Modeling the spectral absorption of tripton using exponential and hyperbolic models

Modelling the spectral absorption of tripton using exponential and

hyperbolic models

YUNLIN ZHANG*,BOQIANG QIN,MINGLIANG LIU,GUANGWEI ZHU,

ZHIJUN GONG and YUNLIANG LI

Taihu Lake Laboratory Ecosystem Research Station,State Key Laboratory of Lake Science and Environment,Nanjing Institute of Geography and Limnology,Chinese

Academy of Sciences,73East Beijing Road,Nanjing 210008,PR China

(Received 16September 2008;in final form 29July 2009)

The optical properties of tripton,and the correlation between the absorption coeffi-cient and tripton concentration,were investigated based on a large dataset of 727samples,collected from different regions of shallow Lake Taihu,in China,from July 2004to April 2007.Four models describing tripton absorption spectra in the visible domain (400–700nm)were examined to find the optimal model.The conventional single exponential model performed the poorest.Statistically,the most ‘useful’model was the hyperbolic model;judged by the root mean square error (RMSE)and the magnitude of the F statistic from an analysis of variance,this was found to give a closer fit for the measured absorption (70.1%reduction in RMSE and 449.7%increase in F value)than did the simple exponential model method.The mean S d value derived for the hyperbolic model was 5.98?0.30nm –1,with a very small coefficient of variation of 5.0%.Significant linear correlations were found between a d (440)and total suspended matter,inorganic suspended matter and tripton con-centrations,but with the minimal RMSE of a d (440)estimation (0.815m –1)for tripton.The results demonstrate that it is possible to develop regional models for the estimation of tripton absorption coefficient from the concentration.

1.Introduction

Light attenuation is regulated by the composition and concentration of various attenuating constituents,including water itself,chromophoric dissolved organic mat-ter (CDOM),phytoplankton and tripton (Kirk 1994).Water and CDOM generally attenuate light through the process of absorption,while phytoplankton and tripton attenuate light through both absorption and scattering (Kirk 1994,Babin et al .2003).The absorption properties of CDOM and particulate matter (phytoplankton and tripton)constitute the inherent optical properties (IOPs)of a water body.These IOPs play an important role in determining the underwater light climate,phytoplankton primary production and remote sensing reflectance (Kirk 1994).Thus,the IOPs are key parameters in bio-optical algorithms for water quality assessment using remote sensing,radiative transfer models for water columns,and bio-optical models for estimation of primary production (Kutser et al .2001,Stro ¨mbeck and Pierson 2001,Albert and Mobley 2003,Magnuson et al .2004,Tilstone et al .2005,Kutser et al .2006,Gitelson et al .2008).

*Corresponding author.Email:ylzhang@https://www.360docs.net/doc/5517668879.html,

International Journal of Remote Sensing

ISSN 0143-1161print/ISSN 1366-5901online #2011Taylor &Francis

https://www.360docs.net/doc/5517668879.html,/journals DOI:10.1080/01431161003801310

International Journal of Remote Sensing Vol.32,No.14,20July 2011,3917–3933

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

During the last decade,there has been considerable attention given to the spectral absorption by CDOM and phytoplankton as important attenuating constituents,because this regulates the dynamics of these variables in many productive areas of the oceans and inland waters (Allali et al .1997,Laurion et al .2000,Stedmon et al .2000,Simis et al .2005,Va ¨ha ¨talo et al .2005,Giardino et al .2007).It is only in recent years that there has been increasing focus on the spectral absorption of tripton (Babin et al .2003,Stramski et al .2004,Binding et al .2008).However,our current under-standing of variations in tripton absorption is still very limited,especially for shallow lakes.This situation is rather surprising,because tripton absorption dominates the total absorption in some coastal waters and shallow lakes,due to input of suspended inorganic matter by surrounding rivers and frequent sediment resuspension (Phlips et al .1995,Christian and Sheng 2003,Doxaran et al .2005,Tyler et al .2006,Zhang et al .2007).

Cyanobacterial blooms are an increasingly common phenomenon in many eutrophic lakes and coastal waters,and are attracting the attention of environmental agencies,water authorities and the general public because of their potential threat to human health through the consumption of water contaminated by the toxic blooms.Remote sensing is an effective tool to monitor water quality and cyanobacterial blooms (Simis et al .2005,Kutser et al .2006,Ma et al .2006,Giardino et al .2007,Wang and Shi 2008).Retrieval of chlorophyll a (chl-a )concentration,primary production and cyanobacter-ial blooms from remote sensing data appear to be dependent on the ability of the chosen model to take tripton absorption into account (Kutser et al .2006,Giardino et al .2007).Therefore,it is vital to measure and model the spectral absorption coefficient of tripton with high precision for development of bio-optical algorithms of optically active sub-stances,estimating primary production,and improving measurements of the under-water light field for submerged aquatic vegetation growth.

The absorption coefficient of tripton is measured using the quantitative filter technique (QFT)(Mitchell 1990,Cleveland and Weidemann 1993,Ferrari and Tassan 1999,Oubelkheir et al .2007).Some studies show that the exponential func-tions used to describe the spectrum of CDOM typically also fit the spectrum of tripton a d (l )(Babin et al .2003,Giardino et al .2007,Binding et al .2008):

a d el T?a d el 0Texp ?S d el 0àl T ;

(1)

where a d (l )is the absorption coefficient at wavelength l ,a d (l 0)is the absorption coefficient at a reference wavelength l 0,which is generally chosen to be 440nm,and S d is the spectral slope as a measure of absorption decrease with increasing wave-length.However,other recent studies have demonstrated that such a simple exponen-tial model does not give the best fit to the spectra of CDOM.For example,Stedmon et al .(2000)and Kowalczuk et al .(2006)added a background constant at the right-hand side of equation (1).Twardowski et al .(2004)compared six different models,and found that a hyperbolic model was the most ‘useful’model for describing the spectral absorption of CDOM in the visible range.Considering the similar spectral shape of CDOM and tripton absorption,the use of a simple exponential model to fit tripton spectral absorption,combined in a bio-optical model,may cause a marked error in estimations of remote sensing reflectance and water quality parameters (Dall’Olmo and Gitelson 2006,Kutser et al .2006,Giardino et al .2007).

It is therefore timely to model the spectral absorption of tripton,and examine the correlation between tripton absorption and concentration.To address the need for accurate information on tripton,the aims of our present study were:(i)to compare

3918Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

four different tripton spectral absorption models to find the best fit,in order to improve tripton correction in water colour remote sensing applications;and (ii)to investigate the relationship between tripton absorption at a typical wavelength and the concentrations of tripton,and both total and inorganic suspended matter (ISM)in order to develop a robust model describing the relationship between tripton absorption and concentration due to the dominant role in light attenuation in turbid Case 2waters.2.Materials and methods 2.1

Study area

Lake Taihu is the third largest freshwater lake in China,with a water surface area of 2338km 2and a mean depth of 1.9m (Qin et al .2007).It is located between 30 560–31 330N and 119 5530–120 5360E.The lake is spatially heterogeneous,with macrophyte-dominated zones (East Lake Taihu,Xukou Bay)and algal-dominated zones (Meiliang Bay,Wuli Bay and Zhushan Bay)(figure 1).The rapid

economic

Figure https://www.360docs.net/doc/5517668879.html,ke Taihu showing the different regions sampled.The inflow rivers of Changzhou and Wuxi cities are the Liangxi,Taige and Zhihu;the major contributors of water to Lake Taihu are the Tiaoxi and Yili rivers;the only outflow is the Taipu.

Modelling the spectral absorption of tripton 3919

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

growth in the urban and rural areas around Lake Taihu in the last two decades has resulted in greatly increased wastewater,sewage and pollution discharge into the lake.Consequently the lake is becoming increasingly eutrophic,which presents serious problems in Meiliang Bay and Zhushan Bay in the northern part of the lake.The main inflowing rivers located in the northern and south-western regions,including Liangxi,Zhihu,Taige,Yili and Tiaoxi,brought high concentrations of particles and dissolved organic matter into the lake (figure 1)(Zhang et al .2004).In recent summers,the accumulation of surface blooms of the blue-green algae Microcystis spp.in Meiliang Bay has impeded the normal operation of the drinking water plants for Wuxi city.In 2007,serious contamination caused by algal blooms in Gonghu Bay interrupted the drinking water supply to Wuxi city for several days (Wang and Shi 2008).

Lake Taihu is located in the northern subtropical monsoon climate zone,and is affected by typhoons in summer.The wind velocity around the lake is high all year.Being a typical large shallow lake,Taihu is subject to severe sediment resuspension by wind-induced waves.This can cause a marked increase in the concentrations of total suspended matter (TSM),especially tripton,in the water column (Zhang et al .2004,2006).In Lake Taihu,tripton accounts for a high percentage of TSM,and dominates the light attenuation (Zhang et al .2007).2.2

Sample collection

Our sampling objective was to encompass a large range of variation in tripton absorption properties of Lake Taihu.Therefore field samples were collected on 26cruises between July 2004and April 2007,covering all 12months of the year,and 727samples in the lake (figure 1).Surface water samples (z ,0.5m)for the analysis of tripton absorption coefficients,phytoplankton pigments and suspended particles were collected in 1500ml bottles.2.3

Absorption measurements

The absorption coefficients of tripton a d (l )were determined by the QFT (Mitchell 1990).Water samples (50–400ml)were collected and filtered onto a 47mm diameter Whatman fibreglass GF/F filter (England)under low vacuum pressure in order to ensure that the measured optical density of particulate matter was less than 0.4.Absorption spectra were recorded every 1nm from 350to 800nm using a Shimadzu UV–2401PC UV–Vis spectrophotometer (Japan).A blank filter,wetted with filtered water,was used as a reference.All spectra were set to zero at 750nm to minimize differences between sample and reference filter.Theoretically,the QFT method requires that all light scattered by the filter should be received by the spectro-photometer detector,but in practice the detector has a limited aperture so that some of the scattered light will be lost.In order to minimize the loss of the scattered light,we placed the filter as close as possible to the detector.Measured D f (l )values were corrected for the increase in path length caused by multiple scattering in the fibreglass filter using the equation of Cleveland and Weidemann (1993):

D s ?0:378D f t0:523D 2f ;D f 0:4;

(2)

where D s and D f are the corrected and measured optical densities of the particulate

matter respectively.

3920Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

The absorption coefficients of particulate matter a p (l )were calculated as follows (Cleveland and Weidemann 1993):

a p el T?2:303D s el T?S =V ;

(3)

where 2.303is the factor used to convert base 10to a natural logarithm,S is the filter clearance area and V is the filtered volume.

After each measurement of the optical densities of the total particles,the filter was soaked in methanol for 4hours to dissolve phytoplankton,and rinsed with filtered water;the particles remaining on the filter were non-phytoplankton particles.The absorption spectra of the soaked filter were then measured again to obtain the optical densities of the non-phytoplankton particles.The absorption coefficient of non-phytoplankton particles a d (l )was determined similarly using equations (2)and (3).2.4

Measurement of other parameters

Samples for chl-a and phaeophytin a (p-a )were filtered on Whatman GF/C fibreglass filters.The chl-a and p-a were extracted with ethanol (90%)at 80 C and analysed spectrophotometrically at 750and 665nm with correction for p-a .

To obtain TSM,water samples were filtered through pre-combusted Whatman GF/C fibreglass filters (450 C for 4h)to remove suspended organic matter,dried (105 C for 4h)and weighed.The filters were recombusted at 450 C for 4h,and weighed again to obtain ISM.By subtracting ISM from TSM,organic suspended matter (OSM)was obtained.

In order to separate the dry weight of tripton from the dry weight of total particles,the dominant species of Microcystis and Scenedesmus in Lake Taihu were cultured in the laboratory to measure dry weight,chl-a and p-a concentrations in different growth periods.Surface algal bloom samples were collected during calm weather conditions and cleared using distilled water to obtain the relative pure phytoplankton (excluding tripton).Then the sample was put under dark conditions.Every three days,the sample was collected to measure the dry weight,chl-a and p-a concentrations.We found that a simple linear equation could describe the relation between the dry weight of phytoplankton and the sum of chl-a and p-a concentrations.

C phytoplankton ?0:09C chl -a tp -a

eR 2?0:98;N ?31;p <0:001T;

(4)

where C phytoplankton is the dry weight of phytoplankton (mg l -1),and C chl-a tp-a is the sum of chl-a and p-a concentrations (m g l -1).The concentration of tripton (C tripton )(mg l -1)is obtained as the difference of TSM (C TSM )(mg l -1)and phytoplankton dry weight (C phytoplankton )(mg l -1).2.5

Spectral absorption models

We modelled the tripton absorption spectra using four different models,by applying the linear or nonlinear fitting methods in the visible spectral range of 400–700nm.The description of four ((a )–(d ))models is shown in table 1.2.6

Fitting the algorithm and testing the model

Model fits were applied by using the lsqcurvefit function in Optimization Toolbox in MATLAB.The lsqcurvefit solves nonlinear curve-fitting (data-fitting)problems by using the least-squares approach.The MATLAB optimization parameters

Modelling the spectral absorption of tripton 3921

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

MaxFunEval (maximum number of function evaluations allowed),MaxIter (maximum number of iterations allowed),Tolx (termination tolerance on the minimized function)and TolFun (termination tolerance on the function value)were set at 1010,1010,10-6and 10-6,respectively.The fitting determination coefficient (R 2),the root mean square error (RMSE),relative error (RE)and the F statistic from an analysis of variance were used to assess the usefulness of all four models.

The RMSE and the RE of a regression can be derived with equations as follows:

RMSE ????????????????????????????????????????????????P n i ?1ex mod ;i àx mea ;i T2

n

s (5)

RE ?

ex mod ;i àx mea ;i T

x mea ;i

?100%;

(6)

where x mod,i and x mea,i are the modelled and observed values,respectively;n is the number of data points.

The similarity coefficient (SC)was used to assess the similarity of the measured and modelled tripton absorption spectra.SC can be derived with the following equation:

SC ?P 700

l ?400a d el Tmea a d el Tmod

???????????????????????????????????????????????????????????????????P 700l ?400a d el T2mea P 700l ?400a d el T2

mod q ;(7)

where SC is the similarity coefficient of two spectra,i.e.the cosine value of the angle

between two vectors.a d (l )mea and a d (l )mod are the measured and numerically fitting tripton absorption spectra.SC ?1represents the parallel of two spectra,in other words their complete similarity.SC ?–1represents their complete dissimilarity.The F parameter is computed as

F ?R 2=D m

e1àR 2T=D e

;

(8)

where R 2is the determination coefficient for the regression from a least-squares fit,D m is the degrees of freedom of the model and D e is the degrees of freedom of the error

Table 1.The four models used as descriptors of tripton absorption spectra.

Model description

Function Modelled parameters Fitting method 1.Single exponential:a linear regression of the natural logarithm of the absorption coefficient versus wavelength

ln a el T?a 1àS 1l a 1,S 1Linear 2.Single exponential:a nonlinear regression of the absorption coefficient versus wavelength

a el T?a 2e S 2e440àl T

a 2,S 2

Nonlinear 3.Single exponential:as model 2but with background parameter

a el T?a 3e S 3e440àl TtK a 3,S 3,K Nonlinear 4.Hyperbolic function:a nonlinear

regression of the absorption coefficient versus wavelength

a el T?a 4el =440TS 4

a 4,S 4

Nonlinear

3922Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

or unexplained variability.If the number of model parameters is p ,and the number of data points used in the fit is n ,D m is (p –1)and D e is (n –p ).

While R 2is an indicator of how well the model fits the data,the RMSE and F parameters provide a better test of the usefulness of the model based on the number of data points used in the fit and the number of model parameters.A good model should have as few parameters as possible,while exhibiting a high correlation coefficient and small RMSE.3.Results and discussion 3.1

Model performance

Although no single model was consistently the best,overall the hyperbolic model (model 4)was the top performer.Models 3and 4were better than models 1and 2for describing the tripton absorption spectrum.Our data supporting this is presented as follows:means,standard deviations and medians of five statistical parameters (R 2,mean RE,RMSE,SC,F )for each model are provided in table 2;comparisons of R 2,mean RE,RMSE,F of each models for all samples are provided in figure 2;compar-isons of measured and modelled a d (l )spectra using four different models are provided in figure 3;and the spectral RE of four models for four representative samples in different seasons is shown in figure 4.

Model 1consistently ranked last or next to last for the five statistical parameters (table 2);this is consistent with a previous CDOM study showing that a linear fit on

Table https://www.360docs.net/doc/5517668879.html,parison of statistical parameters and the value S d of four models.

Model 1

Model 2

Model 3Model 4R 2

Range 0.9433–0.99890.9787–0.99970.9929–0.99970.9899–0.9996Mean ?Std 0.9889?0.00890.9967?0.00200.9986?0.0008

0.9982?0.0014

Median 0.99150.9971

0.99880.9987Mean RE (%)Range

2.8–24.3

3.3–22.1 2.4–16.2 2.5–25.7Mean ?Std 7.7?2.610.4?3.0

4.9?1.6 6.4?3.1Median 7.310.1 4.6

5.6RMSE (m –1)

Range

0.008–0.7880.004–0.3650.003–0.3000.006–0.281Mean ?Std 0.217?0.139

0.091?0.060

0.060?0.044

0.064?0.041

Median

0.190

0.075

0.0480.054SC

Range 0.9880–0.99990.9953–0.99990.9983–0.99990.0076–0.9999Mean ?Std 0.9972?0.00180.9992?0.00050.9997?0.0002

0.9996?0.0003

Median 0.99750.9993

0.9997

0.9997

F

Range 3023–26842013761–104260020840–54443029262–804690Mean ?Std 43160?31212127076?93886140392?73991237258?120500Median 35025101680122050228800S d

Range

8.61–13.959.40–14.6010.04–16.82 4.57–6.76Mean ?Std 11.22?0.75

12.69?0.71

13.87?0.96

5.98?0.30

Median 11.2212.7113.92 5.99CV(%)

6.7

5.6

6.9

5.0

Mean RE is the mean of the absolute value of RE,CV is a coefficient of variation and Std is standard deviation.The unit of S d is m m –1for models 1–3,and nm –1for model 4.

Modelling the spectral absorption of tripton 3923

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

log-transformed data to determine spectral slope was the worst model (Stedmon et al .2000,Twardowski et al .2004,Kowalczuk et al .2006).The mean RMSE decreased 58.1%for the simple exponential model using the linear fittings (model 1)and non-linear fittings (model 2),thus care should be exercised when undertaking an expo-nential fitting algorithm in Microsoft Excel and SPSS.Model 1did not perform well in the shortwave range when compared to model 2(figure 3(a )and (b )).

The R 2,SC and F values of models 3and 4were significantly higher than those of models 1and 2,and the mean RE and RMSE of models 3and 4were significantly lower than those of models 1and 2(ANOVA,p ,0.001)(table 2and figure 2),which indicated that models 3and 4were better than models 1and 2.Furthermore,the fitness and the variation of RE of models 3and 4were also better than those of models 1and 2(figures 3and 4).

When comparing the measured and modelled values for a d (412)derived from each of the four models (figure 5),it is evident that the scatter distributions of models 3and 4are very close to the line of 1:1and overlap each other.In contrast,the scatter distributions of models 1and 2depart markedly from the line of 1:1,and the higher the value of a d (412),the larger is the deviation,especially in model 1.Because log transformation puts more weight on samples with low absorption values at high wavelength,which are less precisely determined than at low wavelength,the traditional single exponential model methods (models 1and 2)fail to model spectral absorption at shorter wavelengths,leading to a marked decrease in these wavelength ranges.

No model was consistently better than the others,but overall the hyperbolic model (model 4)was the best.The R 2,mean RE,RMSE,SC values of models 3and 4were better than those of models 1and 2,and for these parameters model 3was better than

700(a )

(b )

(c )

(d )

5004003002001000

0–55–10

RE (%)

RMSE (m –1

)

10–1515–20

20–25

Model 1Model 2Model 3Model 4

600500400300200100S a m p l i n g n u m b e r S a m p l i n g n u m b e r 0

700600

500400300200100S a m p l i n g n u m b e r

700600500400300200100

S a m p l i n g n u m b e r 0

0.94–0.950–0.15

0.15–0.30.3–0.450.45–0.60.6–0.750.75–0.9

0–2×10

5

0–2×1050–2×105

F

0–2×1050–2×105

0.95–0.960.96–0.970.97–0.980.98–0.990.99–1

R 2

Figure https://www.360docs.net/doc/5517668879.html,parison of sampling number of (a )determination coefficients (R 2);(b )relative error (RE);(c )root mean square error (RMSE);and (d )F values of four models.

3924

Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

model 4.However,the F statistic of model 4was significantly improved compared to model 3(ANOVA,p ,0.001).When considering the mean F value,that of model 4was 1.69times that of model 3,however because the means can be strongly affected by a few spectra with high or low values,this parameter may not be the most useful.In contrast,the medians can be used as a better measure of model usefulness.The median F value of model 4was 1.87times that of model 3,the higher value being better.A coefficient of variation estimated S d of model 3was 6.9%,as opposed to 5.0%for model 4(table 2).More importantly,like models 1and 2,model 4also has the convenience of describing the shape of the tripton spectrum with only one parameter.

Therefore,we conclude that the hyperbolic model (model 4)is preferred to the three other models for describing tripton spectra in the visible range.The hyperbolic model results in a 70.1%reduction in RMSE,and a 553.2%increase in the median F value when compared to the simple exponential model method.Furthermore,the hyper-bolic model is considered less dependent on the spectral range used in the fit than the exponential model (Twardowski et al .2004).Although the performance of the hyper-bolic model is better than the other three models,the large literature base and historical precedence for using exponential models will provide momentum for their continued use.Indeed,consistently using the correct exponential model with a back-ground constant remains an effective method to model the spectral absorption of tripton (D’alimonte et al .

2004).

Figure https://www.360docs.net/doc/5517668879.html,parison of measured and modelled tripton spectral absorption of ((a )–(d ))four models for a typical sample.

Modelling the spectral absorption of tripton 3925

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

3.2Variation in spectral slope

The three different methods for estimating S d using an exponential model (models 1–3)have a systematic effect on its value (table 2).We note that the common use of a linear fit on log-transformed a d (l )data to determine S d (model 1),gave the lowest mean value of S d .This finding,consistent with a previous study of CDOM (Stedmon et al .2000,Kowalczuk et al .2006),is mainly due to the fact that a log transformation puts more weight on samples with low absorption values at high wavelength than at short wavelength,which was less precisely determined (Stedmon et al .2000).

Because we recommend the hyperbolic model for estimation of the spectral absorp-tion of tripton,the variation of S d estimated using the hyperbolic model is discussed in detail.The spectral slope for the wavelength range of 400–700nm ranges from 4.57to 6.76nm –1,with a mean value of 5.98?0.30nm –1using the hyperbolic model (model 4).The R 2for the fit of S d is usually higher than 0.99,with a mean value of 0.9982(of 727samples only two had R 2lower than 0.99).

The overall variations in spectral slope using the hyperbolic model are shown in figure 6.The frequency distribution of the S d values basically follows a normal (Gaussian)distribution (skewness ?–0.542,the absolute of skewness ,1.0),with a skewness to the left.The percentages of the S d values less than 5.5nm –1and larger than 6.5nm –1are only 5.2%and 3.3%respectively.

The overall variability observed in S d was rather small in the present study (given the large diversity of the waters examined),with a coefficient of variation of

5.0%,

Figure https://www.360docs.net/doc/5517668879.html,parison of spectral relative error of four models for four different seasons:(a )spring;(b )summer;(c )autumn and (d )winter.

3926Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

thus a constant for S d can be used in remote sensing semi-analytical,models of Lake Taihu.A coefficient of variation of 10.3%was found for 348samples taken from various coastal waters around Europe,including the English Channel,Adriatic Sea,Baltic Sea,Mediterranean Sea and North Sea using an exponential model (model

2)

Figure https://www.360docs.net/doc/5517668879.html,parison of (a )measured and (b )modelled a d (412)using four

models.

Figure 6.Frequency distribution of spectral slope S d of tripton using hyperbolic model (model 4).

Modelling the spectral absorption of tripton 3927

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

(Babin et al .2003).In the present study,the dataset is larger (727samples)and the coefficient of variation is smaller than in the study of Babin et al .The difference is attributed to two reasons:(i)the hyperbolic model we used (model 4)can give a more accurate estimation of spectral absorption of tripton than does the exponential model (model 2);and (ii)all the measurement and analyses in the present study were done using exactly the same procedures for all samples.

The spectral shape of CDOM is often used as a proxy for CDOM composition and source,and is usually negatively correlated to CDOM absorption and to the specific absorption coefficients (Yacobi et al .2003,Magnuson et al .2004,Kowalczuk et al .2006).For tripton,no significant correlations were found between S d and tripton absorption a d (440),and specific absorption coefficient.The same results were observed for the S d of models 1–3.This demonstrates that the composition and source of tripton have no effect on the spectral shape,although there was a wide range of particles and relative proportions of mineral and organic matter found in the Lake Taihu samples.The percentage of OSM accounting for TSM indicating the composition of particles ranged from 8.3%to 87.0%in this study.Twardowski et al .(2004),when reviewing the literature,considered that about three-quarters of the variability in the spectral shape of CDOM could be explained by the different spectral ranges and methods,and not by the difference of CDOM composition and source.It was concluded that the variation of tripton spectral slope was attributed to the fitting method not the composition.3.3

Spectral absorption model of tripton in Lake Taihu

The water samples contained very variable amounts of TSM (mean:67.5?45.6mg l –1,range:6.6–285.6mg l –1)and tripton (mean:61.9?45.1mg l –1,range:4.4–281.7mg l –1).The a d (440)ranged from 0.35to 12.93m –1with a mean value of 3.75?2.19m –1,covering nearly three orders of magnitude of absorption,with a maximal value being 36.9times the minimal value.The peak of the a d (440)frequency distribution was located at around 2.0m –1,and decreased to about 13m –1(figure 7).

The statistical parameters between tripton absorption a d (440)and the concentra-tions of TSM,ISM and tripton are shown in table 3.The correlation between a d (440)and tripton concentration has the lowest RSME (0.815m –1:21.8%from the mean measured a d (440)),the maximal R 2and the second rank in mean RE.

Therefore,

Figure 7.Frequency distribution of tripton absorption coefficient a d (440).

3928Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

tripton concentration is the best parameter for estimating the absorption coefficient a d (440).The scatterplot of tripton concentration and a d (440)is shown in figure 8.Although the calculation of tripton concentration is based on an empirical correla-tion,our results show that tripton concentration is still a better predictor of the absorption coefficient than TSM and ISM.Because TSM includes tripton and phy-toplankton particles but ISM does not include the organic particles of tripton,the correlation between a d (440)and the concentrations of TSM,ISM are lower than that of tripton.The significant difference in ratios of tripton absorption to TSM and ISM (0.040and 0.137m 2g –1for a d (440)/TSM and a d (440)/ISM,respectively)observed in Lake Erie demonstrated that previous studies actually have not given the accurate estimation of tripton absorption coefficient using TSM or ISM concentration (Babin et al .2003,Binding et al .2008).Of course,the regional correlation to calculate the concentration of tripton from the concentrations of TSM and phytoplankton pigment in Lake Taihu may give a slight difference when used in other waters.For example,a different coefficient (0.07)was used to calculate the dry weight of tripton from phytoplankton pigment concentration in some other lakes (Kutser et al .2001,Giardino et al .2007).

For various coastal waters around Europe,the linear slope was 0.031between a d (443)and the concentration of TSM,when applying a linear regression with a null intercept.The overall average a d (443)/C TSM ratio was 0.041m 2g –1with a 56%coefficient of variation (Babin et al .2003),and the a d (440)/C TSM ratio was 0.040m 2g –1with a 76%coefficient of variation (Binding et al .2008).In the present

study,

Figure 8.Correlation between tripton absorption coefficient a d (440)and tripton concentration.

Table https://www.360docs.net/doc/5517668879.html,parison of statistical parameters between a d (440)and C TSM ,C ISM ,C tripton .

Slope

Intercept R 2Range of RE (%)Mean RE*(%)RMSE (m –1)a d (440)and C TSM 0.04480.72570.8639-52.8to 297.221.00.833a d (440)and C ISM 0.0484 1.16480.8466-66.4to 361.924.00.884a d (440)and C tripton

0.0453

0.9398

0.8689

-49.3to 333.8

23.0

0.815

*C TSM ,C ISM ,C tripton are the concentrations of TSM,ISM and tripton,respectively.Mean RE is the mean of the absolute value of RE.

Modelling the spectral absorption of tripton 3929

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

the linear slope was 0.0522,0.0619and 0.0552m 2g –1between a d (440)and the concentrations of TSM,ISM and tripton respectively,with a null intercept,which is markedly higher than those in coastal waters around Europe (Babin et al .2003),and those in a relatively clear,large,deep lake (Lake Erie)(Binding et al .2008).In our dataset,the mean values and coefficients of variation of a d (440)/C TSM ,a d (440)/C ISM and a d (440)/C tripton are 0.060m 2g –1,28.4%;0.085m 2g –1,43.6%;and 0.069m 2g –1,37.8%respectively over nearly three orders of absorption magnitude at any wave-length,values which are also higher than those observed in the coastal and clear lake waters (Babin et al .2003,Binding et al .2008).However,we also note that our mean a d (440)/C tripton is lower than the value reported in Lake Garda (0.069versus .0.080m 2g –1)(Giardino et al .2007),mean a d (550)/C tripton is lower than the value reported in Moreton Bay (0.0176versus 0.0187m 2g –1)(Brando and Dekker 2003),and a d (665)/C ISM is slightly lower than that observed in the Irish Sea (0.0080versus 0.0090m 2g –1)(Binding et al .2005).The differences of the a d (440)/C TSM ,a d (440)/C ISM and a d (440)/C tripton ratios in different waters are attributed to differences in the composition and size of particles (Stramski et al .2004),and the calculation of tripton concentration.For example,the percentage of OSM accounting for TSM is 24.6%,which is sig-nificantly lower than the 47.5%observed in Lake Erie (Binding et al .2008).Furthermore,particles in a shallow lake such as Lake Taihu are generally larger than those in coastal waters and large deep lakes.For the separation of the dry weight of tripton from the dry weight of total particles,an approximate coefficient of 0.07reported in Dutch inland waters was used in Lake Garda and Moreton Bay (Brando and Dekker 2003,Giardino et al .2007)but the value of 0.09measured in Lake Taihu was used in this study.

The spectral absorption of tripton is the key input parameter in the semi-analytical and analytical models of water colour remote sensing.Many such models require that tripton absorption can be extrapolated to the visible range from the measurement of absorption at a typical wavelength,or tripton concentration,in order to estimate chl-a concentration and potential productivity using derived phytoplankton absorption spectra (Lee and Carder 2003,Magnuson et al .2004,Ciotti and Bricaud 2006,Giardino et al .2007).

The previous discussion in this study has shown that the hyperbolic model allowing a constant for S d of 5.98nm –1can be used to model the spectral absorption of tripton in Lake Taihu.Spectral absorption therefore can also be obtained through the measurement of tripton concentration in a remote sensing model using the following equation:

a d el T?e0:0453C tripton t0:9398Tel =440Tà5:98

(9)

4.

Conclusions

Models 3and 4give the most appropriate estimation of tripton spectral absorption (judged by RMSE).However,model 4has few model parameters and a marked increase in F value.Therefore,model 4is recommended to model the spectral absorption of tripton in this study.The mean S d value derived for Lake Taihu was 5.98?0.30nm –1for the range of 400–700nm,with relatively little variability for a large dataset of 727samples.Significant linear correlations were found between the tripton absorption coefficient a d (440)and TSM,ISM and tripton concentrations,but with the minimal RMSE of a d (440)estimation (0.815m –1:21.8%from the mean

3930Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

measured a d (440))using tripton concentration.The results demonstrate that it is possible to develop a regional model a d (l )?(0.0453C tripton t0.9398)(l /440)-5.98,for the optical properties of tripton which will then allow higher precision in remote sensing applications and underwater irradiance transmission models.The approach developed in Lake Taihu from knowing the tripton concentration to model the whole tripton absorption spectrum using a hyperbolic model could be applied elsewhere.Acknowledgements

This study was jointly supported by the Knowledge Innovation Project of CAS (KZCX1-YW-14-6),and the National Natural Science Foundation of China (Grant No.40601099,40730529,40971252,40825004).We would like to thank Sheng Feng,Jiang Ji,Rongshu Qian,Junsheng Li and Qiaohua Zhao for their help with sample collection in the field.References

A LBERT ,A.and M OBLEY ,C.D.,2003,An analytical model for subsurface irradiance and remote

sensing reflectance in deep and shallow case–2waters.Optics Express ,11,pp.2873–2890.

A LLALI ,K.,

B RICAUD ,A.and

C LAUSTRE ,H.,1997,Spatial variations in the chlorophyll-specific

absorption coefficients of phytoplankton and photosynthetically active pigments in the equatorial pacific.Journal of Geophysical Research ,102,pp.12413–12423.

B ABIN ,M.,S TRAMSKI ,D.,F ERRARI ,G.M.,

C LAUSTRE ,H.,B RICAU

D ,A.,O BOLENSKY ,G.and

H OEPFFNER ,N.,2003,Variations in the light absorption coefficients of phytoplankton,nonalgal particles,and dissolved organic matter in coastal waters around Europe.Journal of Geophysical Research ,108,pp.1–20.

B INDING ,C.E.,B OWERS ,D.G.and M ITCHELSON -J ACOB ,E.G.,2005,Estimating suspended sedi-ment concentrations from ocean colour measurements in moderately turbid waters;the impact of variable particle scattering properties.Remote Sensing of Environment ,94,pp.373–383.

B INDING ,C.E.,J EROME ,J.H.,B UKATA ,R.P.and B OOTY ,W.G.,2008,Spectral absorption

properties of dissolved and particulate matter in Lake Erie.Remote Sensing of Environment ,112,pp.1702–1711.

B RANDO ,V.E.and D EKKER ,A.G.,2003,Satellite hyperspectral remote sensing for estimating

estuarine and coastal water quality.IEEE Transactions on Geoscience and Remote Sensing ,41,pp.1378–1387.

C HRISTIAN ,D.and S HENG ,Y.P.,2003,Relative influence of various water quality parameters on

light attenuation in Indian River Lagoon.Estuarine,Coastal and Shelf Science ,57,pp.961–971.

C IOTTI ,A.M.and B RICAU

D ,A.,2006,Retrievals of a size parameter for phytoplankton and

spectral light absorption by colored detrital matter from water-leaving radiances at SeaWiFS channels in a continental shelf region off Brazil.Limnology and Oceanography:Methods ,4,pp.237–253.

C LEVELAN

D ,J.S.and W EIDEMANN ,A.D.,1993,Quantifying absorption by aquatic particles:a

multiple scattering correction for glass–fiber filter.Limnology and Oceanography ,38,pp.1321–1327.

D’ALIMONTE ,D.,Z IBORDI ,G.and B ERTHON ,J.F.,2004,Determination of CDOM and NPPM

absorption coefficient spectra from coastal water remote sensing reflectance.IEEE Transactions on Geoscience and Remote Sensing ,42,pp.1770–1777.

D ALL ’O LMO ,G.and G ITELSON ,A.A.,2006,Effect of bio-optical parameter variability and

uncertainties in reflectance measurements on the remote estimation of chlorophyll-a concentration in turbid productive waters:modeling results.Applied Optics ,45,pp.3577–3592.

Modelling the spectral absorption of tripton 3931

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

D OXARAN ,D.P.,C HERUKURU ,R.C.N.and L AVENDER ,S.J.,2005,Use of reflectance band ratios

to estimate suspended and dissolved matter concentrations in estuarine waters.International Journal of Remote Sensing ,26,pp.1763–1769.

F ERRARI ,G.M.and T ASSAN ,S.A.,1999,A method using chemical oxidation to remove light

absorption by phytoplankton pigments.Journal of Phycology ,35,pp.1090–1098.

G IARDINO , C.,B RANDO ,V.E.,D EKKER , A.G.,S TRO

¨MBECK ,N.and C ANDIANI ,G.,2007,Assessment of water quality in Lake Garda (Italy)using Hyperion.Remote Sensing of Environment ,109,pp.183–195.

G ITELSON ,A.A.,D ALL ’O LMO ,G.,M OSES ,W.,R UNDQUIST ,D.C.,B ARROW ,T.,F ISHER ,T.R.,

G URLIN ,D.and H OLZ ,J.,2008,A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters:Validation.Remote Sensing of Environment ,112,pp.3582–3593.

K IRK ,J.T.O.,1994,Light and Photosynthesis in Aquatic Ecosystems (Cambridge,UK:

Cambridge University Press).

K OWALCZUK ,P.,S TEDMON ,C.A.and M ARKAGER ,S.,2006,Modeling absorption by CDOM in

the Baltic Sea from salinity and chlorophyll.Marine Chemistry ,101,pp.1–11.

K UTSER ,T.,H ERLEVI ,A.,K ALLIO ,K.and A RST ,H.,2001,A hyperspectral model for interpreta-tion of passive optical remote sensing data from turbid lakes.Science of the Total Environment ,268,pp.47–58.

K UTSER ,T.,M ETSAMAA ,L.,S TRO

¨MBECK ,N.and V AHTMA ¨E ,E.,2006,Monitoring cyanobacterial blooms by satellite remote sensing.Estuarine,Coastal and Shelf Science ,67,pp.303–312.

L AURION ,I.,V ENTURA ,M.,C ATALAN ,J.,P SENNER ,R.and S OMMARUGA ,R.,2000,Attenuation of

ultraviolet radiation in mountain lakes:Factors controlling the among-and within-lake variability.Limnology and Oceanography ,45,pp.1274–1288.

L EE ,Z.P.and C ARDER ,K.L.,2003,Absorption spectrum of phytoplankton pigments derived

from hyperspectral remote sensing reflectance.Remote Sensing of Environment ,89,pp.361–368.

M A ,R.H.,T ANG ,J.W.and D AI ,J.F.,2006,Bio-optical model with optimal parameter suitable

for Taihu Lake in water colour remote sensing.International Journal of Remote Sensing ,27,pp.4305–4328.

M AGNUSON ,A.,H ARDING J R ,L.W.,M ALLONEE ,M.E.and A DOLF ,J.E.,2004,Bio-optical model

for Chesapeake Bay and the Middle Atlantic Bight.Estuarine,Coastal and Shelf Science ,61,pp.403–424.

M ITCHELL ,B.G.,1990,Algorithms for determining the absorption coefficient of aquatic parti-culates using the quantitative filter technique (QFT).SPIE ,1302,pp.137–148.

O UBELKHEIR ,K.,C LAUSTRE ,H.,B RICAUD ,A.and B ABIN ,M.,2007,Partitioning total spectral

absorption in phytoplankton and colored detrital material contributions.Limnology and Oceanography:Methods ,5,pp.384–395.

P HLIPS ,E.J.,A LDRIDGE ,F.J.and S CHELSKE ,C.L.,1995,Relationships between light availability,

chlorophyll a,and tripton in a large,shallow subtropical lake.Limnology and Oceanography ,40,pp.416–421.

Q IN ,B.Q.,X U ,P.Z.,W U ,Q.L.,L UO ,L.C.and Z HANG ,Y.L.,2007,Environmental issues of Lake

Taihu,China.Hydrobiologia ,581,pp.3–14.

S IMIS ,S.G.H.,P ETERS ,S.W.M.and G ONS ,H.J.,2005,Remote sensing of the cyanobacterial

pigment phycocyanin in turbid water.Limnology and Oceanography ,50,pp.237–245.

S TEDMON ,C.A.,M ARKAGER ,S.and K AAS ,H.,2000,Optical properties and signatures of

chromophoric dissolved organic matter (CDOM)in Danish coastal waters.Estuarine,Coastal and Shelf Science ,51,pp.267–278.

S TRAMSKI ,D.,W OZNIAK ,S.B.and F LATAU ,P.J.,2004,Optical properties of Asian mineral dust

suspended in seawater.Limnology and Oceanography ,49,pp.749–755.

3932Y.Zhang et al.

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011

S TRO

¨MBECK ,N.and P IERSON ,D.C.,2001,The effects of variability in the inherent optical properties on estimations of chlorophyll a by remote sensing in Swedish freshwaters.Science of the Total Environment ,268,pp.123–137.

T ILSTONE ,G.H.,S MYTH ,T.J.,G OWEN ,R.J.,M ARTINEZ -V ICENTE ,V.and G ROOM ,S.B.,2005,

Inherent optical properties of the Irish Sea and their effect on satellite primary produc-tion algorithms.Journal of Plankton Research ,27,pp.1–22.

T WARDOWSKI ,M.S.,B OSS ,E.,S ULLIVAN ,J.M.and D ONAGHAY ,P.L.,2004,Modeling the spectral

shape of absorption by chromophoric dissolved organic matter.Marine Chemistry ,89,pp.69–88.

T YLER ,A.N.,S VAB ,E.,P RESTON ,T.,P RE

′SING ,M.and K OVA ′CS ,W.A.,2006,Remote sensing of the water quality of shallow lakes:A mixture modelling approach to quantifying phytoplankton in water characterized by high-suspended sediment.International Journal of Remote Sensing ,27,pp.1521–1537.V A ¨HA ¨TALO ,A.V.,W ETZEL ,R.G.and P AERL ,H.W.,2005,Light absorption by phytoplankton

and chromophoric dissolved organic matter in the drainage basin and estuary of the Neuse River,North Carolina (U.S.A.).Freshwater Biology ,50,pp.477–493.

W ANG ,M.H.and S HI ,W.,2008,Satellite-observed algae blooms in China’s Lake Taihu.Eos,

Transactions,American Geophysical Union ,89,pp.201–202.

Y ACOBI ,Y.Z.,A LBERTS ,J.J.,T AKA

′CS ,M.and M CELVAINE ,M.,2003,Absorption spectroscopy of colored dissolved organic carbon in Georgia (USA)rivers:the impact of molecular size distribution.Journal of Limnology ,62,pp.41–46.

Z HANG ,Y.L.,Q IN ,B.Q.,C HEN ,W.M.and L UO ,L.C.,2004,A study on total suspended matter

in Lake Taihu.Resources and Environment in the Yangtze Basin ,13,pp.266–271(in Chinese with English abstract).

Z HANG ,Y.L.,Q IN ,B.Q.,Z HU ,G.W.,G AO ,G.,L UO ,L.C.and C HEN ,W.M.,2006,Effect of

sediment resuspension on underwater light field in shallow lakes in the middle and lower reaches of the Yangtze River:A case study in Longgan Lake and Taihu Lake.Science in China Series D–Earth Sciences ,49(Suppl.I),pp.114–125.

Z HANG ,Y.L.,Z HANG ,B.,M A ,R.H.,F ENG ,S.and L E ,C.F.,2007,Optically active substances

and their contributions to the underwater light climate in Lake Taihu,a large shallow lake in China.Fundamental and Applied Limnology ,170,pp.11–19.

Modelling the spectral absorption of tripton 3933

D o w n l o a d e d b y [U n i v e r s i t y o f N e w H a m p s h i r e ] a t 06:14 17 N o v e m b e r 2011