Optical closure of parameterized bio-optical relationships

Chinese Journal of Oceanology and LimnologyVol. 32 No. 2, P. 480-489, 2014http://dx.doi.org/10.1007/s00343-014-3177-4

Optical closure of parameterized bio-optical relationships*

HE Shuangyan (贺双颜) 1, 2, 3 , * * , FISCHER Jürgen 1 , SCHAALE Michael 1 , HE Ming-xia (贺明霞) 2 1 Institute for Space Sciences , Freie Universität Berlin , Berlin D-12165 , Germany 2 Ocean Remote Sensing Institute , Ocean University of China , Qingdao 266003 , China 3 Ocean College , Zhejiang University , Hangzhou 310058 , China

Received Jun. 15, 2013; accepted in principle Jul. 31, 2013; accepted for publication Aug. 14, 2013 © Chinese Society for Oceanology and Limnology, Science Press, and Springer-Verlag Berlin Heidelberg 2014

Abstract An optical closure study on bio-optical relationships was carried out using radiative transfer model matrix operator method developed by Freie Universität Berlin. As a case study, the optical closure of bio-optical relationships empirically parameterized with in situ data for the East China Sea was examined. Remote-sensing refl ectance ( R rs ) was computed from the inherent optical properties predicted by these bio-optical relationships and compared with published in situ data. It was found that the simulated R rs was overestimated for turbid water. To achieve optical closure, bio-optical relationships for absorption and scattering coeffi cients for suspended particulate matter were adjusted. Furthermore, the results show that the Fournier and Forand phase functions obtained from the adjusted relationships perform better than the Petzold phase function. Therefore, before bio-optical relationships are used for a local sea area, the optical closure should be examined.

Keywords : optical closure; ocean color; remote sensing; bio-optical relationship

1 INTRODUCTION

Remote sensing of the ocean color is an important method of determining the concentrations of chlorophyll, sediments, and colored dissolved organic matter (CDOM) in ocean water (Gordon et al., 1980; Morel 1980; Tassan, 1994). This measuring method requires knowledge of the optical properties of the ocean water as functions of the concentration of the water constituents and the wavelength of sunlight, the so-called bio-optical relationships (Chang et al., 2003; Tzortziou et al., 2006, 2007; Gallegos et al., 2008). Bio-optical relationships either predict the inherent optical properties (IOPs, such as absorption, scattering, and attenuation) or the apparent optical properties (such as radiance, irradiance, and remote-sensing refl ectance) (Morel, 2001).

One of the methods used to obtain the bio-optical relationships is to fi t an (semi-)empirical relationship using in situ measurements (Wang et al., 2004; Zhu and Li, 2004a, b; Bai et al., 2006; Li et al., 2006; Qiu, 2006; Song and Tang, 2006; Liu, 2007; Liu et al., 2007). A general problem with employing this method is that these fi ts are often only valid for limited ranges

of the wavelength and concentration, or that there is large scatter in the data resulting in rather small coeffi cients of determination ( R 2 ). Some bio-optical relationships are even strongly discontinuous at certain values of the concentration or wavelength (e.g., absorption coeffi cients in Qiu, 2006). In fact, if one is interested in accurate determinations of the concentration of ocean water constituents at a certain location via remote sensing, it is desirable to test bio-optical relationships obtained from in situ data at this location. Effi cient testing can be conducted using radiative transfer models, such as that of the matrix operator method (MOMO) (Fischer and Grassl, 1984; Fell and Fischer, 2001). These models compute the remote sensing refl ectance ( R rs ) from the IOPs given by bio-optical relationships. The computed R rs can be compared with in situ data of R rs . If measurements

* Supported by the State Scholarship Fund of the China Scholarship Council, the National Natural Science Foundation of China (Nos. 60638020, 41206006, 41176021, 41276028, 41306035), the National Basic Research Program of China (973 Program) (No. 2011CB409803, 2011CB403503), and the State Key Laboratory Program (No. SOED1206) ** Corresponding author: [email protected]

481No.2 HE et al.: Optical closure of parameterized bio-optical relationships

and simulations agree well, one speaks of optical closure (Zaneveld, 1994).

In this study, as a case study, the optical closure of bio-optical relationships obtained from in situ data for the East China Sea was examined using MOMO developed by Freie Universität Berlin. We do so by comparing the outputs of MOMO for different choices of the bio-optical relationships for the absorption, (back-) scattering coeffi cients and scattering phase function with in situ measurements of R rs in the East China Sea. To achieve optical closure for the East China Sea, the bio-optical relationships for the absorption and scattering coeffi cients of suspended particulate matter (SPM) were adjusted in this study. The performances of two different scattering phase functions were also compared.

This paper is subdivided into fi ve sections. The in situ data and MOMO are described in Section 2, and the parameterized bio-optical relationships including the absorption by phytoplankton, CDOM, SPM, scattering by particles, and a semi-analytical formula for R rs are outlined in Section 3. Infl uences of different bio-optical relationships on simulated R rs are shown and compared in Section 4. A conclusion is presented in Section 5.

2 DATA AND METHOD

In situ data obtained by Liu et al. (2004) were used in this study. These data included R rs , the chlorophyll concentration (CHL), SPM, and the CDOM absorption coeffi cient measured at 35 sites in the East China Sea. Figure 1a shows R rs in seven bands (412, 443, 490, 520, 565, 670, and 780 nm), while Fig.1b shows R rs for SPM concentrations below 4.0 g/m 3 (at 20 sites). In Fig.1b, most R rs values at 780 nm are larger than 0.001/sr. This is unusual because, in water having a low SPM concentration, the in situ R rs at 780 nm is generally close to zero owing to strong water absorption. This might have been due to the above-water measurement method employed (Tang et al., 2004). When employing this method, the estimation of how much of the sky radiance should be removed from the upward radiance relies on the investigator’s experience. In fact, removing the appropriate amount of sky radiance is one of the most critical steps when obtaining the in situ R rs data (Mueller et al., 2003). To make the 20 in situ measurements in Fig. 1b consistent with R rs (780 nm)≈0, the data were adjusted by subtracting R rs (780 nm), as shown in Eq.1 ( λ in nm, R rs in /sr). The new R rs values ( R rs ) are shown in Fig.1c. Note that the in-water method has usually

been preferred for clear water. However, it has been demonstrated that the spectrally averaged uncertainties of carefully measured R rs when employing the two

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Fig.1 (a) In situ R rs at 35 sites (Liu et al., 2004), original (b) and adjusted (c) R rs for SPM concentrations below 4.0 g/m 3 The different colors correspond to different sites.

482 CHIN. J. OCEANOL. LIMNOL., 32(2), 2014 Vol.32

methods are within 4% or 6% (Hooker et al., 2004; Zibordi et al., 2012).

rs rs rs( ) ( ) (780)R ' R R . (1)

The radiative transfer model MOMO (Fischer and Grassl, 1984; Fell and Fischer, 2001) was used to simulate R rs spectra in the East China Sea in this study. Using MOMO, azimuthally dependent radiance in an atmosphere-ocean can be calculated with high computational effi ciency. The maximal validation errors for MOMO simulations were reported to be on the order of 5% (Fell and Fischer, 2001), which is comparable to the error of radiometric measurements. In the simulations of this study, wavelengths of 412.5, 442.5, 490, 510, 560, 620, 665, 709, 779, and 865 nm were chosen as these bands are commonly used for ocean color sensors. The U.S. Standard Atmosphere (1962) was used. The atmosphere and ocean were considered as consisting of 11 layers and one layer, respectively. For the vertical aerosol distributions in the atmosphere, the setup recommended in the ESA MERIS handbook (Antoine and Morel, 2011) was used, while for the air-sea interface, a fl at sea surface was considered. The IOP inputs of MOMO were computed using bio-optical relationships for the East China Sea, which are further explained in the next part.

3 ADJUSTMENTS OF PARAMETERIZED BIO-OPTICAL RELATIONSHIPS

3.1 Phytoplankton absorption

The bio-optical relationships of phytoplankton absorption include the spectral absorption model expressed by Eq.2 and the relationship between the chlorophyll concentration, CHL (in mg/m 3 ), and absorption coeffi cient, a ph (in /m), expressed by Eq.3. The parameters in these relationships were obtained by Zhu and Li (2004) from in situ data for the East China Sea. The dimensionless parameters Y 0 and Y 1 in Eq.2 are those derived by Zhu and Li (2004).

1( )ph 0 ph( ) ( ) (675)Ya Y a , (2)

CHL=16.109 a ph (675) 0.802 2 , R 2 =0.806 4. (3) The phytoplankton absorption within the spectral

range from 412 to 675 nm can be calculated using Eqs.2 and 3. To get the absorption values at wavelengths longer than 675 nm, the phytoplankton absorption spectral model of Lee (1998) was used:

ph 0 1 ph ph( ) ( ) ( ) ln (440) (440)a a a a a .(4)

Comparing with the phytoplankton absorption spectra measured by Zhu and Li (2004), the modeled phytoplankton absorption spectra at different chlorophyll concentrations were found to be reasonable.

3.2 CDOM absorption

The CDOM absorption spectral shape is usually modeled in exponential form:

g g 0 g 0 0( ) ( )exp[- ( )] 400 nma a S . (5) Using the spectral exponential slope ( S g ) of 0.017 5

from Zhu and Li (2004), the CDOM absorption ( a g in /m) spectra can be modeled.

3.3 Non-algal particulate absorption

The non-algal particulate absorption spectral shape is usually modeled in exponential form as

d d 0 d 0 0( ) ( )exp[- ( )] 440 nma a S . (6) A spectral exponential slope ( S d ) of 0.010 3 from

Zhu and Li (2004b) was used in this study. The relationship between the non-algal particulate (or SPM) concentration and absorption coeffi cient was taken from Qiu (2006):

a d (400)=0.028SPM 0.8398 , when SPM≤100 g/m 3 , R 2 =0.496, (7)

a d (400)=0.002SPM 1.66 , when SPM>100 g/m 3 , R 2 =0.998. (8)

Using Eqs.6, 7, and 8, the SPM spectral absorption coeffi cient ( a d ) can be modeled as shown in Fig.2a, in which each simulated spectrum is labeled with the SPM concentration. There is a large difference in a d between the SPM concentrations of 100 and 110 g/m 3 . This gap is due to the inconsistency between Eqs.7 and 8, which show a strong discontinuity of a d at SPM=100 g/m 3 . Because the coeffi cient of determination for SPM≤100 g/m 3 is rather small ( R 2 =0.496), we decided to use a different bio-optical relationship for such values of the SPM; the bio-optical relationship obtained by Babin (2003a) (Eq.9) yields a consistent SPM absorption model. That relationship was used in exchange of Eq.7 in this study. Using Eqs.6, 8, and 9, the SPM absorption spectra were modeled as shown in Fig.2b. Comparing with the fi eld SPM absorption coeffi cient spectra reported by Zhu and Li (2004b), the modeled spectra were found to be reasonable. It is thus clear that the continuous SPM absorption spectra are better modeled by Eqs.6, 8, and 9 than by Eqs.6–8.

a d (443)=0.031SPM, when SPM≤100 g/m 3 . (9)


3.4 Particulate scattering

3.4.1 Modeling particulate scattering

Table 1 lists two particulate scattering bio-optical relationships, A and B, derived by Song and Tang (2006) and Liu (2007), respectively, using in situ data for the East China Sea (particle scattering coeffi cient b p in /m, particulate backscattering coeffi cient b b p in /m). Additionally, two other b p spectral models (C and D) are listed for comparison (Babin, 2003b). We note that the λ - 1 dependency (D) form is usually the preferred choice if no local b p spectral model exists. Here the four particulate scattering models are specifi ed in Table 1, and their b p spectra are shown in Fig.3.

Figure 3a and b shows that, when the SPM concentration is higher than 1.0 g/m 3 , the green lines are steeper than others; however, when the SPM concentration is lower than 1.0 g/m 3 , black lines are

steepest, and blue lines are very fl at in the blue bands. The black and red b p spectra have some differences in the spectral slope; however, this has little effect on the simulated R rs spectral shapes, which will be referred to later.

3.4.2 Modeling the particulate backscattering probability

The backscatter probability, B p , is defi ned as

bpp

p

( )( )

( )b

Bb

. (10)

Using the particulate scattering relationships for b bp , b p , and SPM obtained from Song and Tang (2006) (i.e., model A in Table 1), the B p spectra for various SPM concentrations can be calculated; see Fig.4a. According to in situ data for the East China Sea shown by Liu et al. (2007), B p varies in the range of [0.01, 0.05] and depends little on the wavelength. It is seen

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Fig.2 Modeled SPM absorption ( a d ) spectra Plot a is modeled using Eqs.6, 7 and 8, while plot b is modeled using Eqs.6, 9 and 8. In plot b, the blue lines are modeled using Eqs.6 and 9, while the black lines are modeled using Eqs.6 and 8.

Table 1 Particulate scattering models

No. Particulate scattering models Reference

A Black line 1.323

bp p0.0142b b , b bp (532)=0.0031SPM 1.4602, bp 0

bp 0

( )( )

nbb

, λ 0 =532 nm ,

n =0.1954 b bp (532) -0.326 , b bp (532) 0.013/m, n =0.81, b bp (532) 0.013/m

Song and Tang, 2006

B Red line 1.323

bp p0.0142b b , b bp (532)=0.0031SPM 1.4602, 0.525

p p555( ) (555)b b

Song and Tang, 2006 , Liu, 2007

C Blue line b p (555)=0.51SPM, b p ( λ )=A( λ ) b p (555) Babin, 2003b

D Green dashed 1.323bp p0.0142b b , b bp (532)=0.0031SPM 1.4602 , b p ( λ )= b p (532)(532/ λ ) Song and Tang, 2006 , λ -1 dependency


that the B p range in Fig.4a is smaller than the in situ data range shown by Liu et al. (2007). This could be due to the overestimation of particulate scattering coeffi cients. Therefore, the b bp -SPM relationship was recombined using the linear equation for water for SPM concentrations over 30 g/m 3 , and using the exponential equation for SPM concentrations less than 30 g/m 3 (Song and Tang, 2006):

b bp (532)=0.0031SPM 1.4602 , when SPM≤30 g/m 3 , R 2 =0.93;

b bp (532)=0.0101SPM+0.141 9, when SPM>30 g/m 3 , R 2 =0.87. (11) Note that the offset of the linear relationship is

slightly modifi ed in this study to keep the two models continuous at SPM=30 g/m 3 . In addition, some other minor modifi cations were made to the B p modeling: when SPM≤30g/m 3 and B p >0.02, B p =0.02; when SPM>30g/m 3 , B p = B p –0.013.

Figure 4b shows the modifi ed modeled B p spectra. The range of B p is comparable to the in situ data range shown by Liu et al. (2007).

3.4.3 Modeling scattering phase function

Using three sets of Petzold’s measurements taken in waters with a high particulate load, Mobley (1994) derived the phase functions for marine particles commonly used in ocean optics; the phase functions are displayed in Fig.5a. The volume scattering functions (VSFs) measured by Petzold (1972) in very clear seawater, coastal ocean water, and turbid harbor water are presented in cyan, green, and blue, respectively. The averaged particle phase function obtained by Mobley (1994) is shown in red. The dark purple line corresponds to the VSF for pure seawater obtained by Morel (1974).

In addition, analytical phase functions are also

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Fig.3 Modeled b p spectraIn plots a (linear axis) and b (logarithmic axis), black denotes model A, red denotes model B, blue denotes model C and green denotes model D, and each b p spectrum is labeled with the SPM concentration .

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Fig.4 Comparison of B p derived from b p for model A in Table 1 (a) and that derived from modifi ed b p (b)


frequently used. Fournier and Forand (FF) derived an approximate analytic expression for the phase function of an ensemble of particles having a Junge-type particle size distribution, with each particle scattering according to the anomalous diffraction approximation to the exact Mie theory. The FF phase function can be obtained from a given B p . When B p =0.018 3, the FF phase function is a good fi t to the averaged particle phase function; see the black dashed line in Fig.5a.

As shown in Fig.4, B p changes greatly with the SPM concentration. According to the FF equation, the different particle phase functions can be calculated using the modifi ed bio-optical relationships of Song and Tang (2006) for b bp , b p , and SPM, which are displayed in Fig.5b and c. Figure 5b shows the phase functions at 560 nm for different backscatter fractions, which are related to SPM concentrations of 0.2, 1.0, 5.0, 20.0, 60.0, and 160.0 g/m 3 . Figure 5c shows phase functions in the fi rst nine MERIS (MEdium Resolution Imaging Spectrometer) bands, and the red lines represent longer bands that relate to three SPM concentrations at 0.5, 5.0 and 160.0 g/m 3 . It is clear that the phase functions vary much more with the SPM concentration than with the wavelength, and the phase functions vary more with the wavelength in waters with low SPM concentrations than in very turbid water.

3.5 R rs semi-analytical formula

According to the form of the semi-analytical formula for the remote-sensing refl ectance just below the sea surface ( r rs in /sr) of Gordon et al. (1988),

rs 0 1( ) ( ( )) ( )r g g u u , (12)

where r rs ( λ )=L u (0 – , λ )/E d (0 – , λ ), u = b b /( a t + b b ), Wang et al. (2004) obtained g 0 =0.067 7 and g 1 =0.040 3 using in situ data for the East China Sea.

Liu (2007) derived the relationships between R rs and r rs for fi ve bands (412, 443, 490, 555, and 670 nm) after analyzing in situ data, and the range of the parameter c in Eq.13 is between 0.709 and 0.938. Here, this study uses the mean value of 0.825 3.

R rs ( λ ) = r rs ( λ ) c (13) Using Eqs.12 and 13, the R rs spectra can be

calculated.

4 RESULT

4.1 Effect of the particulate scattering model on the R rs simulation

Table 1 lists four types of particulate scattering models. To show their effects on R rs , R rs simulated with different scattering models employing MOMO is compared with in situ data. Note that the Petzold scattering phase function was used in the MOMO simulation. Figure 6 shows the scatter plot for simulated versus in situ R rs in seven bands at 35 sites. In addition to the four models listed in Table 1 (A, B, C, D), another model, which is referred to as model C2, is used here. First, we calculate b p (555) with model A and then use the particulate spectral model in model C from Babin (2003b). Therefore, models C2 and C have the same spectral shape, while the relationships between b p and SPM are different.

Figure 6 shows that all the particulate scattering models perform similarly, and the modeled R rs differs greatly from in situ data when R rs is above 0.031/sr. However, model C has the worst performance, with its data scattering farther from the 1:1 line than the data of other models. This is due to the unsuitable relationship between b p and SPM. The model of b p and SPM used in model C was derived for European coastal water by Babin (2003b), while the other models used a model obtained for the East China Sea

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Fig.5 (a) Measured VSFs for three different natural waters obtained by Petzold (1972) and pure seawater, and the averaged particle phase function obtained by Mobley et al. (1994). FF phase functions derived from modifi ed b bp , b p and SPM models of Song and Tang (2006) at different B p (corresponding to different SPM concentrations) (b) and different wavelengths (c)


by Song and Tang (2006). This also shows that the relationship between b p and SPM plays a more important role than the particulate scattering spectral shape in R rs simulation.

4.2 Effect of the particulate scattering model on the R rs SA simulation

R rs can also be simulated using the semi-analytical (SA) method with particulate scattering models (the backscattering probability model is also included). Here the particulate scattering model A (referred to as the original model) was used fi rst, and particulate scattering model A with a modifi ed b bp -SPM relationship (Eq.11) (referred to as the new model) was then applied. Using these two types of particulate scattering models, the original and new R rs were derived and compared with in situ data, as shown in Fig.7a (linear axis) and 7b (logarithmic axis). It is

apparent that the red crosses are closer to the 1:1 line than the black triangles when R rs exceeds 0.01/sr. The root-mean-square error (RMSE) of R rs for old versus new models is 0.008 2 versus 0.003 7, and R 2 is 0.87 versus 0.91. The new scattering model thus performs better than the original one. This also demonstrates that the modifi cation of the b bp -SPM relationship in the particulate scattering model is reasonable.

4.3 Effect of the particulate scattering phase function on the R rs simulation

The particulate scattering phase functions of Petzold (1972) and FF are commonly used in ocean radiative transfer modeling. To get a clear understanding of their performance for the East China Sea, R rs values simulated by MOMO with these two phase functions as input were compared with in situ data. Figure 8 shows the scatter plot of simulated R rs

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Fig.7 Scatter plots of in situ R rs versus SA R rs derived using original and new particulate scattering models a is plotted using a linear/linear scale, and b using a log/log scale.

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Fig.6 Scatter plots of in situ R rs versus R rs simulated using different particulate scattering models a is plotted using a linear/linear scale, and b using a log/log scale.


versus in situ data. The FF phase function is derived using the known particulate backscattering probability ( B p ), which in turn can be calculated using particulate scattering models. Therefore, R rs was obtained using MOMO with both original and new particulate scattering models, giving pha_FF and pha_FF2, respectively, in Fig.8. Furthermore, R rs obtained by MOMO is compared with that obtained by SA in Fig.9. Figures 8 and 9 show that R rs is most accurate for pha_FF2, no matter whether comparing with in situ R rs or with SA R rs . The particulate scattering phase function plays an important role in the R rs simulation, and here the results show that the suitable scattering models (modifi ed) and FF phase function can give reasonable simulation results for waters with a wide range of SPM concentrations.

4.4 Effect of the particulate scattering phase function spectral model on the R rs simulation

The FF phase function changes with wavelength. To show the effect of this spectral dependence on simulated R rs , R rs simulated using pha_FF2( λ ) (referred to as pha_FF2) and only pha_FF2(532) (referred to as pha_FF2nowav) were compared with in itu and SA R rs , as shown in Fig.10. It is seen that the spectral dependence of the phase function has very little effect on the R rs simulation. In fact, the difference in the RMSE for ‘in situ vs pha_FF2’ and ‘in situ vs pha_FF2nowav’ is 0.000 1. In addition, the spectral dependence of phase function has more effect on the R rs spectral shape in clear and not very turbid water than in very turbid water, because the phase functions

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Fig.8 Scatter plot of in situ R rs versus R rs simulated by MOMO with a Petzold (1972) average phase function and FF phase function pha_FF and pha_FF2 were derived from original and new particulate scattering models. a. Plotted using a linear/linear scale; b. Using a log/log scale.

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Fig.9 Scatter plot of SA R rs versus R rs simulated by MOMO with a Petzold (1972) average phase function and FF phase function pha_FF and pha_FF2 were derived from original and new particulate scattering models. a. Plotted using linear/linear scale; b. Using a log/log scale.


vary more with wavelength in water with low SPM concentrations than in very turbid water.

5 CONCLUSION

In this study, some published bio-optical relationships for the East China Sea were examined employing MOMO. Reasonable agreement between the simulated and measured remote-sensing refl ectances ( R rs ) was obtained when replacing the bio-optical relationship of Qiu (2006) for the SPM absorption by that of Babin (2003), adjusting the particulate backscattering relationships with both linear and exponential relationships between b bp and SPM of Song and Tang (2006), and using FF phase functions. Moreover, we found that the spectral dependence of the phase function has overall only little effect on the simulated R rs ; however, it has more infl uence on R rs in water with low SPM concentrations than in water with high SPM concentrations.

Bio-optical relationships are usually obtained from in situ data in a certain sea area with limited spatial and temporal coverage. Thus, these bio-optical relationships should be applied cautiously. However, optical closure of the bio-optical relationships was achieved after our adjustments in this study. We believe that the optical closure here works for the data at 35 sites, but may fail for other cases. Therefore, it is strongly recommended that, before the bio-optical relationships for a certain local sea area are used, the optical closure should be examined. By doing so, the inconsistency of bio-optical relationships can be avoided or reduced. However, to obtain good bio-optical relationships, which play an important role in ocean color remote sensing in China, a high-quality in

situ dataset covering all seasons and sea areas is critically needed.

6 ACKNOWLEDGEMENT We would like to thank Prof. HUANG Daji, the

postdoctoral co-mentor, for helpful discussion and Dr. Thomas Pähtz for discussion and help with English.

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Optical closure of parameterized bio-optical relationships