Yanqun Pan and Fang Shen
State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai China
e-mails: [email protected] and [email protected]
Summary
The scattering reflectance of aerosol(ra(l)) is difficult to be estimated accurately when doing
atmospheric correction for ocean color satellite images over turbid waters where the
assumption of zero-reflectance at near-infrared (NIR) domain is invalid. Besides, absorbing
aerosol also increasing the difficulty of this problem(Gordon et al.1997). In the past decades,
lots of efforts have been made to solve this problem, such as algorithms based on iterative
scheme(Siegel et al. 2000,Baily et al.2010, Shi et al.2012), spectral match
algorithm(SOM)(Gordon et al.1997) and spectral optimize algorithm(SOA) (Chomko et
al.1998,2001, Kuchinke et al.2009a,2009b). SOA retrieves multiple parameters that includes
aerosol and water parameters simultaneously, and avoids the extrapolation method when
estimate ra(l). However, there some limits when applied to turbid waters. This research
proposes an improved Spectral Optimize Algorithm(SOA) to do atmospheric correction for
turbid estuarine and coastal waters through estimating four parameters based on the genetic
algorithm (GA) with different aerosol and water models. The four parameters include relative
humidity (RH), fine-mode fraction (FMF), aerosol optical thickness in the NIR wavelength
(ta(865)) and suspended particulate matter (SPM) concentration (Cspm). The first two
parameters determine the aerosol model which was developed by Ahmad(2009). When
aerosol model and optical depth are known, then remote sensing reflectance(Rrs(l)) can be
calculated. This algorithm is first validated with synthetic data sets. Assuming that the
aerosol model in study area is homogeneous, then Rrs(l) can be estimated from pixel by
pixel. This new algorithm was implemented within the Multi-Sensor Level 1 to Level 2
Products Generator (l2gen,http://oceancolor.gsfc.nasa.gov/WIKI/OCSSW(2f)l2gen.html).The
computed results of this algorithm was validated using the Geostationary Ocean Color
Imager (GOCI) imagery and in situ measured data of Rrs(l). Results show that this algorithm
is very appropriate for the turbid waters dominated by the SPM. This new atmospheric
correction algorithm provides an alternative for ocean color data processing for GOCI
imagery over turbid estuarine and coastal regions, like the Yangtze estuary, the Hangzhou
Bay and most Eastern China coastal ocean.
Aerosol and water models
The classical atmospheric correction algorithm estimates aerosol reflectance using 12
aerosol models(M50, M70, M90, M99, C50, C70, C90,C99, T50, T80,T99,O99). These
models represents non-absorbing and weakly-absorbing aerosols. Ahmad et al.(2010)
develops a suit of aerosol models based on the Aerosol Robotic Network (AERONET)
observations. In the new aerosol models, there are eight relative humidity(RH) values
(30%,50%,70%,75%,80%,85%,90% and 95%) that stands for coarse-mode and, for each
coarse-mode there are ten fine-mode fraction (FMF) which values from 0 to
1(0,0.01,0.02,0.05,0.1,0.2,0.3,0.5,0.8,0.95). Coarse-mode particles are non-absorbing and
fine-mode particles leads to absorption(Fig.1). Fig.1 shows that the absorption through
calculation aerosol reflectance different FMF. For the reason that the new 80 aerosol models
having narrower bimodal lognormal distributions and the characteristics of the absorption, we
use the new aerosol models here instead of the previous 12 aerosol models. Assume that
RH ,FMF and (865) are known, reflectance of aerosol and diffuse transmittance can be
estimated using look up tables(LUTs) of this aerosol model.
In SOA(2009), GSM was chosen as the water model. The GSM comprehensively considered
the impacts of many variables from three components on the Rrs, so that it was complicated
for the optimization process. With regard to highly turbid waters dominated by SPM, this
algorithm employed the simple SERT model (Shen et al.2010,2013,2014) with a few
variables. The SERT model uses a system of Rrs(l) vs. Cspm equations derived from the
Kubelka-Munk (KM) two-flux radiative transfer model at adjusted wavelength so that provide
maximum of sensitivity Rrs(l) on SPM:
where Cspm refers to the concentration of SPM in arbitrary units. The constants a(l) and b(l)
(see Shen et al., 2010, 2013, 2014) have a simple, but meaningful interpretation.
Optimize based on genetic algorithm
We use rm(l) represents the reflectance removed Rayleigh scattering ,reflectance of white-
cap and glint reflectance from reflectance of top of atmosphere(TOA),
rm(l,RH,FMF,ta(865),Cspm) represents the sum of water-leaving
reflectance(rw(l,RH,FMF,ta(865),Cspm)) and aerosol reflectance(ra(l,RH,FMF,ta(865)))
estimated with the four unknown parameters. Obviously, rm(l) are equal to rm
(l,RH,FMF,ta(865)) , then the four unkown parameters are estimated using optimize
algorithm. Finally, remote sensing reflectance based on the optimal four parameters
(Rrs(l,RH,FMF,ta(865),Cspm)) is calculated using the equation below:
,where ,t(l,RH,FMF,ta(865) )and t’ (l,RH,FMF,ta(865) ) refer to diffuse transmittance from
sea to sensor and from sun to sea surface, respectively. In SOA , traditional nonlinear
optimize algorithms(such as Gausi–Newton and L-BFGS-B(Zhu et al., 1997) was used to
retrieve unknown parameters. Such optimize algorithms belong to local optimization
algorithm, for the difficulty to determine the initial values of the variables, it is difficult to get
the global optimal solution. GA searches the optimal result using the objective function and
fitness value, not derivatives or other something, through a series of operations such as
selection, crossover and mutation, etc., and it is a kind of global optimization algorithm.
Therefore, GA is introduced to solve the problem in this research.
Atmospheric Correction for GOCI image over turbid estuarine and coastal waters
based on genetic algorithm
Fig.4. Comparison of in-situ SPM and the optimization result of SPM (1:1 line
shown for reference). Red circle refers to low turbidity, while black circle refers to
high turbidity follow (Cspm>80gm-3).
Results
To validate the implementation of the improved SOA to see if it performs well . The improved
SOA was first tested with synthetic data that contained different levels of
noise(0,2%,5%)(Maritorena et al. 2002).,We created synthetic data sets using the aerosol and
water models mentioned above in a forward model with different values of the four
parameters(parameters(RH,FMF, ta(865), Cspm). Values of the four parameters are generated in
random ranged from [30,95],[0,100],[0.01,0.5] and [10,1000], respectively. We use the values
of the four parameters simulate 500 data sets. All tests were conducted with the first 7GOCI
bands. For the data set without added noise, the retrieved parameters are close to the initial
values with a maximum RMSE of 0.01 and minimum R2 0.98(RH). These excellent agreements
demonstrate that the present approach can solve for the four unknowns in the complex,
nonlinear system. Fig.3 shows the retrieved versus actual values for Cspm and and Rrs(l) for
each of the synthetic data sets when the sets of parameters returned by the new algorithm are
used. The modeled Cspm and Rrs(l) were retrieved with high fidelity throughout the
concentration range even for the 5% noise case. This demonstrates that the annealing
procedure can determine reasonably successful parameter candidates even in the presence of
significant noise.
The improved SOA was also validated with match-up pairs . In situ data sets include SPM and
Rrs ,SPM was used for validating the optimization result, while Rrs(l) is for atmospheric
correction. Both of them were collected from cruise surveys in May 2011, March 2012 and
March 2013. The cruise surveys covered the Hangzhou Bay, Changjiang estuary and its
adjacent East China Sea. From the optimization Cspm , retrieved and in-situ SPM are consistent
well with each other for highly turbid sites(Cspm >80gm-3)(Fig.4) . Retrieved Rrs, based on the
optimization results that listed in Table 4 are presented in Fig.5. Fig.5(a) shows that in-situ and
retrieved Rrs(l) are relatively consistent with each other. Besides, the new algorithm can
produce the spectral distribution of the in-situ remote sensing reflectance with similar mean
value and standard deviation(Fig.5(b)). Assuming that the aerosol model in study area is
homogeneous ,GOCI images in match-up pairs are processed with this improved SOA . The
result images are shown in Fig.6 and Fig.7.
Conclusions
In this study, we propose an improved SOA for atmospheric correction in turbid waters based on GA. In this
improved SOA, aerosol model developed by Ahamad and SERT model are used. From the validation with
synthetic data sets and match-up pairs , this new algorithm can retrieve SPM, ta(865) and Rrs(l) well. This
new algorithm needs the assumption that the aerosol model in study area is homogenous for the reason
that GA is high time consuming, When it is used for large scale remote sensing image processing . Results
show that this algorithm is very appropriate for the turbid waters dominated by the SPM. This new
atmospheric correction algorithm provides an alternative for ocean color data processing for GOCI imagery
over turbid estuarine and coastal regions, like the Yangtze estuary, the Hangzhou Bay and most Eastern
China coastal ocean.
spm
spm spm
( ) ( )( ) ,
1 ( ) 1 2 ( )rs
CR
C C
l ll
l l
m a ars
a a
( ) ( ,RH,FMF, (865))( )
( ,RH,FMF, (865)) '( ,RH,FMF, (865))R
t t
r l r l tl
l t l t
Fig.3.Retrieved SPM (left panels) and Rrs(l)(right panels) versus the actual values in the
synthetic data sets(500) with no noise (upper panels), 2% noise(middle panels), and 5%
noise (lower panels).
Fig.5 Comparison of In-situ Rrs and retrieved Rrs. (a) Comparison between measured
and retrieved of all wavelengths(except for 865(nm)), The 1:1 reference line, and
RMSE, between retrieved and measured are shown. (b)Spectral distributions of the
mean value and standard deviation of Rrs.
Fig.6. The Rrs(l) retrieved by GOCI using the new algorithm combined with the
homogeneous assumption of aerosol distribution at : (a) 412 nm; (b) 443 nm; (c) 490
nm; (d) 555 nm; (e) 660 nm; (f) 680 nm; (g) 745 nm; (h) 865 nm. (i) The RGB false
color image using TOA reflectance in 660 nm(Red), 555 nm(Green), 443 nm(Blue).
Fig.7 GOCI retrieved Rrs(660nm) using the algorithm combined with homogenous
assumption of aerosol distribution on 7 May 2011. The time label on (a)-(h) are the
corresponding observing time(Beijing time)
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Fig.2 Remote-sensing reflectance spectra
Rrs(l) calculated by the SERT model for the
waters containing suspended solids only
(shown in the legend in g m-3).
Fig.1 Aerosol reflectance ra(l) calculated by the
aerosol model developed by Ahamad for
different FMF(from the upper to the lower
curves ) with RH =70(%), solar zenith angle q0
sensor zenith angle q=30,relative azimuth angle
j =120 and ta(865)=0.1.