationship proposed by Ivanoff (1975) supposes that the scattering coefficient of suspensions increases with decreasing particle size, and increases with both increasing refractive index and increasing density of particles. The inversion of the ocean colour model proposed by Lahet et al. (2000) was used to compute the refractive index of the particles, mainly quartz, observed in the Arcachon inlet. By implementing in situ SM concentrations and measured reflectances, the model retrieves accurately the reflectance between 400 and 700 nm for a mean refractive index of about 1.13, which is lower than the refractive index of the Gironde’s clays that is equal to 1.179 (Doxaran, 1999). It can be also reasonably assumed that quartz, which has a silt size, is larger and rounder than clay. This includes a weakening of light diffusion (Latimer, 1984). Furthermore, as clays are smaller and lighter than silts, the suspension density is higher in the Gironde than in the inlet of Arcachon. Therefore, Arcachon suspensions diffuse the light slightly, which explains the low reflectance measured in the yellow-green and red wavelengths. Further investigations have to be done to measure accurately both the particle size and their density, and even better, the total area of backscattering cross-section of the particles. 3.3.2. Shallow water The reflectance just above the water surface changes fast with water depth. Spectra recorded in 1997, close to the

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Fig. 4. Reflectance spectra (Ris) of emerged sand (spectrum a), shallow water (spectra b – j), and deep water (spectrum k) obtained close to the Banc du Chien.

Banc du Chien, are represented on Fig. 4. The sediment colour and the turbidity are constant. The shape of the spectra is directly linked to the water depth. The reflectance of emerged sands (spectrum a, Fig. 4) increases with wavelength. Submerged sand spectra (b – k, Fig. 4) clearly point out the absorption of light, and particularly of NIR radiation, by water molecules (Defant, 1961). Between spectra a and b, the reflectance decreases by 71%. At slightly greater water depths (c – d, Fig. 4), the whole infrared spectrum is affected, except around 800 nm. However, the absorption coefficient of water shows a drop of absorption around 800 nm (Huot, De Kruijf, & Delwart, 1996). From Arenz, Lewis, and Saunders (1996) and Han (1997), this maximum depends on the scattering effect of nonorganic particulate matter in suspension. In offshore deep waters, this maximum seems to vary with the chlorophyll concentration (George, 1997a). In this case, the light reflected by the bottom is responsible for the slight increase of the reflectance around 800 nm. This effect disappears below a depth of 0.3 m (e – k, Fig. 4). NIR reflectance is then lower than 0.1%. Therefore, NIR reflectance can be used to accurately find out the limit between emerged and submerged areas. For a depth of 0.1 m, XS3 water reflectance reaches 10%; this limit can be used to determine the interface between submerged and emerged sand. VIS light is least attenuated in the yellow-green wavelengths (500 – 600 nm). The highest reflectances are situated between 560 and 580 nm, which is consistent with previous measurements (Maritorena, 1996; Spitzer & Dirks, 1987). At these wavelengths, the reflectances decrease regularly with depth. Therefore, wavelengths included between 500 and 700 nm (XS1 and XS2) should be adapted to determine the water depth. However, we must take into account that SM, DOC, or P concentration changes affect the reflectances at these wavelengths. In shallow waters, when the bottom is visible, it is particularly difficult to separate the effects of water depth from suspended or dissolved water content in the VIS

wavelengths (Tolk, Han, & Rundquist, 2000). Furthermore, it seems that the influence of water content increases with depth (Estep, 1994; Tassan, 1998). During in situ sampling, P concentrations ranged between 1.4 mg
1 and 3.5 mg
1 (Table 2). This concentration range influences Ris in the yellow-green and red wavelengths slightly (Morel & Prieur, 1977) particularly with SM concentrations lower than 10 mg l
1 (Bukata, Jerome, Koundratyev, & Podzdnyakov, 1995). From 500 to 700 nm, the influence of DOC concentration variations is negligible for concentrations below 2 mg l
1 if the chlorophyll concentrations are in the range of values measured in the inlet (Bukata et al., 1995; Kutzer & Arst, 1994). Thus, DOC concentration variations have a small influence on reflectance values. To assess the impact of SM concentration changes on reflectance, XS1 and XS2 equivalent values of the whole set of in situ records have been plotted (Fig. 5), with white and black marks representing, respectively, XS1 and XS2 values. Triangles and circles represent, respectively, the data recorded in 1997 and 1998. Regarding both wavebands, Ris depends more on the depth

Fig. 5. In situ reflectance (Ris) calculated by averaging in situ spectroradiometric measurements for wavelength varying between 500 and 590 nm (XS1) and between 610 and 680 nm (XS2). White and black marks representing, respectively, XS1 and XS2 reflectances. Circles represent low SM concentration and triangles represent high SM concentration.

V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

143

Fig. 6. Reflectance measured at the Banc d’Arguin just above the sea surface (Ris (XS1)) according to depth (z) (black squares). The curve represents the regression equation between z and Ris, with R2 being the regression coefficient. Insert shows an evaluation of the in situ depth determination relationship. Error on depth determination is about 51 cm. The principal figure shows also the calibration of Relation (2) with in situ reflectance and attenuation coefficient data. White circles represent depth computation considering low SM concentrations. White squares represent depth computation considering high SM concentrations.

changes than on SM concentration changes at least in the first 6 m of water. 3.3.3. In situ relationship between Ris (XS1) and depth in the shallow water From the reflectance data measured in the field, a relationship providing Ris (XS1) as a function of depths is carried out (Fig. 6): z ¼ 16:707e
0:3866Ris ðXSIÞ

ð16Þ 2

This relationship is representative (R =.93) and valid for SM concentrations lower than 9 mg l
1 and for depths lower than 6 m. Using Eq. (16), depths are retrieved with an accuracy of 51 cm (Fig. 6). Relation (2) has been calibrated D with in situ values of rrs , RrsB , KD, and KuB. These results have been added (Fig. 6). Values of KD corresponding to low (white circle) and high (white square) SM concentrations have been tested. The influence of varying vertically

Fig. 7. Comparison of measured depth with computed depth calculated with Relation (15) applied to XS1 waveband and calibrated with in situ shallow water reflectance measurements.

averaged attenuation coefficients is visible in the first meters of water. Therefore, the approximation made on K to simplify Relation (2) and retrieve depth (Relation (15)) may induce errors on depth computation of 40 cm at uppermost in the shallowest water. 3.4. Calibration of usual optical models with in situ measurements 3.4.1. Depth simulation using XS1 waveband Amongst the single-band optical models tested (Benny & Dawson, 1993; Lee et al., 1998; Loubersac et al., 1989), the one developed by Lee et al. is the best adapted to depth determination in the inlet of Arcachon. The results obtained for the calibration of Relation (15) with in situ values of K, rrsD , and RrsB is presented in Fig. 7. It appears that computed depths are slightly underestimated. Depths are retrieved with an accuracy of 59 cm.

Fig. 8. Comparison of measured depth with depth calculated with Relation (15) applied to XS1 and XS2 wavebands and calibrated with in situ shallow water reflectance measurements.

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Table 4 SM concentration measured in the North and South Channels a few days before and after the SPOT images were recorded Date

SM in the North Channel (mg l
1)

SM in the South Channel (mg l
1)

September 29, 1989 October 9, 1989 September 4, 1991 September 11, 1991 June 29, 1995 August 19, 1997 August 27, 1997

5.6 8.9 4.2 4.6 6.2 6 5.8

8.5 7.3 7.9

3.4.2. Depth simulation using and XS1 and XS2 wavebands Depth computation carried out from Eq. (15) calibrated with XS1 and XS2 reflectance values measured in the field is compared to in situ depth measurements on Fig. 8. Depths are always underestimated. Depth computation accuracy is now 51 cm. Therefore, accuracy is significantly increased. 3.5. Application and validation of bathymetric relationships 3.5.1. Complete bathymetric method (1) Geometric and atmospheric corrections are applied to the images. (2) The air – water interface is determined on XS3 SPOT waveband. Pixels with XS3 reflectance higher than 10% represent emerged sands (Fig. 4). Then, this limit is superimposed on the XS1 image to mask the emerged areas. (3) The calibration equation determined in the field (Eq. (16)), together with Relation (15), using either XS1 or both XS1 and XS2 wavebands, has been applied to the emerged zone of the SPOT image recorded in 1997. The zero level represents the water surface. (4) The altitude of the water surface above the reference level of hydrographic charts (the hydrographic zero) is computed with a tidal model (Castaing et al., 1991). For example, on the image recorded in 1997, the water surface is situated at 2.1 m above the reference level. Thus, spatial depths can be compared to hydrographic depths.

Fig. 9. Application of depth computation algorithms to the SPOT image recorded in 1997. Hydrographic depths (measured depth) are compared with spatial depth computed with Relation (15) applied to XS1 waveband (white triangle), computed with Relation (15) applied to XS1 and XS2 wavebands (white squares), and computed with in situ relationship (black circles).

Fig. 10. Comparison of measured depth with computed depth calculated with Relation (15) applied to XS1 waveband and calibrated with in situ reflectance measurements and the recalculated value of the effective attenuation coefficient.

3.5.2. Application and validation Total SM concentrations in the inlet for images recorded in 1989, 1991, 1995, and 1997 are reported on Table 4. They are included in the range of values typical of in situ measurements. Therefore, on one hand, the relationship carried out from field measurements has been directly applied to the SPOT images. On the other hand, Relation (15) has been calibrated with K values of 0.49 m
1 in XS1 and 0.87 m
1 in XS2. Fig. 9 shows the comparison between depth measurement and depth carried out from the image recorded in 1997. Black circles represent the results obtained using in situ relationships; white triangles represent the results obtained using Relation (15) parameterized with XS1 waveband; and white squares represent the results obtained using Relation (15) parameterized with both XS1 and XS2 wavebands. Obviously, Relation (15) enables to compute depths with a greater accuracy, particularly when only XS1 reflectances are taken into account (RMS = 45 cm). Accuracy decreases when using both XS1 and XS2 reflectances (RMS = 66 cm). Regarding the first 2 m of water, RMS is 29 cm considering XS1, and RMS is 28 cm considering XS1 and XS2. Therefore, using both XS1 and XS2 does not improve significantly depth calculations. In situ relationship gives intermediate accuracy (RMS = 50 cm), and leads to slightly underestimate depths below a depth of 3 m, and to slightly overestimate them above a depth of 4 m. Globally, depths are underestimated using optical model, which means that K may be overestimated. K has been retrieved from Eq. (14) calibrated

Fig. 11. Plot of the difference between measured depths and computed depths, | zmes
zcomp|, versus measured depths. The mean depth computation error (RMS) and the relative depth computation error (relative difference) are represented respectively by Lines 1 and 2.

V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

Fig. 12. Spatial bathymetric map of the inlet of Arcachon based on XS1 SPOT image recorded in August 23, 1997. Relation (15) from Lee et al. (1998) has been used to calculate the depth.

with depth measurements. Computed K is 0.44 m
1 more or less 0.07 m
1. Relation (15) used with computed K as value allows us to improve depth determination. In this case, RMS is 36 cm and depths are no longer underestimated (Fig. 10). Plotting the difference between measured depth and com-

145

puted depth versus measured depth shows that the error made on depth computation increases with depth. Therefore, it seems more accurate to calculate a relative error rather than a constant error (RMS) (Fig. 11). Spatial depths computed from XS1 SPOT image recorded in 1997 using Relation (15) (calibrated with a K value of 0.44 m
1) are shown by Fig. 12. The result of the comparison between hydrographic depth and spatial depth, for the images recorded in 1986, 1989, and 1995 (Fig. 13), shows that z is retrieved with a greater accuracy when using Relation (15), but for the image recorded in June 1995. As in that particular case, depths are globally underestimated, calculation of effective attenuation coefficient adapted to 1995 image has been performed. Considering a K value of 0.39 m
1, relative error decreases down to 22%. Using optical model, relative error is 16% in 1986 considering 56 control points, 20% in 1989 considering 109 control points, 36% in 1991 considering 69 control points, 22% in 1995 considering 68 control points, and 10% in 1997 considering 53 control points. Therefore, mean error made on depth computation is about 20%. The best agreement between depth computations and depth measurements is obtained for the image recorded in 1997, and henceforth with the stronger tidal current speeds. Therefore, the amount of sand put in suspension by tidal currents seems to be restricted to water bottom layer, for tidal currents lower than 1 m s
1. However, combining waves, wave breaking, and strong currents may induce transportation of larger suspended load in the water mass. Moreover, field data represent discrete measurements at a precise location, whereas depth computation based on SPOT images are

Fig. 13. Comparison of hydrographic depths (measured depth) with spatial depths (computed depth) calculated with the in situ calibration relationship (black squares) and with Relation (15) (white triangles) for the SPOT images recorded in 1986, 1989, 1991, and 1995. 1:1 correlation line and estimation of relative errors have been added.

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averaged values for a pixel area (400 m2). Furthermore, the accuracy of the geometric correction is about one pixel. Finally, we must consider that sandbank movements occurred in the shallow waters during the time elapsed between the record of the SPOT image and the corresponding record of the hydrographic map. This last parameter is mainly responsible for the large error made on the calibration of the image recorded in 1991 because the water colour is homogeneous.

4. Discussion and conclusion A simple bathymetric methodology, based on Hydrolight radiative transfer code calibrated with in situ bottom reflectance and effective attenuation coefficient measurements, has been developed to determine the depth from SPOT images and carry out topographic maps of the tidal inlet of Arcachon. In a first time, atmospheric and geometric corrections are applied to the images. XS3 image is used to determine the limit between emerged and submerged area. Then, depth is carried out from XS1 SPOT image of the submerged places. Computing depth with both XS1 and XS2 wavebands may increase the accuracy of depth determination within the first meter of water, which is not clearly demonstrated in this study as very few control points are situated in very shallow waters. Finally, hydrographic surveys are used to validate depth computations. The mean error on the depth determination is 20%. We demonstrated that the bathymetric equation used provides realistic results down to 6 m below the water surface and for SM concentration ranging from 0.2 to about 9 mg l
1. Moreover, preliminary tests also show that this spatial bathymetric method can be successfully applied to beaches outside the inlet. Besides, to explain the weak influence of varying SM concentrations on XS1 reflectance, it would be interesting to obtain field values of the absorption and scattering coefficients of the water together with its content. Then, the shallow water colour models could be better adapted to the inlet of Arcachon, by taking into account the properties of silts for instance. Finally, the optical model used has been calibrated with in situ measurements of the bottom reflectance, of the vertically averaged attenuation coefficient for upwelling radiance (Ku), and also with measurements of the vertically averaged attenuation coefficient for downwelling radiance (KL), instead of the vertically averaged attenuation coefficient for downwelling irradiance (Kd). The sum of Ku and KL provides an effective attenuation coefficient varying with wavelength, with water depth and with SM concentration. A mean effective attenuation coefficient (K) was calculated, which varies with the waveband only. Using K as value to calibrate the depth determination algorithm gives accurate results, which means that mean value of the sum of the vertically averaged attenuation coefficients integrates the difference between the vertically averaged attenuation coefficient for downwelling radiance and the vertically averaged attenuation coefficient for

downwelling irradiance. However, the value of K may be artificially corrected by the instrumentation used to measure the attenuation coefficients: the optic fiber has a field of view larger than 6. Therefore, Ku is too large and Kd (approached by KL) too small, and henceforth, to calculate more accurately depth from space, it would be interesting to obtain in situ values of Ku and Kd with suitable instruments. As the sandbank sides are steep, the error made on depth computation does not affect the measurement of sandbanks or channel movements. However, this error affects, respectively, area and volume computation on a range of about 10 –11% (Lafon, 1999). Therefore, to assess the shallow water morphology in the Arcachon inlet and its variation with time, the accuracy obtained by the SPOT calibration method proposed is correct and allows us to put in evidence several mechanisms of evolution of the inlet (Lafon, 1999; Lafon, Froidefond, & Castaing, 2000). In the future, with the better spatial resolution of multiband SPOT 5 images (10  10 m), the movement of smaller sandbanks at a shorter time scale during the high-energy winter storms will be studied. These data will be valuable for morphodynamic models (Cayocca, 1996). These results prove that SPOT images are well adopted to map the submarine morphology of the tidal inlet of Arcachon down to a depth of 6 m when the water is clear. The same procedure may be used in other moderately turbid coastal areas with success, if wave breaking is not observed, and if bottom colour and attenuation coefficients are evaluated either in the field or from space (Lyzenga, 1978). For greater water depths, other remote sensing bathymetric methods should be applied: radar imagery, laser, or Compact Airborne Spectrographic Imager (CASI). Radar imagery provides bathymetric information even in turbid waters (Vogelzang, 1993) when colour satellite imagery is no longer applicable. However, the accurate localization of submarine sandbanks based on radar imagery is difficult to obtain (Vogelzang, Wensik, Calkoen, & Van der Krooij, 1997). CASI performances, already demonstrated in clear lake waters (George, 1997b) as well as in turbid waters (Bagheri, Stein, & Dios, 1998), would certainly be useful as they permit to choose the right wavelength to calculate regression between depth and reflectance. Finally, to apply the method to greater water depths, airborne lasers seems to give good results down to two to three times the Secchi depth at 532 nm (Lyllicrop & Estep, 1995).

Notation DOC Ed Es i Ku KuB

dissolved organic carbon downwelling irradiance solar irradiance at the top of the atmosphere waveband index vertically averaged diffuse attenuation coefficient for upwelling radiance vertically averaged diffuse attenuation coefficient for upwelling radiance measured in shallow water

V. Lafon et al. / Remote Sensing of Environment 81 (2002) 136–148

KuD

vertically averaged diffuse attenuation coefficient for upwelling radiance measured in deep water Ld downwelling radiance Lsky sky radiance Lu upwelling radiance Ldsp downwelling radiance measured on a spectralon plate Lw water leaving radiance Lz apparent radiance ratm atmospheric reflectance rr Rayleigh reflectance n Angstro¨m number NC SPOT numerical count NIR next infrared P chlorophyll a + pheopigments Ris in situ reflectance rrs marine reflectance Rrs remote sensing reflectance rrsd marine reflectance of deep water RrsB bottom reflectance Rsp backscattering coefficient of the standard SM total suspended matter t atmosphere transmittance VIS visible l wavelength ms zenith solar angle r target reflectance r* reflectance at the top of the atmosphere ra Mie reflectance ma cosine of the zenith solar angle

Acknowledgments This work has been funded by the Service Maritime et de Gironde (SMGN) directed by M. Vedrine. M. Albin-Amiot (Direction Re´gionale de l’Environmental) assisted greatly the project by acting as the head of the project’s communication network. IFREMER and SEPANSO provided the MES data, and the Port Autonome de Bordeaux the hydrographic data. The authors wish to thank the Laboratoire de Biologie Marine (LOB Arcachon) that helped us with field data collection, particularly Mr. Ollivier, our sailorman and Ms. Lemaire, who guided us in the laboratory and realized the chlorophyll concentration measurements. We also thank Dr. Etcheber (DGO) who determined DOC concentrations. Most importantly, we thank Dr. Labourg (LOB), Dr. Bouchet (IFREMER Arcachon), and M. Boubert (SEPANSO) whose knowledge was really valuable in the field. This is a DGO-EPOC contribution no. 1416.

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