INT. J. REMOTE SENSING, VOL.
25,
NO.
10–20 7–8, 1517–1525
APRIL,
2004,
Single-wavelength algorithms for in situ or remote sensing estimation of mean pigment concentration L. SOKOLETSKY*{, Z. DUBINSKY{, M. SHOSHANY{§ and N. STAMBLER{ {Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, 52900, Israel {Department of Geography, Bar-Ilan University, Ramat-Gan 52900, Israel
Abstract. The bio-optical relationships between inherent and apparent optical properties, and between optical properties and phytoplankton pigment concentration (C) averaged in a layer (DZ), were derived from analysis of data collected during the period 1996–1998 in the Gulf of Aqaba (Eilat). Parametrization of these relationships was based on radiative transfer theory, Gershun’s equation, minimization of model errors by least-square fitting, and on known optical models relating underwater remote sensed reflectance (Rrsw) with the ratio of backscattering (bb) to vertical attenuation coefficient (Kd) [or to absorption coefficient (a)]. These relationships explain a frequently used form of remote sensing algorithms for C estimation using ratio of water-leaving radiances measured at two or more wavelengths (l). In this study, the possibility of using for this purpose a single wavelength in the blue range (l~443 nm) within the framework of in situ and remote sensing algorithms for Case 1 waters was assessed.
1.
Introduction Estimation of phytoplankton in marine and freshwater bodies is an important goal in ecosystem research and monitoring, development of global climate change scenarios, and in environmental quality control. In recent years, due to the availability of new airborne video cameras and satellite sensors such as Sea viewing Wide Field of view Sensor (SeaWiFS) or Moderate Resolution Imaging Spectroradiometer (MODIS), new Remote Sensing (RS) algorithms, based on data from such sensors, were developed, allowing estimation of phytoplankton pigment concentration (C) (e.g. Gordon et al. 1988, Morel 1988, Hoge 1994, Morel and Gentili 1996, Gitelson et al. 1996, O’Reilly et al. 1998, Avard et al. 2000, Gross et al. 2000). These algorithms are typically based on four radiation characterizations: (a) spectral water-leaving radiance Lw(l); or (b) Lw(l) normalized to atmospheric transmittance: Lwn (l)~Lw(l)/Ta(l); or (c) Lw(l) normalized to incoming solar irradiance, that is, remote sensing reflectance Rrs~Lw(l)/Ed(l, 0z); or (d) ratio of *Present address: Israel Oceanographic and Limnological Research, Yigal Allon Kinneret Limnological Laboratory, PO Box 447, Migdal 14950, Israel; e-mail:
[email protected] §Present address: Department of Transportation and GeoInformation Engineering, Faculty of Civil and Environmental Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel. An updated version of a paper originally presented at Oceans from Space ‘Venice 2000’ Symposium, Venice, Italy, 9–13 October 2000. International Journal of Remote Sensing ISSN 0143-1161 print/ISSN 1366-5901 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/01431160310001592535
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upwelling radiance to downwelling irradiance just below the sea surface, that is underwater remote-sensed reflectance Rrsw(l)~Lu(l, 02)/Ed(l, 02). Empirical data for the verification of these algorithms were collected from basin-specific seasonal measurements or from generalization of regional datasets. In both these cases, great caution in utilization of existing algorithms for other water bodies and seasons is necessary. The aim of this study was to simplify these models by utilizing a single wavelength band, which could potentially contribute to their geographical generalization. The spectral band we selected was the 443 nm, which was found as the most suitable for this purpose (Gordon et al. 1988, Morel 1988, Tilzer et al. 1994, Bricaud et al. 1995, Waters 1995, Stramska and Dickey 1998, Berwald et al. 1998, Antoine and Morel 1999). Assessing a single wavelength band modification of existing models with an extensive dataset derived for the Gulf of Aqaba (Eilat), is expected to expand our understanding of the relationships between phytoplankton concentration and backscattered solar radiation under different conditions due to its varying circulation patterns. Yet another important aspect of this study is the potential application of cheaper, single wavelength band sensors for the estimation of phytoplankton distributions. 2.
Study area According to most ‘chlorophyllous definitions’ of the trophic state of water bodies (e.g. Shifrin 1988, Morel and Berthon 1989, Dera 1995, Antoine et al. 1996, Vinogradov et al. 1997), waters of the Gulf of Aqaba exhibit meso-oligotrophic rather than oligotrophic-type characteristics. For example, according to the classification of Dera (1995), the trophic state of the northern part of the Gulf varies from oligotrophic type O3 during the May–October stratified period to mesotrophic type M1 during the November–April mixing period. The primary productivity measured in the Gulf of Aqaba (Levanon-Spanier et al. 1979, Lindell and Post 1995, Iluz 1997) also confirms the seasonal meso-oligotrophicity of the Gulf. To date, only a limited number of phytoplankton concentration studies have been performed in the Gulf of Aqaba, and these have been limited to single dates and locations (Levanon-Spanier et al. 1979, Dubinsky et al. 1990, Stambler 1992, Lindell and Post 1995, Iluz 1997, Badran and Foster 1998). Since phytoplankton is a sensitive reporter of the trophic state of any water body and that, in turn, affects the sensitive coral reefs of the Gulf, there is an urgent necessity for the development of new bio-optical and RS algorithms for that region. An extensive oceanographic survey consisting of about 70 cruises was conducted in the Gulf between January 1996 and December 1998. The chosen site for the measurement of optical, hydrophysical and other characteristics was station A1 (29‡28’ N, 34‡56’ E), situated at the northern tip of the Gulf about 5 km off the shore. Bottom depth at this station is approximately 700 m, and it was determined to be a good representative of the offshore waters in the Gulf (Lindell and Post 1995). 3.
Data acquisition and pre-processing Phytoplankton concentrations and radiometer measurements were obtained for depths Z from 0 to ca 100 m. The determinations of C(Z) concentration in the water column profile were performed by the standard fluorometric method (HolmHansen et al. 1965, Schanz et al. 1997) followed by linear or polynomial smoothing
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(maximal order of polynomials is three). The spectra of the downwelling irradiance Ed(l, Z), and upwelling radiance Lu(l, Z) were acquired with a submersible Profiling Reflectance Radiometer (Model PRR-600 from Biospherical Instruments Ltd) at seven spectral bands (412, 443, 490, 510, 555, 665, and 694 nm) with 10 nm bandwidths. All spectra were measured every several centimetres and in two directions (down and up). For more exact assessment of the instantaneous downwelling irradiance just below the sea surface Ed(l, 02), additional meteorological data of incoming global solar irradiance at Eilat in 1990–1998 and estimates obtained from the regional algorithm at l~443 nm (Sokoletsky et al. 2000), were also used. In order to reduce the effects of noise in the data, the third-order polynomials were used (henceforth, the symbol l will be omitted): ð1Þ ln½Ed ðZ Þ~{ a0 za1 Zza2 Z 2 za3 Z3 , where coefficients a0, a1, a2, and a3 were determined by the nonlinear least-square method (NLSM). Equation (1) was found to be highly significant (in most cases the coefficient of determination R2 was greater than 0.99). The vertical attenuation coefficient Kd(Z) for downwelling irradiance, which is determined by L ln½Ed ðZ Þ LZ was then derived from equations (1) and (2) as follows: Kd ðZ Þ~{
Kd ðZ Þ~a1 z2a2 Zz3a3 Z 2 :
ð2Þ
ð3Þ
Kd(Z) can then be utilized for the parametrization of the Kd2C bio-optical model, as developed in the following section. In situ (Kd2C) bio-optical model The dependence of diffuse attenuation coefficient (Kd, in m21) on depth (Z, in m), pigment concentration (C, in mg m23) and the downwelling average cosine of underwater light field (m¯d) at the same depth can be described as follows: 4.
Kd ðZ, C, md Þ%
aðC Þ aw, dis zaa C ba % ð4Þ m¯ ðZ, C, m¯ d Þ m¯ ? zðm¯ 0 {¯m? Þ exp½{bðC ÞZ ð1{¯ms Þ=¯md ðZ, C, mw Þ
where a and b are the absorption and scattering coefficients (in m21), respectively; m¯0 and m¯‘ are the average cosine of the underwater light field just below the sea surface, and at a large (asymptotic) depth, respectively; m¯s is the average cosine of single scattering; mw is the cosine of solar zenith angle just below the sea surface. Equation (4) may be considered a form of Gershun’s equation (Gershun 1939), if it is assumed that KE, the vertical attenuation coefficient for net irradiance Ed2Eu (Eu is upwelling irradiance), may be approximated by Kd. Mathematical proof of this statement (under the condition that reflectance coefficient R~Eu/Edvv1) can be found in McCormic (1995). The expression for m¯(Z) is a generalized form of radiative transfer models developed by Berwald et al (1995) and Kirk (1999). Several additional assumptions were also made. 1. Power dependence for absorption coefficient vs. pigment concentration is: a~aw, dis zaa C ba ,
ð5Þ
where aw, dis is absorption coefficient for water and dissolved matter. 2. The ratio of particle backscattering (bbp~bb2bbw) to particle scattering
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L. Sokoletsky et al. (bp~b2bw) (Ulloa et al. 1994, Sathyendranath et al. 2001) is: bbp ~0:0078{0:0042 log10 C: bp
ð6Þ
3. Power dependence for backscattering coefficient vs. pigment concentration (e.g. Gordon et al. 1988, Sathyendranath and Platt 1988) is: bb ~bbw zabb C bbb ,
ð7Þ
21
where bbw (~0.00239 m ) is the water backscattering coefficient. 4. Exponential dependence for average cosine of single scattering vs. bb/b, is expressed by equation (8), which was derived by approximation of the data from Kirk (1991, table 1), is: ms ~0:975 expð{2:594bb =bÞ:
ð8Þ
5. The relationship between m¯ d, m¯ and R (e.g. Aas 1987, Morel and Gentili 1991) is: md ~
mð1z2RÞ : 1{R
ð9Þ
6. Relationships for m¯ 0 and m¯ ‘ vs. the b/a ratio were taken from Berwald et al. (1995), and for R vs. the cosine of solar zenith angle in air (ma), bb/a and bbw/ bb ratios—from Morel and Gentili (1991). The five parameters necessary for parametrization of the above model were found by NLSM, based on 30 samples for which phytoplankton concentration and radiance data were derived from interpolation to zero depth (table 1). Testing of the above model for Kd at l~443 nm shows that error increases from 8.4% just below surface to 37.6% at a depth of 100 m. Transfer from particular depth Z to layer DZ may be obtained by the numerical integration of the last right-hand part of equation (4). In situ/remote sensing (Rrsw2C) bio-optical model This model was obtained by using the approximation of Kirk (1994) for underwater remotely sensed reflectance Rrsw (in sr21): 5.
ð10Þ
Rrsw ~0:083bb =a,
where the optical parameters a and bb are defined from equations (5), (7) and table 1. 6.
Simplified bio-optical models Although the above-presented in situ and RS bio-optical models give the possibility to solve the direct problem (estimation of Kd and Rrsw from mw, C and Z), the solution of the inverse problem (estimation of C from above-mentioned Table 1.
aw,
dis
0.0186
Values of inherent optical property parameters, estimated at l~443 nm. aa
ba
abb
bbb
0.0297
0.788
0.00175
0.253
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parameters) may, in some cases, lead to absurd results. With the aim of removal of such situations and simplification of the solution of the inverse problem, the following simplified models were developed and used (at l~443 nm, 0¡C¡1 mg m23 and 0¡Z¡100 m): Kd ðZ Þ~Kw, dis ðZ ÞzaK ðZÞ½CðZÞbK ,
ð11Þ
where Kw, dis(Z) is downwelling attenuation coefficient for water and dissolved matter: aw, dis Kw, dis ðZ Þ~ 1zk1 Zzk2 Z 2 , ð12Þ m¯ 0 aK(Z) is a positive coefficient: aK ðZ Þ~
aa 1za1 Zza2 Z2 , m¯ 0
Rrsw ~0:015{0:0241C0 z0:0290ðC0 Þ2 {0:0125ðC0 Þ3 ,
ð13Þ ð14Þ
2
where C0 is sub-surface (i.e. at Z~0 ) pigment concentration; bK was assumed equal to ba~0.788, and m¯0 was computed as m0 ~mwmw0 :
ð15Þ
Here m¯w0 is sub-surface average cosine at mw~1 (i.e. at zenith Sun). The values of parameters for this simplified in situ model were estimated from comparison with the main in situ model by NLSM (table 2). 7.
Relationships between pigment concentrations averaged in select layers For the aim of estimation of C averaged in a layer DZ from RS observations, linear regressions between C0 and layer-averaged concentrations vCDZw were established empirically from field measurements of pigment concentrations, following the calculation of ‘photosynthetically active radiation’ [EPAR(Z)]. This characteristic was computed from Ed(l, Z) for the wavelength range of 400–700 nm without preliminary fitting. The concentration of ‘penetration layer’ [i.e. layer extending from sea-surface to depth Zp, in which EPAR(02) is reduced to 1/e ~0:895C0 z0:061 R2 ~0:972 : ð16Þ Analogous expressions for the concentration averaged for the layer Z~0 to 50 m and for the concentration averaged from the surface to the ‘euphotic depth’ [i.e. depth Ze, at which EPAR(02) is reduced to 0.01 from its sub-surface value] were also derived: vC50 > ~0:687C0 z0:172 R2 ~0:856 , ð17Þ vCe > ~0:474C0 z0:290 R2 ~0:725 : ð18Þ The range of variation in Zp and Ze in the Gulf, according to our measurements, Table 2. m¯w0 0.888
Values of parameters for simplified in situ model.
k1 (m21)
k2 (m21)
a1 (m21)
a2 (m21)
21.5161024
1.5161025
0.0104
24.8561025
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was from 13.6 and 73.7 m, respectively, on 4 March 1996, up to 28.9 and 114.2 m, respectively, on 15 June 1998. Thus, equations (11)–(18) create a basis for development of the singlewavelength algorithm for estimation of phytoplankton pigment concentration in different layers. In situ/RS estimation of layer-averaged pigment concentrations The in situ and RS versions of bio-optical relationships presented above allowed development of an algorithm for estimation of layer-averaged pigment concentrations from the measured quantities of mwKd(443) or Rrsw(443). It would be reasonable to begin from estimation of the sub-surface pigment concentration C0, and, then, to use equations (16)–(18) to estimate vCDZw. An approximate solution for in situ estimated C0 was found by inversion of equation (11) taking into consideration equations (12), (13) and (15) at Z~02 as follows: ( 0, if mw Kd ð0{ Þv0:0209 m{1 C0 ~ ð19Þ 74:8½mw Kd ð0{ Þ{0:02091:270 , otherwise:
8.
Analogously, an analytical solution for C0 estimated by our RS algorithm was found by inversion of equation (14) as follows: C0 ~4:440{653:1Rrsw z24061ðRrsw Þ2 :
ð20Þ
Comparisons between modelled (by both algorithms) and measured euphotic layer-averaged pigment concentrations (table 3) demonstrate sufficiently high and approximately the same accuracy of in situ and RS algorithms. The values of pigment concentration predicted by both algorithms during the mixing period (November–April) were in good agreement with those of the observed data, giving a higher correlation and a slope closer to unity than during the stratified period (May–October) (figure 1). However, it should be noted that rms. errors estimated for both periods and by both algorithms were close to one another (from 20.0% to 24.9%) and exceeded the level of accuracy specified by the National Aeronautics and Space Administration (NASA) for satellite chlorophyll retrieval (35%). 9.
Conclusions Both in situ and remotely sensed bio-optical models for the Gulf of Aqaba were developed and verified for the blue range of the spectrum. The results outlined in
Table 3.
Comparison of the statistical verification of in situ and remote sensing (RS) algorithms for averaged (in euphotic layer) pigment concentration.
Algorithm
Slope
Intercept
NRMSE (%)
R2
p
In situ RS
0.731 0.989
0.116 0.017
20.0 24.9
0.555 0.559
2.3661026 2.0561026
NRMSE is normalized (to average values of the ‘true’ optical property) rms. error, R2 is a coefficient of determination and p is a significance level.
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Figure 1. Comparison between modelled and measured euphotic layer-averaged pigment concentrations: (a) during mixing period; (b) during stratified period. The points corresponding to in situ and remote sensing (RS) algorithms are shown by closed squares and open triangles, respectively. The regression lines are also shown.
this paper indicate that a single wavelength band centred on 443 nm may be utilized for C estimation even in a strongly stratified water column. It is worth noting that single-wavelength algorithms, possibly, can be preferable in some situations to widely used two- and multi-wavelength algorithms. For example, the authors’ analysis of the spectral radiance data of Wang and Gordon (1994) showed that, for C values in the range of 0.1–1 mg m23, the single-wavelength (at l~443 nm) RS algorithm yields accuracy better by 5.5% than the RS algorithm, based on the Lwn(443)/Lwn(550) ratio. Nevertheless, the conclusions here concerning the feasibility, and even advantage, of single-wavelength usage have only preliminary validity. It is necessary to carry out additional experimental (particularly, in different sites of the Gulf) and theoretical investigations for further verification of this conclusion, examination of its generality, as well as with the aim of refinement of the presented one-wavelength algorithms.
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Acknowledgments This study was part of the PhD study of the first author and was conducted within the framework of the ‘Red-Sea Program’, a joint German, Egyptian, Palestinian and Israeli programme funded by the German Ministry of Science, Technology and Education (BMBF). The authors thank J. T. O. Kirk (Kirk Marine Optics), A. Morel (Universite Pierre et Marie Curie), R. H. Stavn (University of North Carolina), K. J. Voss (University of Miami) and N. J. McCormick (University of Washington) for valuable suggestions and comments offered. References AAS, E., 1987, Two stream irradiance model for deep waters. Applied Optics, 26, 2096–2101. ANTOINE, D., ANDRE´, J.-M., and MOREL, A., 1996, Oceanic primary production 2. Estimation at global scale from satellite (coastal zone color scanner) chlorophyll. Global Biogeochemical Cycles, 10, 57–69. ANTOINE, D., and MOREL, A., 1999, A multiple scattering algorithm for atmospheric correction of remotely sensed ocean colour (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones. Journal of Geophysical Research, 20, 1875–1916. AVARD, M. M., SCHIEBE, F. R., and EVERITT, J. H., 2000, A potential tool for estimating chlorophyll concentration in lakes and reservoirs. Journal of Freshwater Ecology, 15, 125–133. BADRAN, M. I., and FOSTER, P., 1998, Environmental quality of the Jordanian coastal waters of the Gulf of Aqaba, Red Sea. Aquatic Ecosystem Health and Management, 1, 75–89. BERWALD, J., STRAMSKI, D., MOBLEY, C. D., and KIEFER, D. A., 1995, Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field. Limnology and Oceanography, 40, 1347–1357. BERWALD, J., STRAMSKI, D., MOBLEY, C. D., and KIEFER, D. A., 1998, Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean. Limnology and Oceanography, 43, 564–576. BRICAUD, A., BABIN, M., MOREL, A., and CLAUSTRE, H., 1995, Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: analysis and parameterization. Journal of Geophysical Research, 100, 13 321–13 332. DERA, J., 1995, Underwater irradiance as a factor affecting primary production. Dissertation and monographs (Sopot: Institute of Oceanology of the Polish Academy of Sciences), 7, 112. DUBINSKY, Z., STAMBLER, N., BEN-ZION, M., MCCLOSKEY, L., MUSCATINE, L., and FALKOWSKI, P. G., 1990, The effect of external nutrient resources on the optical properties and photosynthetic efficiency of Stylophora pistillata. Proceedings of the Royal Society of London B, 239, 231–246. GERSHUN, A. A., 1939, The light field. Journal of Mathematical Physics, 18, 51–151. GITELSON, A., KARNIELI, A., GOLDMAN, N., YACOBI, Y. Z., and MAYO, M., 1996, Chlorophyll estimation in the Southeastern Mediterranean using CZCS images: adaptation of an algorithm and its validation. Journal of Marine Systems, 9, 283–290. GORDON, H. R., BROWN, O. B., EVANS, R. H., BROWN, J. W., SMITH, R. C., BAKER, K. S., and CLARK, D. K., 1988, A semi-analytic model of ocean color. Journal of Geophysical Research, 93, 10 909–10 924. GROSS, L., THIRIA, S., FROUIN, R., and MITCHELL, B. G., 2000, Artificial neural networks for modeling the transfer function between marine reflectance and phytoplankton pigment concentration. Journal of Geophysical Research, 105, 3483–3495. HOGE, F. E., 1994, Asymmetrical spectral curvature algorithms: oceanic-constituents sensitivities. Applied Optics, 33, 7764–7769. HOLM-HANSEN, O., LORENZEN, C. J., HOLMES, R. W., and STRICKLAND, J. D. H., 1965, Fluorometric determination of chlorophyll. Journal du Conseil Permanent International Pour L’Exploration de la Mer, 30, 3–15. ILUZ, D., 1997, The light field, phytoplankton pigmentation and productivity in the Gulf of Elat (in Hebrew) (PhD Thesis, Bar-Ilan University, Ramat-Gan, Israel).
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