Yanqun Pan and Fang Shen

State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai China

e-mails: panyq213@163.com and fshen@sklec.ecnu.edu.cn

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)

References

Ahmad, Z., Franz, B. a, McClain, C. R., Kwiatkowska, E. J., Werdell, J., Shettle, E. P., & Holben, B. N.

(2010). New aerosol models for the retrieval of aerosol optical thickness and normalized water-leaving

radiances from the SeaWiFS and MODIS sensors over coastal regions and open oceans. Applied

Optics, 49(29), 5545–60.

Bailey, S.W., Franz, B. a & Werdell, P.J., 2010. Estimation of near-infrared water-leaving reflectance for

satellite ocean color data processing. Optics express, 18(7), pp.7521–7527.

Chomko, R.M. et al., 2003. Simultaneous retrieval of oceanic and atmospheric parameters for ocean

color imagery by spectral optimization: a validation. Remote Sensing of Environment, 84(102C), pp.208–

220.

Chomko, R.M. & Gordon, H.R., 2001. Atmospheric Correction of Ocean Color Imagery: Test of the

Spectral Optimization Algorithm with the Sea-Viewing Wide Field-of-View Sensor. Applied Optics, 40(18),

p.2973

Chomko, R.M. & Gordon, H.R., 1998. Atmospheric Correction of Ocean Color Imagery: Use of the

Junge Power-Law Aerosol Size Distribution with Variable Refractive Index to Handle Aerosol Absorption.

Applied Optics, 37(24), p.5560.

Gordon, H.R., Du, T. & Zhang, T., 1997. Remote sensing of ocean color and aerosol properties:

resolving the issue of aerosol absorption. Applied optics, 36(33), pp.8670–8684.

Kuchinke, C.P., Gordon, H.R. & Franz, B. a., 2009. Spectral optimization for constituent retrieval in Case

2 waters I: Implementation and performance. Remote Sensing of Environment, 113(3), pp.571–587.

Kuchinke, C.P. et al., 2009. Spectral optimization for constituent retrieval in Case 2 waters II: Validation

study in the Chesapeake Bay. Remote Sensing of Environment, 113(3), pp.610–621.

Maritorena, S., Siegel, D. a & Peterson, A.R., 2002. Optimization of a semianalytical ocean color model

for global-scale applications. Applied optics, 41(15), pp.2705–2714.

Shen, F. et al., 2010. Satellite Estimates of Wide-Range Suspended Sediment Concentrations in

Changjiang (Yangtze) Estuary Using MERIS Data. Estuaries and Coasts, 33(6), pp.1420–1429.

Shen, F. et al., 2013. Remotely sensed variability of the suspended sediment concentration and its

response to decreased river discharge in the Yangtze estuary and adjacent coast. Continental Shelf

Research, 69, pp.52–61

Shen, F. et al., 2014. Satellite multi-sensor mapping of suspended particulate matter in turbid estuarine

and coastal ocean, China. International Journal of Remote Sensing, 35(11-12), pp.4173–4192

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.