There has been considerable success1,2 in optical re-mote sensing of chlorophyll a in case 1 waters wherehe variation of optical properties ~absorption andcattering! is dominated by phytoplankton and asso-iated material, and some consensus is emergingith regard to appropriate algorithms. In contrast,
hlorophyll a retrieval in case 2 waters, where theptical properties of inorganic suspended matter andolored dissolved organic matter ~CDOM! must also
K. G. Ruddick [email protected]! is with the Manage-ment Unit of the North Sea Mathematical Models ~MUMM!, 100Gulledelle, B-1200 Brussels, Belgium. H. J. Gons is with theNetherlands Institute of Ecology, Centre for Limnology, Ri-jksstraatweg 6, Nieuwersluis, P.O. Box 1299, 3600 BG Maarssen,The Netherlands. When this research was performed, M. Rijke-boer was with the Institute for Environmental Studies, Free Uni-versity of Amsterdam, De Boelelaan 1115, 1081 HV Amsterdam,The Netherlands. She is now with The Netherlands Institute ofEcology, P.O. Box 1299, 3600 BG Maarssen, The Netherlands. G.Tilstone was with the Universite Libre de Bruxelles, Ecologie desSystemes Aquatiques, Campus de la Plaine, CP221, B-1050 Brus-sels, Belgium. He is now with the Plymouth Marine Laboratory,The Hoe, Plymouth PL1 3DH, England.
Received 17 August 2000; revised manuscript received 20 Feb-ruary 2001.
e considered, is still a matter of intense researchactivity, and few convincing examples are available ofsatellite-derived chlorophyll a concentrations forsuch waters. However, the demand for detailedmonitoring of chlorophyll a concentrations in case 2waters is high because of the need to manage inlandand coastal eutrophication4,5 and because of the im-portance of estuarine and coastal phytoplankton foratmospheric carbon dioxide6 and hence possible cli-mate change.
Because of the additional independent optically ac-tive constituents in case 2 waters the blue-green two-band ratio algorithms popular for case 1 waters arenot appropriate and alternative approaches must besought. In the case of Belgian coastal waters Fig. 1illustrates the difficulties involved. For this samplein the 400–500-nm spectral range the absorptionfrom tripton ~particulate matter after removal of phy-toplankton pigments! is generally greater than phy-toplankton absorption, and the total particulateabsorption coefficient shows an exponentially de-creasing form for the 400–570-nm range, typical oftripton ~detrital! absorption. Although there are de-partures from this detrital form at 440 and 470 nmassociated with phytoplankton pigments, these sig-nals are small. Considering that a satellite-basedsensor sees only the effect of the total absorptioncoefficient ~particulate plus dissolved matter plus
ure water!, it is clearly important to be able to dis-
20 July 2001 y Vol. 40, No. 21 y APPLIED OPTICS 3575
tr
swps
twsfdgpf
3
tinguish phytoplankton-related features at least inthe total particulate absorption spectrum. In thecase illustrated in Fig. 1, decomposition of anysatellite-derived total absorption coefficient into com-ponents arising from phytoplankton and other mate-rial will clearly be difficult without use of the 670-nmchlorophyll a absorption feature. This is the focus ofhis paper, although alternative approaches for chlo-ophyll a retrieval exist in which fluorescence7 or
combined absorption and backscatter from phyto-plankton is also considered phenomena to be ex-ploited.
Because of the greater number of independent op-tically active constituents, a number of multibandalgorithms have been developed for case 2 waters.8–12
In such algorithms a system of equations for a num-ber of bands ~possibly all bands available from a givensensor! is inverted to yield a solution set for typicallytwo or three optically active constituents, e.g., totalsuspended matter concentration, chlorophyll a con-centration, and CDOM absorption at a referencewavelength. Alternatively, algorithms can be devel-oped to determine only chlorophyll a concentration.For such an approach, provided the water is turbidenough to produce a measurable signal in the near-infrared ~NIR!, the chlorophyll a absorption featurenear 670 nm ~Fig. 1! is particularly attractive sincethis part of the spectrum minimizes interference fromtripton and CDOM absorption. A chlorophyll a re-trieval algorithm for case 2 water was developed andtested for airborne imagery,13 based on the ratio ofreflectances at 676 and 706 nm, and an approach inwhich similar wavelengths are used, in combinationwith backscatter estimated from reflectance at athird NIR wavelength, has been used to retrieve chlo-rophyll a successfully from above-water radiancemeasurements for a wide range of coastal and inlandwaters.14 Similarly in another study15 an empiricalrelationship between the ratio of reflectances at 670and 705 nm and chlorophyll a concentration wasfound for both natural water and in an experimentwith cultured algae.
In this study a similar two-band redyNIR isadopted. However, instead of using an algorithmwith two fixed bands, as is the case for nearly all
Fig. 1. Example of an absorption spectrum for Belgian near-shorecoastal waters for total particulates ~upper, thick solid curve! andits components arising from tripton ~lower, thin solid curve! andphytoplankton ~dashed curve!.
576 APPLIED OPTICS y Vol. 40, No. 21 y 20 July 2001
conventional algorithms, the wavelength of the sec-ond band, away from the chlorophyll a absorptionfeature, is allowed to vary. This extra degree of free-dom allows adaptive optimization of the algorithm toreduce errors in chlorophyll a retrieval associatedwith imperfect atmospheric correction.
In this paper the theoretical background to thisadaptive two-band approach to chlorophyll a re-trieval is described. Particular attention is paid tothe effect of errors in reflectance measurements be-cause, although often neglected, such an error anal-ysis is vital16 to ensuring that resources are notwasted chasing an ultimately impossible goal. Themethod is then tested by using a data set of spectralreflectances and chlorophyll a concentrations mea-ured in Dutch inland waters and in Belgian coastalaters. Finally, perspectives are discussed for ap-lication of the method to future hyperspectralatellite-based sensors.
2. Theory
A. Steps for Chlorophyll a Retrieval
The estimation of chlorophyll a concentration fromsatellite measurements of upwelling spectral radi-ance by using an analytical approach can typically beaccomplished in four steps:
~1! Atmospheric correction consists of calculatinghe atmospheric effects to yield above-water up-elling radiance ~i.e., water-leaving radiance plus
unlight and skylight reflected at the air–sea inter-ace! and downwelling irradiance from at-sensor ra-iance. This step is far from easy and couldenerate considerable errors. However, significantrogress has been made in modeling atmospheric ef-ects,17,18 including consideration of turbid water ef-
fects on the NIR range used for correction ofscattering from aerosols,19–23 and fairly reliable up-welling radiances can now be derived from satellitesensors.
~2! Air–sea interface correction consists of calcu-lating subsurface irradiance reflectance from theabove-water upwelling radiance and downwelling ir-radiance by removing the reflection of sunlight andskylight at the air–sea interface, accounting fortransmission and refraction of light through the in-terface and for the ratio of radiance to irradiance.This step is relatively simple, although there is un-certainty regarding the angular distribution of up-welling radiance.24
~3! Bio-optical modeling consists of estimating thephytoplankton absorption coefficient at a designatedwavelength from subsurface irradiance reflectance.This step seems to represent the greatest obstacle atpresent to chlorophyll a retrieval in case 2 waters andis the focus of this study.
~4! Finally, conversion of the phytoplankton ab-sorption coefficient into chlorophyll a concentrationcan introduce significant errors in chlorophyll a re-trieval inasmuch as the chlorophyll-specific phyto-plankton absorption coefficient can vary as a function
iocp
tb
ner
cl
w
l
29
s
fl
fi
~rafi
u
wiwttsmp
of a number of factors, including phytoplankton spe-cies composition and the trophic state.25 Moreoverthis conversion factor depends on the precise mean-ing of the phytoplankton absorption coefficient and ofthe measurement method used for chlorophyll a con-centration ~pigment extraction and analysis!. Ann-depth analysis of such matters is beyond the scopef this study. In this study this step is effectivelyombined with bio-optical modeling to obtain chloro-hyll a directly from the bio-optical model.
B. Description of General Two-Band RedyNear-InfraredAlgorithm
As a basis for this study we used the well-establishedfamily of models26 that expresses subsurface irradi-ance reflectance R as a function of the total absorp-ion coefficient a and the total backscatter coefficientb:
R~l! 5 fbb~l!
a~l! 1 bb~l!, (1)
where l is the wavelength and f is an empirical factor,which depends on the incident light field and thevolume-scattering function of the water. Althoughconsiderable variation in the numerical value of f hasbeen reported,27 over limited spectral ranges thewavelength dependence of f is limited and in thisstudy is considered negligible. Note that similar ex-pressions exist for remote-sensing reflectance,28 al-though with a different numerical value anddependence on solar zenith angle for f. As seen inEq. ~24!, this empirical factor disappears from the
ew adaptive algorithm described here, which is thusqually applicable to subsurface irradiance oremote-sensing reflectances.
Two wavelengths are used to deduce chlorophyll aoncentration from reflectance. The first wave-ength l1 is located within the region of the red chlo-
rophyll a absorption peak, and the secondavelength l2 is located within the 700–740-nm
range. The following assumptions14 with regard toinherent optical properties are used in the theoreticaldevelopment of this model:
~1! The total absorption coefficient at l1 is dominatedby absorption from pure water aw1 and phytoplanktonpigments aphy1 with negligible contributions fromCDOM and tripton:
a~l1! 5 aw1 1 aphy1. (2)
~2! The total absorption coefficient at wavelength2 is dominated by absorption from pure water aw2
alone, and contributions from phytoplankton pig-ments, CDOM, and tripton can be neglected:
a~l2! 5 aw2. (3)
~3! The backscatter coefficient is assumed to beindependent of wavelength over the limited redyNIRpectral range considered here:
bb~l1! 5 bb~l2! 5 bb0. (4)
Thus, when Eqs. ~1!–~4! are used, the ratio g of re-ectances at l2 and l1 denoted by R2 and R1 can be
expressed as
g 5R2
R15
aw1 1 aphy1 1 bb0
aw2 1 bb0. (5)
This can easily be inverted to give
aphy1 5 g~aw2 1 bb0! 2 aw1 2 bb0. (6)
Then, supposing that the chlorophyll a specific phy-toplankton absorption coefficient at l1, aphy1*, as de-
ned by
aphy1* 5aphy1
C(7)
is known, the chlorophyll a concentration C can besimply found from
C 5aphy1
aphy1*5
1aphy1*
@g~aw2 1 bb0! 2 aw1 2 bb0#. (8)
With the choices of l1 5 672 nm and l2 5 704 nm, Eq.8! is exactly equivalent to Eq. ~5! of Ref. 14, which iseferred to as G99, although in Eq. ~6! of that papern additional empirical calibration as exponent of thenal term 2bb in Eq. ~8! is introduced.An important and well-known advantage of this
type of algorithm is that, by taking a ratio of reflec-tances, the problems associated with the evaluationof f have been removed. However, an estimation ofbb is still required for evaluation of Eq. ~8!. This isperformed in G99 by use of a third wavelength, fur-ther into the NIR ~776 nm!, and inversion of Eq. ~1! by
se of an estimate of f based on an empirical relationinvolving the average cosine of downward irradi-ance.30 Thus
bb0 5aw3R3
f 2 R3. (9)
This procedure exposes the algorithm to somedegree to errors associated with the calculationof f. A second more important weakness of Eq. ~8!,
hen applied to satellite-derived reflectance data,s that the estimation of chlorophyll a concentrationill be affected by wavelength-independent reflec-
ance errors through the ratio g. The purpose ofhis study is to analyze the two-band algorithm’sensitivity to reflectance errors and hence deter-ine the optimal choice of wavelengths for chloro-
hyll a retrieval.
20 July 2001 y Vol. 40, No. 21 y APPLIED OPTICS 3577
Isfcia
t
e
ε t ε
C
rtc2
p
T
s
3
C. Theoretical Analysis of Reflectance Errors
An imperfect removal of aerosol-path radiance inthe case of satellite measurements and air–sea in-terface correction for all above-water measure-ments will give an offset error to R, which canbesignificant but is spectrally fairly flat. Thus, de-noting the measurement error as Rε and the true~error-free! reflectance as Rt, the measured reflec-tance Rm is given by
R1m 5 R1
t 1 R1ε, (10)
R2m 5 R2
t 1 R2ε, (11)
R3m 5 R3
t 1 R3ε. (12)
n this section our purpose is to estimate the effect ofuch reflectance errors on the chlorophyll a retrievedrom Eq. ~8!. Thus the reflectance ratio, backscatteroefficient, and retrieved chlorophyll a concentrationn the presence of reflectance measurement errorsre defined by setting ~R1, R2, R3! 5 ~R1
m, R2m, R3
m!in Eqs. ~5!, ~8!, and ~9!:
gm 5R2
m
R1m , (13)
bb0m 5
aw3R3m
f 2 R3m , (14)
Cm 51
aphy1*@gm~aw2 1 bb0
m! 2 aw1 2 bb0m#, (15)
and similar expressions ~with superscript m replacedby the superscript t! for the true ~error-free! reflec-ance ratio gt, the backscatter coefficient bb0
t, and thechlorophyll a concentration Ct are defined by setting~R1, R2, R3! 5 ~R1
t, R2t, R3
t!. Then the error in thestimation of reflectance ratio gε, the backscatter co-
efficient error bb0ε, the chlorophyll a retrieval error
Cε, as defined by the difference between the mea-sured and the error-free estimations, can be evalu-ated to first order as follows:
bb0ε 5 bb0
m 2 bb0t
5aw3~R3
t 1 R3ε!
f 2 ~R3t 1 R3
ε!2
aw3R3t
f 2 R3t
5aw3R3
t
f 2 R3t F 1 1 R3
εyR3t
1 2 R3εy~ f 2 R3
t!2 1G
5 bb0t R3
ε
R3t
f~ f 2 R3
t!1 OSRε
RtD2
, (16)
gε 5 gm 2 gt
5R2
m
R1m 2
R2t
R1t 5
R2t 1
R1t
R2ε
R1t 1 R1
ε 2R2
t
R1t
578 APPLIED OPTICS y Vol. 40, No. 21 y 20 July 2001
51
R1t S R2 2 g R1
1 1 R1εyR1
tD5
R2ε 2 gtR1
ε
R1t 1 OSRε
RtD2
, (17)
ε 5 Cm 2 Ct
51
aphy1*$gm~aw2 1 bb0
m! 2 gt~aw2 1 bb0t! 2 bb0
m
1 bb0t%
51
aphy1*$gεaw2 1 gmbb0
m 2 gtbb0t 2 bb0
ε%
51
aphy1*$gε~aw2 1 bb0
t! 1 ~gt 2 1!bb0ε% 1 O SRε
RtD2
51
aphy1*HR2
ε 2 gtR1ε
R1t ~aw2 1 bb0
t!
1 ~gt 2 1!bb0t R3
ε
R3t
f~ f 2 R3
t!J 1 OSRε
RtD2
51
aphy1*f bb0
tHR2ε 2 gtR1
ε
R1tR2
t
1 ~gt 2 1!R3
ε
R3t~ f 2 R3
t!J 1 OSRε
RtD2
. (18)
Equation ~18! for the error in chlorophyll a retrievalhas a number of important implications for the choiceof wavelengths l1 and l2. Considering the first fac-tor, it can be seen that l1 should be chosen to maxi-mize aphy1*. ~This rather obvious condition isimportant enough to fix l1.! Also, as noted in a pre-vious study,13 choosing l2 so that R2 is as large aspossible, while keeping l1 and l2 as close as possiblespectrally, is preferred. However, one can achieve amore effective reduction of error by considering theprobable spectral correlation of reflectance errors.Two types of reflectance error are considered here:
~a! Reflectance errors arising from imperfect atmo-spheric correction ~especially removal of aerosol-pathadiance! are strongly correlated spectrally and overhe narrow redyNIR range considered here can beonsidered as spectrally fairly flat ~see Table 1 of Ref.1!. Thus, substituting
R1ε 5 R2
ε 5 R3ε 5 Rε (19)
into Eq. ~18! gives to first order ~dropping the t su-erscript from the notation!
Cε 51
aphy1*f bb0~1 2 g!H 1
R1 R22
1R3~ f 2 R3!
JRε. (20)
hus, when l2 is chosen as the wavelength whereR1 5 R2 and thus g 5 1, the consequent error inchlorophyll a retrieval is exactly zero, Cε 5 0, i.e., foruch a choice of l2 spectrally flat reflectance errors will
c
aw
A
bd
tagS~
tr
ao
f
generate absolutely no error in the chlorophyll a con-entration.
~b! Reflectance errors associated with sensor noisere typically uncorrelated in the spectral sense andill vary in time. Thus the error term Cε is best
estimated by taking the least favorable case whereR1
ε and R2ε are of opposite sign and R3
ε has the samesign as R1
ε or R2ε, depending on whether g is less
than or greater than one. In this case Eq. ~18! givesto first order in RεyR
uCεu 51
aphy1*f bb0HuR2
εu 1 guR1εu
R1 R2
1 ug 2 1uuR3
εuR3~ f 2 R3!
J . (21)
lthough in Eq. ~21! the obvious requirement is sug-gested that all three bands be chosen for wavelengthsat which relative noise-equivalent reflectance RεyR islow, such considerations are usually specified in thesensor design31 and, in general, will have little effecton the design of algorithms. In this case of spec-trally uncorrelated error, as seen below, the absoluteerror in chlorophyll a retrieval Cε is strongly depen-dent on backscatter ~high backscatter is favorable!ut almost independent of C itself ~the only depen-ence is by R1!, and thus the relative error CεyC is
expected to be greatest for low C.
D. New Adaptive Two-Band Algorithm
The preceding analysis motivates development of anew adaptive two-band chlorophyll a retrieval algo-rithm. Taking advantage of the hyperspectral re-flectance data that will be available on futuresatellite sensors @e.g., the technology-proving com-pact high-resolution Imaging Spectrometer ~CHRIS!o be launched in 2001# and is already available forirborne sensors @e.g., the Compact Airborne Spectro-raphic Imager ~CASI!, the Environmental Probeystem ~EPSA!, and the Airborne Prism Experiment
APEX!#, it is possible to set wavelength l2 for eachinput spectrum individually. The new algorithm de-veloped here makes the choice l2 5 l2
c, where l2c is
the critical wavelength, found by use of a simplesearch algorithm, for which
R~l2c! 5 R1. (22)
This is illustrated in Fig. 2. With such a choice, g 51, and defining the residual pure water as absorptioncoefficient
aw9 5 aw2 2 aw1, (23)
Eq. ~8! reduces to
C 5 aw9yaphy1*. (24)
This can be understood simply by taking into consid-eration that, if the reflectances at two wavelengthsare equal, and it is assumed that the backscattercoefficients are equal, the total absorption coefficientsare equal at the two wavelengths. Thus, using as-
sumptions ~2! and ~3!, the phytoplankton absorptioncoefficient at l1 is simply equal to the difference inpure-water absorption coefficients and one can calcu-late the chlorophyll a concentration by dividing bythe specific phytoplankton absorption coefficient.This new algorithm, referred to as Chlorophyll a re-trieval using an adaptive two-band algorithm~CRAT!, shares the advantages of the more conven-ional fixed two-band redyNIR reflectance ratio algo-ithms but with two important extra properties:
~1! Equation ~24! for chlorophyll a retrieval re-quires no estimation of the backscatter coefficient orthe reflectance scaling factor f. Moreover, with thispproach chlorophyll a retrieval is even independentf the underlying form @Eq. ~1!# assumed for reflec-
tance as the function of a and bb0 because for otherforms such as the simpler3 R 5 fbb0ya or a morecomplex second-26 or higher-order expansion in termsof bb0y~a 1 bb0!, the same reasoning applies, leadingto Eq. ~24!. Similarly, use of remote-sensing reflec-tances in the selection of l2
c by Eq. ~22! gives exactlythe same result since the equality of subsurface irra-diance reflectances implies the equality of remote-sensing reflectances given only the assumption of thewavelength independence of the empirical scalingfactor f over this narrow spectral range for both pa-rameters.
~2! As illustrated in Fig. 2, any spectrally flat errorthat offsets the measured reflectance will have noinfluence on wavelength l2 and hence no influence onchlorophyll a retrieval.
This algorithm is represented graphically in Fig. 3,which shows the residual pure-water absorption co-efficient as a function of wavelength as well as thecorresponding chlorophyll a concentration accordingto Eq. ~24!. Thus, for a range of possible retrieval
Fig. 2. CRAT algorithm for a sample reflectance spectrum in case2 water. A constant offset of the reflectance spectrum produces nodifference in the critical wavelength l2
c used by CRAT and hencerom Eq. ~24! no difference in the retrieved chlorophyll a concen-
tration. The first band with a wavelength greater than 672 nm isshown for the medium resolution imaging spectrometer ~MERIS!and the moderate resolution imaging spectrometer ~MODIS! sen-sors for subsequent comparison with the CRAT approach.
20 July 2001 y Vol. 40, No. 21 y APPLIED OPTICS 3579
m
peCi
t
cc
u
wsp
tEbtrr~r
i
Fcfe
a
tw
f
t
3
wavelengths given by 704 nm # l2 # 740 nm ~avoid-ing the 740–760-nm range because of the tempera-ture dependence of the pure-water absorptioncoefficient32!, the corresponding CRAT chlorophyll aretrieval range is given by 12.0 mg m23 # C # 117.6
g m23. If higher chlorophyll a concentrations areto be retrieved ~and suitable reflectance data areavailable!, the same concept could be applied also tothe wavelength range for l2 $ 825 nm ~see Fig. 3!
rovided absorption of bacteriochlorophylls can bexcluded. For lower chlorophyll a concentrationsRAT is, however, less appropriate because the crit-
cal wavelength l2c, if it exists, will lie within the
range 672 nm # l2 # 704 nm and the assumptionhat aw2 is not affected by phytoplankton absorption
is no longer valid. Although a correction term couldbe envisaged, for example, replacing the denominatorof Eq. ~24! by aphy1* 2 aphy2*, where aphy2* is thehlorophyll-specific phytoplankton absorption coeffi-ient at l2, such an approach may be hazardous if
aphy2* is poorly known or if the sensor bandwidth issignificant. Thus, in this study, we performed chlo-rophyll a retrieval for l2
c # 704 nm by reverting tothe fixed two-band algorithm @Eq. ~8!# with l2 5 704nm and with bb0 estimated from a third wavelength,l3 5 776 nm. In a similar way, for l2
c $ 740 nm thealgorithm reverts to the fixed two-band algorithm@Eq. ~8!# with l2 5 740 nm and bb0 estimated from athird wavelength, l3 5 776 nm.
The performance of this new algorithm and theassociated fixed-band algorithms are considered inSection 3 where both numerically simulated reflec-tance data and reflectance spectra measured from aship are used.
3. Numerical Simulations
A. Simulation Methods
The effect of both types of reflectance error discussedin Section 2 for chlorophyll a retrieval when Eq. ~8! is
sed can be illustrated by a model simulation,
Fig. 3. Residual pure-water absorption coefficient aw9 tabulatedrom the data of Buiteveld et al.34 ~solid curve! and of Palmer and
Williams41 ~dotted curve! and the CRAT chlorophyll a concentra-ion for the corresponding critical wavelength l2
c, where parame-ters aw1 5 0.415 m21 and aphy1* 5 0.018 m2 mg21 are used.
580 APPLIED OPTICS y Vol. 40, No. 21 y 20 July 2001
hereby a simple forward model is used to generateubsurface irradiance reflectances for specified inputairs of bb0 and C. These reflectances are then per-
turbed by a reflectance error of atmospheric correc-tion and sensor noise types, respectively, and theresulting measured reflectances are inverted to giveretrieved chlorophyll a. In the forward model, thereflectance model @Eq. ~1!# is used with the assump-ions that the inherent optical properties conform toqs. ~2!–~4! and that phytoplankton absorption cane represented in the form of Eq. ~7!. The reflec-ance errors are added to forward model generatedeflectances as in Eqs. ~10!–~12!, and the resultingeflectance ratio and backscatter coefficient from Eqs.13! and ~14! are input to Eq. ~8! to give the resultingetrieved chlorophyll a. Typical parameters14,30 of
f 5 0.275 and aphy1* 5 0.018 m2 mg21 were used withinput backscatter coefficients, bb0 5 0.1 m21 andbb0 5 1.0 m21, and input chlorophyll a concentrationsranging from low ~C 5 1.0 mg m23! to high ~C 5 215mg m23! to cover conditions likely to be encounteredn coastal and inland waters. For bb0 5 0.1 m21 only
C , 100.0 mg m23 is shown because the backscatterfrom phytoplankton and phytoplankton-derived trip-ton33 will render this backscatter coefficient unreal-istic at higher concentrations. To illustrate how theerror properties vary with choice of wavelength, sim-ulations have been performed with a 672:704-nm al-gorithm, as in G99 ~and similar to the 665:705-nmbands available from MERIS!, and with a 667:748-nm algorithm ~corresponding to MODIS bands!.
or describing error behavior it is sufficient here toonsider a central wavelength approach with a delta-unction sensor response. Pure-water absorption co-fficients are taken from Ref. 34, giving ~aw1, aw2! 5
~667 nm, 748 nm!. In all cases backscatter is esti-mated from l3 5 776 nm where aw 5 2.71 m21.
For atmospheric-correction-type errors both posi-ive and negative near-white errors are simulatedith Rε, which are supposed to vary linearly from
R1ε 5 60.010 to R3
ε 5 60.008 ~chosen from experi-ence and theoretical estimates for Belgian coastalwaters!. For sensor-noise-type errors the valuesR1
ε 5 R3ε 5 0.0005 and R2
ε 5 20.0005 were used~typical of the MERIS specification35!.
B. Simulation Results
The results of simulations of the performance of Eq.~8! for atmospheric-correction-type errors and forsensor-noise-type errors are shown in Figs. 4 and 5,respectively.
Figure 4 shows that atmospheric-correction-typeerrors of the magnitude considered will cause notice-able chlorophyll a retrieval errors for the conven-tional fixed two-band algorithms. The greatesterrors occur in conditions of low backscatter, becauseCε is inversely proportional to the backscatter coeffi-cient through the reflectances appearing in Eq. ~20!.Results for the 667:748-nm algorithm were similar tothe 672:704-nm algorithm for the high backscatter
nsa4kef
z
s1
ttgS
wti
d
b
b
sR
w
0
coefficient ~since reflectance errors are then less sig-ificant compared with the total signal! and are nothown. However, for lower backscatter a consider-ble difference is found and a key implication of Fig.is that for each pair of wavelengths used in this
ind of two-band reflectance-ratio algorithm therexists a critical value of chlorophyll a concentrationor which spectrally flat reflectance errors produce a
Fig. 4. Simulated effect on chlorophyll a retrieval when using Eq.~8! of atmospheric-correction-type reflectance errors. For the 672:704-nm simulations are shown R1
ε 5 0.010, R3ε 5 0.008 ~filled
markers! and R1ε 5 20.010, R3
ε 5 20.008 ~open markers! withb0 5 0.1 m21 ~circles! and 1.0 m21 ~squares!, and for the 667:
748-nm algorithm the simulation R1ε 5 0.010, R3
ε 5 0.008 withb0 5 0.1 m21 ~triangles! is shown.
Fig. 5. Simulated effect on chlorophyll a retrieval in Eq. ~8! ofensor-noise-type reflectance errors: R1
ε 5 R3ε 5 0.0005 and
2ε 5 20.0005 for the 672:704-nm algorithm with bb0 5 0.1 m21
~circles! and 1.0 m21 ~squares! and for the 667:748-nm algorithmith bb0 5 0.1 m21 ~triangles!, and 1.0 m21 ~diamonds!.
ero chlorophyll a retrieval error. In Fig. 4 this isshown by the intersection point of the curves for dif-ferent backscattering with the perfect retrieval ~dot-ted! line, as seen most clearly in the 667:748-nmalgorithm. This occurs when g 5 1, which corre-ponds to a critical chlorophyll a concentration of C 51.9 mgym3 for the 672:704-nm wavelength pair and
C 5 128.4 mgym3 for the 667:748-nm algorithm. Afirst conclusion from this is that if the target chloro-phyll a concentration range is from 1 to 100 mgym3,he 672:704-nm choice is preferred to the pair withhe second wavelength farther into the NIR as re-ards resistance to spectrally flat reflectance errors.econd, it is clear that this critical chlorophyll a con-
centration is a simple function of wavelength, and theintersection point in Fig. 4 will slide along the perfectretrieval line when l2 is varied. This observationmotivated development of the new adaptive two-bandchlorophyll a algorithm @Eq. ~24!# whereby the second
avelength is chosen independently for each spec-rum considered such that the retrieved chlorophyll as equal to the critical chlorophyll a value.
Figure 5 shows that sensor-noise-type errors of themagnitude considered will cause considerable chloro-phyll a retrieval errors in clear water but correspond-ingly lower errors for more turbid waters because ofthe inverse proportionality of Cε to the backscattercoefficient. The 667:748-nm wavelength pair againproduces larger errors compared with the 672:704-nm pair because the lower reflectance R2 is pro-portionally more greatly affected by the absolutemagnitude of the reflectance error.
The same simulations have been performed for theCRAT algorithm. For the atmospheric-correction-type errors ~Fig. 6! the CRAT algorithm gives, byesign, a very low error for the chlorophyll a concen-
Fig. 6. Simulated effect on chlorophyll a retrieval of atmospheric-correction-type reflectance errors for the CRAT algorithm for R1
ε 5.010, R3
ε 5 0.008 ~filled markers! and R1ε 5 20.010, R3
ε 520.008 ~open markers! and with bb0 5 0.1 m21 ~circles! and 1.0m21 ~squares!.
20 July 2001 y Vol. 40, No. 21 y APPLIED OPTICS 3581
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trations within the range of application of Eq. ~24!, i.e.,or which l2
c can be found in the 704–740-nm range.For lower chlorophyll a concentrations results aredentical to the fixed 672-nm:704-nm algorithm,hereas for higher chlorophyll a concentrations theerformance is similar to the two-band 667:748-nmlgorithm ~which is preferable to 672:704 nm for suchery high concentrations!. For the sensor-noise-typerrors the performance throughout is similar to the72:704-nm algorithm shown in Fig. 5 and is thereforeot shown again. For low backscatter conditions theeflectance throughout the redyNIR range is of theame order as the sensor noise, and chlorophyll a re-
trieval with any algorithm is subject to large errors.
C. Field Observations—Method
The new algorithm has been tested with data fromthe IJssel Lagoon ~Dutch inland water! already pre-sented in G99 ~114 samples! and from two cruises inBelgian coastal waters ~28 samples! by the researchessel Belgica on 15–17 April 1998 and 17–19 April000. The coastal water cruises were carried outuring blooms of Phaeocystis globosa, although some
diatoms were also present.Near-surface water samples were taken and ana-
lyzed for chlorophyll a concentration, after removal ofphaeopigments, by the Dutch standard method NEN6520 ~spectrophotometric analysis after pigment ex-traction with hot ethanol!.36 For comparison, in Bel-gian coastal waters a second set of chlorophyll ameasurements was made by using the method ofLorenzen.37 The rms of the difference and of therelative difference between these two data sets ~20values! were 3.6 mg m23 and 30.2%, respectively.For coherence with the IJssel Lagoon data set onlythe data where the Dutch standard method was usedare presented here.
Simultaneously with the water samples, radiancespectra were collected above water with a PR-650SpectraColorimeter ~manufactured by Photo Re-search! as described more fully in Ref. 14. Subsur-face irradiance reflectance is calculated from a set offour measurements ~upwelling radiance from the wa-ter, sky radiance, and upwelling radiance from anexposed reference Lambertian plaque and upwellingradiance from the same plaque but shaded from di-rect sunlight!. To assess temporal fluctuations aris-ing from surface waves and illumination conditions,three spectral scans were made for each set of mea-surements. Patchy clouds during both coastal watercruises caused highly variable illumination condi-tions at many stations. The average of the threescans was used for subsequent chlorophyll a re-trieval. The reflectance spectra were then processedwith the CRAT algorithm.
D. Field Observation Results
The results of the comparison between chlorophyll aoncentration measured in situ from water samplesgainst concentration deduced from above-water ra-iance measurements are presented in Fig. 7. Cal-bration of the phytoplankton absorption coefficient
582 APPLIED OPTICS y Vol. 40, No. 21 y 20 July 2001
retrieved with the CRAT algorithm against the insitu chlorophyll a concentration led to the calibrationconstants of aphy1* 5 0.0198 m2 mg21 and aphy1* 50.0205 m2 mg21 for the Belgian coastal water and theIJssel lagoon data sets, respectively. These valuesare surprisingly close.
Figure 7 shows that the method is promising forremote sensing of chlorophyll a concentration inthese waters. The absolute and relative rms errorsin chlorophyll a retrieval were 4.5 mg m23 and 35%or the Belgian coastal water data and 12.7 mg m23
and 39% for the IJssel lagoon data. In general,greater scatter is seen for lower concentrations,where CRAT reverts to a fixed two-band algorithm.This conforms to the results of the theoretical erroranalysis.
Such algorithm accuracy is similar to that of thefixed-wavelength algorithm described in Refs. 14 and38, and until hyperspectral satellite data becomeavailable the advantages of the adaptive approach inlimiting the effect of atmospheric correction errorswill remain largely theoretical. However, forshipborne-radiance measurements near-white errorscan be expected to result from imperfect air–sea in-terface correction. Thus, tests were made by appli-cation of the CRAT algorithm to each of the tripletspectra measured at the high chlorophyll a Belgiancoastal water stations. In nine of eleven cases therange of the three chlorophyll a estimates wassmaller for CRAT than for the fixed 672:704-nm al-gorithm. The main differences between the threemeasurements being in the sky-radiance reflectionerror rather than in the composition of the waterbeing observed suggests that CRAT is less sensitiveto such errors, although we note that the sky-radiance reflection error for this data set seems not tobe a significant source of chlorophyll a retrieval er-or.38
For comparison, we made further tests on theIJssel lagoon data set by using the eutrophic waterscomponent of the MODIS semianalytical chloro-phyll a algorithm defined in Eq. ~12! of Ref. 28.
Fig. 7. Comparison of chlorophyll a concentration derived fromhipborne radiance measurements by the CRAT algorithm againstater sample measurements. Circles, data for the IJssel Lagoon;
riangles, data for Belgian coastal waters.
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Results were poor, with little correlation betweenmeasured and retrieved chlorophyll a and a relativems error of more than 100%, which is not surpris-ng since such algorithms are not designed to workor such extreme case 2 waters.
4. Discussion
For case 2 waters with strong absorption from triptonor CDOM the main hope for retrieval of chlorophyll aconcentration from satellite-based optical sensors liesin exploiting the signal provided by the chlorophyll ared absorption peak near 670 nm. Two-band algo-rithms based on a ratio of reflectances near 672 and704 nm have already proved successful for highlyturbid coastal and inland waters. A theoreticalanalysis of how errors in reflectance measurementsaffect chlorophyll a retrievals has been made in thisstudy for a two-band redyNIR reflectance-ratio algo-rithm with a general choice of wavelengths. Thisanalysis provides a number of important conclusions:
~a! Errors are greatest in conditions of low back-scatter. In contrast to algorithms in which blue-green spectral bands are used, where nonalgaeparticulate absorption is highly detrimental, partic-ulate backscatter, whether of organic or inorganicorigin, improves redyNIR chlorophyll a retrieval byincreasing the available signal-to-noise ratio ~Fig.4.11 of Ref. 39!.
~b! The absolute errors in chlorophyll a retrievalcaused by spectrally uncorrelated reflectance mea-surement errors, e.g., resulting from sensor noise, areonly weakly dependent on chlorophyll a concentra-tion itself, and hence the relative error CεyC becomesmost significant at low ~e.g., C , 10 mgym3! chloro-phyll a levels.
~c! For reflectance errors that are spectrally flatver the redyNIR range, as is approximately so forhe important case of imperfect atmospheric correc-ion, the effect on chlorophyll a retrieval dependstrongly on the choice of wavelength. Thus a 672:04-nm algorithm performs best in this respect foredium ~C ; 10 mgym3! concentrations, whereas for
he wider-spaced MODIS bands ~667 nm:748 nm!ood performance is achieved only at very high con-entrations ~C ; 100 mgym3!.
Conclusion ~c! has led to development of a com-pletely new type of algorithm, whereby the second,higher wavelength used for retrieval is chosen dis-tinctly for each spectrum to be processed. Thus,when this second wavelength is chosen so that reflec-tance there is equal to the reflectance at the firstchlorophyll a absorption wavelength, the resultingretrieval becomes entirely insensitive to spectrallyflat reflectance errors, giving optimal performance fora wide range of concentrations. A second advantageis that for such a choice of wavelengths chlorophyll aretrieval becomes completely independent of back-scatter retrieval, as noted in a previous study,40 andndependent of any empirical scaling factor depend-
ing on illumination conditions and bidirectional re-flectance effects.
Tests in which in situ measurements of above-ater radiances and near-surface chlorophyll a con-
entration are used in difficult conditions ~highripton and CDOM absorption, highly variable illu-ination! show that this new algorithm is promising.s suggested by the theoretical error analyses, re-ults are best for medium-high concentrations ~C .
10 mgym3!. Because it is these higher concentra-ions that are of most interest for marine managersoncerned with eutrophication issues, the algorithmhould prove particularly useful once satellite-basedensors with sufficient spectral resolution becomevailable, e.g., CHRIS and follow-on missions.It is interesting to compare the present approach to
hlorophyll a retrieval with the discussion of bandsensitivity in Ref. 16. The criterion for choice of l1used here is similar in both studies and is related tooptimizing sensitivity to phytoplankton absorption asexpressed by maximization of 2]R1y]C. However,in that paper l2 is chosen to take advantage of phy-toplankton backscatter by maximization of ]R2y]C
here bb0 is expressed as a function of C as well asincluding backscatter from inorganic particles. Anincrease in C thus has a combined effect on the ratiog by increased absorption at l1 and increased back-scatter at l2. However, with such an approach re-trieval of chlorophyll a ~not described explicitly inthat reference! is then coupled to retrieval of a back-scatter coefficient ~or a related quantity such as totalsuspended matter or inorganic suspended matter!and requires knowledge of the chlorophyll-specificphytoplankton-backscatter coefficient. We avoidedthese two problems by targeting only the absorptionproperties of phytoplankton. Moreover in thepresent study not just spectrally uncorrelated reflec-tance errors are considered, but also atmospheric-correction-type errors are considered, whose effectcan be significantly reduced by exploitation of the factthat such errors are spectrally rather flat over theredyNIR range considered.
The rather simple formulation of the new algo-rithm, defined by Eqs. ~22!–~24!, clearly indicates the
ost crucial measurements that are required for im-rovement:
~a! A prerequisite for application of the algorithm ishe availability of reflectance data with sufficientpectral resolution in the 700–740-nm range andood wavelength accuracy to enable the critical wave-ength l2
c, to be accurately located. In this respectthe present generation of airborne imaging spectrom-eters may already be suitable, while future satellite-based sensors such as CHRIS and follow-on missionslook promising. For concentrations higher than;120 mgym3 as found in some inland waters the830–900-nm spectral range will also be needed foroptimal performance.
~b! As for any analytical algorithm based on chlo-rophyll a absorption, retrieved concentrations are in-versely proportional to the chlorophyll-specific
20 July 2001 y Vol. 40, No. 21 y APPLIED OPTICS 3583
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phytoplankton-absorption coefficient. Any error inthis calibration parameter will thus be transmitteddirectly to an error in the retrievals. At present theregion or species dependence of this calibration pa-rameter is poorly known.
~c! More attention may need to be paid to inputdata for the pure-water absorption coefficient in theredyNIR range, especially to determine the magni-ude of any salinity- or temperature-dependent vari-tions.32
In addition to future research in these directions,testing the algorithm for other case 2 water bodies isnecessary to determine its robustness and clarify therange of conditions in which chlorophyll a retrievalsre reliable.
This research was carried out within the frame-ork of the Belgian Science Policy Office’s Teledetec-
tion Satellitaire ~TELSAT! program under contract4y36y34 ~Multicolor-II!. Gavin Tilstone was also
unded by the National Environmental Researchouncil Thematic Program on Marine Productivity,ontract GST/02/2765. We thank the captain andrew of the research vessel Belgica and the staff of theanagement of the North Sea Mathematical Models
MUMMs! measurement service in Oostende for helpn preparing and carrying out the seaborne cam-aigns. Mark Knockaert, Daniel Saudemont, andvan Swyngedouw are acknowledged for laboratoryhlorophyll a analyses, and MUMM’s computingeam is acknowledged for support. We thank col-eagues in the MUMM’s remote-sensing group and inhe Pre-Operational Water and Environmental Ser-ice ~POWERS! project for sharing their ideas and fortimulating the detailed analysis of errors, whichorms the core of this study. The criticism of annonymous referee was helpful in improving thisext.
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