Optical scattering properties of organic-rich and inorganic-rich particles in inland waters

Optical scattering properties of organic-rich and inorganic-rich particles in inland waters
Kun Shi a ,b ,c ,Yunmei Li b ,⁎,Yunlin Zhang a ,Lin Li c ,Heng Lv b ,Kaishan Song d
a
Taihu Lake Laboratory Ecosystem Station,State Key Laboratory of Lake Science and Environment,Nanjing Institute of Geography and Limnology,Chinese Academy of Sciences,Jiangsu Nanjing 210008China b
Key Laboratory of Virtual Geographic Environment,Ministry of Education,College of Geographic Sciences,Nanjing Normal University,Nanjing 210046China c
Department of Earth Science,Indiana University –Purdue University Indianapolis,723West Michigan Street,SL118,Indianapolis,IN 46202USA d
Northeast Institute of Geography and Agricultural Ecology,Chinese Academy of Sciences,Changchun Jilin 130012China
a b s t r a c t
a r t i c l e i n f o Article history:
Received 19May 2013Accepted 1February 2014
Available online 25March 2014Communicated by Barry Lesht Index words:Lake Taihu
Scattering coef ficient
Mass-speci fic scattering coef ficient Phytoplankton
We present the results from a study of the particulate scattering properties of three bodies of water that represent a wide range of optical properties found in inland waters.We found a positive linear relationship (R 2=0.45,P b 0.005)between the mass-speci fic scattering coef ficient at 532nm (b p *(532))and the ratio of the inorganic suspended material (ISM)to the total suspended material (TSM)in our study areas.In con-trast to earlier studies in which b p *(532)was lower for inorganic particles than for organic particles,we found that the value of b p *(532)for ISM (b p *(532)ISM =0.71m 2/g)was approximately 1.6times greater than the value found for organic suspended materials (OSM)(b p *(532)OSM =0.45m 2/g).We found that the dependence of the particle scattering coef ficient (b p )on wavelength (λ)could be described accurately by a power law (with mean average percent error (MAPE)b 0.07)in waters dominated by inorganic particles.The model errors in waters dominated by organic particles,however,were much larger (MAPE N 0.1),especially in the spectral region associated with strong phytoplankton absorption.The errors could be reduced over this wavelength range by adding a term to the model to account for particle absorption,but the additional term tended to increase the error outside of this range.We conclude that information about the nature of the scatter-ing particles in lake waters is necessary for the selection of an appropriate model for particle absorption and that a hybrid model that includes absorption over some wavelength ranges may be necessary.
©2014International Association for Great Lakes Research.Published by Elsevier B.V.All rights reserved.
Introduction
Inherent optical properties (IOPs)of water are solely dependent on the water contents,such as the concentrations of dissolved water con-stituents and particulate composition,but independent of the distribu-tion of ambient light (Morel,1988).Light scattering is generally considered one of the most fundamental parameters of IOPs and can re-flect the composition and shape characteristics of the total suspended materials (Loisel et al.,2006).Therefore,particulate scattering and a de-tailed understanding of its variability in natural waters are important for aquatic ecosystem sciences related to the knowledge of total suspended materials.The scattering properties of a water body can determine the way light propagates through water,and this information can be used for inferring water contents from data observed using remote sensing systems (Snyder et al.,2008).In turbid inland waters,scattering is very important in the remote sensing of water contents because the
radiometric signal recorded by a sensor onboard a satellite or an aircraft is directly proportional to its intensity (Twardowski et al.,2001).
The majority of scattering is composed of total suspended material (TSM),including organic suspended material (OSM)and inorganic suspended material (ISM).Particulate scattering has been found to be directly associated with the TSM concentration,but the relationship be-tween them varies with the composition of rge differences in TSM compositions are found in different water types which results in signi ficant variation in the speci fic scattering coef ficient.As theoretical-ly expected,the relationship between the scattering,b p (λ),and the con-centration of suspended particles was observed to change signi ficantly with the particle size distribution and refractive index (Babin et al.,2003).Babin et al.(2003)argued that the mass-speci fic coef ficient in Case 2waters with a high inorganic content would be smaller than in Case 1waters with a high organic content.Baker and Lavelle (1984)also suggested that a systematic decrease in the mass-speci fic scattering coef ficient could occur from offshore to inshore waters.The in fluence of the mass-speci fic scattering coef ficient would also be reduced by algal absorption in areas with a high chlorophyll-a concentration (Chl-a ).
On the basis of theoretical considerations,Morel (1988)showed that spectral variations of the scattering coef ficient caused by non-absorbing
Journal of Great Lakes Research 40(2014)308–316
⁎Corresponding author.Tel.:+862585898500.E-mail address:yunmeinjnu@ (Y.
Li).
/10.1016/j.jglr.2014.02.022
0380-1330/©2014International Association for Great Lakes Research.Published by Elsevier B.V.All rights
reserved.
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j o u r n a l h o me p a g e :ww w.e l s e v i e r.c o m /l o c a t e /j gl r
particles follow an inverse power law.This dependency has been used in models of the inherent properties of seawater and inland lake waters (Babin et al.,2003;Morel et al.,2006;Roesler and Boss,2003;Song and Tang,2006;Sun et al.,2009).Based on the observations made in a num-ber of estuaries,Doxaran et al.(2009)confirmed that,in the near-IR spectral region,where light absorption by particles is low,a power law function doesfit the spectral variations in a scattering coefficient with a variable slope.However,this power law function is inappropriate for the visible region of the spectrum where particles absorb more light (Doxaran et al.,2007).Numerous measurements of spectral scattering coefficients have documented significant departures from the power law function in spectral bands associated with strong particulate ab-sorption(Babin et al.,2003;Barnard et al.,1998;Doxaran et al.,2007; Stramski et al.,2001).In Lake Taihu,due to the low OSM to ISM ratio, a power law function is suitable for the spectral variations in a scattering coefficient with variable slope.Therefore,the impact of OSM absorption on the scattering coefficient is negligible in Lake Taihu(Sun et al.,2009). When the TSM has a high OSM ratio,the model canfit spectral varia-tions in the scattering coefficients with variable slopes in wave bands associated with strong particulate absorption by taking into account the particulate absorption effects(Doxaran et al.,2009).
For waters with high inorganic particle contents,numerous studies have been conducted to develop models that simulate the variations in spectral scattering coefficients and to investigate the variations in the relationship between scattering coefficients and TSM and ISM (Boss et al.,2004;Kirk,1981;Loisel and Stramski,2000;Loisel et al., 2006;Whitmire et al.,2007).However,little work has been performed on productive inland waters with high organic particle contents.
This study focuses on the properties of optical scattering in three op-tically distinct regions in China:Lake Taihu,Lake Chaohu,and Lake Dianchi.The two questions we address in this study are(1)how well does a power-law function describe the shape of the particulate scatter-ing spectra in different inland waters(that is,waters with inorganic-rich or organic-rich particles)and(2)can the mass-specific scattering coefficient be related to the amount of organic and inorganic suspended materials?Material and methods
Study areas
The study areas,including Lake Taihu,Lake Chaohu,and Lake Dianchi,are located in the Yangtze River drainage area(Fig.1).Lake Taihu is a large,eutrophic shallow lake with high spatial heterogeneity in the Yangtze Delta plain on the border of the Jiangsu and Zhejiang provinces in China.With an area of2338km2(Zhang et al.,2007),it is the third largest freshwater lake in China.This lake is a typical large shallow lake with an average depth of1.9m,indicating wave-induced sediment resuspension has a significant impact on the water quality of Lake ke Chaohu is located at the juncture of Chaohu and Hefei cities in Anhui Province,China.With a water area of750km2 and an average depth of3m,it is the largest lake in Anhui and one of thefive largest freshwater lakes in China.Similar to Lake Taihu,the water quality of this lake is also severely affected by wave-induced sed-iment resuspension.The optical properties of these two lakes(Lake Taihu and Lake Chaohu)are generally dominated by inorganic particles from resuspended bottom materials and a strong influence from gelbstoff(chromophoric dissolved organic matter;CDOM)with a rela-tively lower contribution from phytoplankton.
Our third study site was Lake Dianchi,located on the Yungui Plateau in China.With a water area of approximately300km2and an average depth of5m,Lake Dianchi is the largest freshwater lake in the Yunnan Province.The optical properties of this lake were typically controlled by phytoplankton with minor influences from inorganic suspended mate-rials(Sun et al.,2012).
These lakes have high concentrations of TSM.However,the TSM composition varied drastically among the three lakes.The waters in Lake Taihu and Lake Chaohu had a high concentration of non-algal par-ticles,i.e.,fine sediments with a combination of silts and clays.Con-versely,there was a high concentration of algal particles in Lake Dianchi.The measurements at Lake Taihu were performed in November 2008(56stations)and April2009(31stations).The measurements at Lakes Chaohu and Dianchi were carried out in June(30stations)
and Fig.1.Geo-location of the three study lakes in China.
309 K.Shi et al./Journal of Great Lakes Research40(2014)308–316
September (25stations)2009,respectively.At each station,optical measurements were conducted on the surface water,and water sam-ples were collected using Niskin bottles.The samples were immediately preserved at a low temperature and taken to a laboratory for analysis that day.
Optical parameter measurements
The particulate absorption coef ficients and attenuation coef ficients were measured at a spectral resolution of 4nm and a measurement ac-curacy of ±0.01m −1using a WETLabs AC-S (WETLabs,Inc.,Philomath,OR)designed with 85spectral channels.To obtain accurate absorption and attenuation data,temperature corrections were performed using Eq.(1)(Sun et al.,2009,2010).The salinity correction is not necessary in these freshwater lakes.In addition,the third method of Zaneveld et al.(1994)was used to correct for particulate absorption and scatter-ing errors using spectral scattering and the measured value at the termi-nal wavelength of the AC-S (Eq.(2)).a mts λðÞ¼a m λðÞ−ψt Ãt −t r ðÞð1Þ
a pg λðÞ¼a mts λðÞ−a mts λref
ð2Þ
where a m is the absorption coef ficient measured from the WETLabs AC-S,ψt is the temperature correction parameter,t is temperature of the water,a mts is the absorption coef ficient after the temperature correction,λdenotes the wavelength at which the corrected value is calculated,λref is the reference wavelength (715nm)at which a pg is assumed to be zero,and a pg is the absorption coef ficient of the particles and gelbstoff after the scattering correction.Therefore,the attenuation coef ficient of the particulates and gelbstoff (c pg (λ))could be calculated from:cpg (λ)=c m (λ)−ψt *(t −t r )‐amts (λref ),where c m (λ)is the attenuation coef ficient measured using the WETLabs AC-S.
Because the scattering coef ficient of gelbstoff was low and therefore could be ignored,the particulate scattering coef ficients (b p (λ))could be obtained from the difference between the attenuation and absorption (Eq.(3)).
bp λðÞ¼cpg λðÞ−apg λðÞ
ð3Þ
where b p (λ)is the particulate scattering coef ficient,c pg (λ)is the atten-uation coef ficient of the particulates and gelbstoff,and λis wavelength.Water-component concentration measurements
The water-component concentrations were measured according to the investigation criteria for lakes in China (Sun et al.,2009).The TSM,OSM,and ISM were measured using a weighing method.Chl-a was ex-tracted with hot ethanol (90%)at 82°C and analyzed spectrophotomet-rically with a correction for phaeopigments.The detailed procedures can be found in Le et al.(2009a).Results
Characteristics of water constituent concentrations
The water component (TSM,ISM,OSM,and Chl-a )concentra-tions and the ratio,ISM/TSM,covered the wide range (TSM:11.4–237.7mg/L;ISM:0–214.87mg/L;Chl-a :3–192.9mg/m 3,and ISM/TSM:0–90%)in the various study areas (Table 1).The highest aver-age values of TSM and ISM concentrations were both found in Lake Taihu.The lowest average values of TSM and ISM concentrations were found in Lake Chaohu and Lake Dianchi,respectively.The
highest and lowest average values of Chl-a were found in Lake Dianchi (97.3mg/m 3)and Lake Taihu (13.5mg/m 3),respectively.
The water in Lake Taihu was highly turbid judging from the variation in TSM concentration,which was 11.4–237.7mg/L,with an average of 56.5mg/pared with other studies,such as sandpit lakes (Dall'Olmo and Gitelson,2005),Chesapeake Bay (Gitelson et al.,2008)and a number of other US lakes (Gitelson et al.,2009),the average con-centrations in our study areas were much higher.A high organic content was observed in Lake Dianchi (from 40%to 100%,with an average value of 80%of the TSM from organic matter).The suspended materials in Lake Chaohu showed a rather high organic content (on average,30%of the suspended materials were organic).In Lake Taihu (both autumn and spring),the TSM was mainly inorganic (from 40%to 90%,with an average of 80%,of the total mass of suspended materials)which has been reported in many studies (Binding et al.,2005;Boss et al.,2001a,b,2004;Bowers and Mitchelson-Jacob,1996;Bricaud and Morel,1986;Bricaud et al.,1998,2007;Clavano et al.,2007;Liu et al.,2004;Ma,2005;Morel,1973;Morel et al.,2007).The resulting dataset can be representative of various turbid,productive,inland waters and various types of particles.
Characteristics of optical scattering coef ficients
The statistics of the b p (λ)values are shown in Table 2.The highest (47.9m −1at 715nm)and lowest (1.8m −1at 715nm)b p (λ)values were found in Lake Taihu in autumn and spring,rge
Table 1
Maximum (Max),minimum (Min),average,and standard deviation (SD)of the measured parameters chlorophyll a (Chl-a ),total suspended matter (TSM),inorganic suspended matter (ISM)and the ratio ISM/TSM)in the three lakes studied.Study areas parameters Max Min Average ke Chaohu
Chl-a (mg/m 3)192.923.862.443.2TSM (mg/L)83.915.743.617.1ISM (mg/L)68.48.430.114.3ISM/TSM
0.80.40.70.1Lake Taihu
Chl-a (mg/m 3)79.8 3.013.514.6TSM (mg/L)237.711.456.548.8ISM (mg/L)214.8 6.046.744.9ISM/TSM
0.90.50.80.1Lake Dianchi
Chl-a (mg/m 3)156.739.097.334.6TSM (mg/L)66.624.745.09.7ISM (mg/L)22.80.08.9 4.1ISM/TSM
0.6
0.0
0.2
0.1
Table 2
Statistics of the b p (λ)values obtained from the AC-S measurements at selected visible and near-IR wavelengths.Normality of the distributions was veri fied successfully using a Kolmogorov –Smirnov test on log-transformed data.The geometric standard devia-tion (SD)is to be applied as a factor.Study areas
b p (m −1)Wavelength (nm)
Max Min Average ke Taihu (autumn)
53244.2 2.219.810.667539.5 1.815.88.671538.4 1.8158.1Lake Taihu (spring)
53255.9102911.267549.68.524.29.671547.98.123.49.2Lake Dianchi
53226.111.517 3.367521.89.614.1 2.871522.29.514.3 2.9Lake Chaohu
53255.61228.712.167546.29.322.910.2715
44.3
9.1
22.1
9.8
310K.Shi et al./Journal of Great Lakes Research 40(2014)308–316
variations were observed in Lake Taihu and Lake Chaohu.The b p (λ)values decreased with increasing wavelength (Fig.2)as observed in the previous studies (Chami et al.,2005,2006;Claustre et al.,1999;Dall'Olmo and Gitelson,2005;Doxaran et al.,2009;Le et al.,2009b;Morel et al.,2006;Sun et al.,2009,2010).
Table 3shows the correlation coef ficients between b p (532)and TSM,ISM and OSM.In Lake Taihu and Lake Chaohu,the coef ficients between b p (532)and both TSM and ISM are higher than between b p (532)and OSM.However,for Lake Dianchi,the relationship between b p (532)and OSM is closer than that between b p (532)and ISM.The correlation coef ficients between b p (532)and ISM are 0.95and 0.97in Lake Chaohu and Taihu while the coef ficient at Lake Dianchi is only 0.55,which indi-cates that inorganic particles dominate the water scattering characteris-tics at Lake Taihu and Lake Chaohu.At Lake Dianchi,the scattering characteristics are dominated by organic particles.
The mass-speci fic particulate scattering coef ficient (b p *(λ),m 2/g)is de fined as the scattering coef ficient per unit of TSM concentration.The values of b p *(532)exhibited region-to-region variations,from 0.29m 2/g to 0.79m 2/g,with an average value of 0.58m 2/g (Table 4).The lowest b p *(532)value was found in Lake Dianchi,with strong local variation.The highest b p *(532)value was observed in Lake Taihu.The b p *(532)values in Lake Taihu (with an average b p *(532)of 0.58m 2/g in autumn and 0.7m 2/g in spring)and Chaohu (with an average b p *(532)of 0.66m 2/g)were higher than in Lake Dianchi (with an average b p *(532)of 0.37m 2/g).
Scattering should be related to the ISM and OSM,which can be used to derive the average mass-speci fic scattering coef ficient for organic and inorganic particulate materials in these waters.The contribution of par-ticles to scattering can be partitioned into two parts,namely an organic and an inorganic contribution (here taking the scattering coef ficient at 532nm for example)(Snyder et al.,2008):bp 532ðÞ¼ISM bp Ã532ðÞISM þOSM bp Ã532ðÞOSM
ð4Þ
where b p (532)is the particle scattering coef ficient at 532nm and b p *(532)ISM (or b p *(532)OSM )is the inorganic or organic mass-speci fic particulate scattering coef ficient.Therefore,the measured particulate scattering coef ficients at 532nm were divided by the measured OSM (or ISM)amounts,and we used a linear correlation of b p (532)/OSM with ISM/OSM for our datasets to de fine the slope and intercept (that is,to derive the values of b p *(532)ISM and b p *(532)OSM )along with their standard uncertainties.Thus,the values of b p *(532)ISM and b p *(532)OSM could be derived using Eq.(4)and a linear regression method (Fig.3)(Snyder et al.,2008).As demonstrated in Fig.3,our re-sults showed that ISM (b p *(532)ISM =0.71m 2/g)has a value approxi-mately 1.6times greater than the organic suspended materials (OSM)(b p *(532)OSM =0.45m 2/g).
The relationship between the mass-speci fic particulate scattering coef ficient and the TSM compositions was further investigated to deter-mine the impact of the TSM compositions on the variations in the mass-speci fic particulate scattering coef ficient in our three study areas (Fig.4).As demonstrated in Fig.4,the b p *(532)values of the three study areas completely coincided with the ratio of ISM to TSM,with the b p *(532)values increasing as the ratio of ISM to TSM increased.
In
Fig.2.The spectral scattering coef ficients (b p )measured in Lakes Taihu (a),Chaohu (b),and Dianchi (c).
Table 3
Correlations between the scattering parameters and the water component concentrations for the study areas.Study areas
TSM ISM OSM b p (532)Lake Taihu (summer)
TSM 1
0.980.370.95ISM 1
0.160.97OSM 10.17b p (532)1Lake Taihu (spring)TSM 1
0.990.620.95ISM 1
0.510.95OSM 1
0.49b p (532)1Lake Chaohu TSM 1
0.960.630.97ISM 1
0.630.97OSM 1
0.63b p (532)1Lake Dianchi TSM 1
0.420.90.92ISM 1
−0.020.55OSM 1
0.83b p (532)
1
Table 4
Global and site-by-site statistics of the mass-speci fic (TSM)particulate scattering coef fi-cient at λ=532nm,i.e.,the b p (532)m 2/g.The maximum (Max),minimum (Min),average,and standard deviations (SD).Study areas
n Max Min Average ke Taihu (autumn)560.790.30.580.1Lake Taihu (spring)310.780.430.70.1Lake Chaohu 300.70.490.660.09Lake Dianchi 250.520.290.370.04All
142
0.79
0.29
0.58
0.08
311
K.Shi et al./Journal of Great Lakes Research 40(2014)308–316
other words,lower b p *(532)values generally were found in waters with lower organic contents.The statically signi ficant relationship (R 2=0.45,P b 0.005)between the b p *(532)values and the TSM compositions sug-gested a key role of the TSM composition in the b p *(532)variations in our study areas.
We also investigated the variations of the particulate single-scattering albedo ω(λ),which was de fined as the ratio b p (λ)/c pg (λ),where b p (λ)and c pg (λ)were the scattering coef ficients and attenuation coef ficients,respectively.The ω(λ)values generally increased with wavelength (Fig.5)because the particulate absorption coef ficient var-ied with wavelength.However,there was a trough at a wavelength of approximately 675nm,which indicated a strong absorption of organic particulates at some stations.In Lake Dianchi,the trough was signi ficant at all stations because of the effects of organic particulate absorption.The values of ω(675)in Lake Dianchi were lower than in Lake Taihu and Lake Chaohu.In Lake Taihu and Lake Chaohu,the ω(675)values from most stations were between 0.97and 0.99.
Spectral dependence of the particulate scattering coef ficient
A power law model was used to simulate the particulate scattering spectra in all the study areas.b p (532)was used as the reference because it has a good relationship with the scattering coef ficients at the other wavelengths and can minimize errors from an overly broad wavelength interval in the regression analysis.For each station,Eq.(5)was fit to the measured b p (λ)spectrum by minimizing the weighted square sum of the difference between the modeled (Eq.(5))and measured b p (λ)values.The visible and near-IR wavelength regions were considered.The average values of the spectral slopes (γ)at Lake Taihu were 0.93and 0.82in autumn and spring,respectively.In Lake Chaohu and Lake Dianchi the mean values were 0.85and 0.47,respectively.We were able to obtain an average γvalue of 0.83throughout the study areas and dates in Lake Taihu and Lake Chaohu.Therefore,the wavelength
dependency slopes are similar to the results obtained in previous stud-ies (Morel,1988;Song and Tang,2006;Sun et al.,2009).bp λðÞ¼bp 532ðÞ
λ532
−γ
ð5Þ
As a result,two models,i.e.,Eq.(6)for Lake Taihu and Lake Chaohu and Eq.(7)for Lake Dianchi were obtained for simulating the particulate scattering spectra:
bp λðÞ¼bp 532ðÞ
λ532
−0:83
ð6Þ
bp λðÞ¼bp 532ðÞ
λ532
−0:47
ð7Þ
MAPE ¼1n X n i ¼1bp λðÞi −bp λðÞi 0bp λðÞi
:
ð8Þ
To assess the precision of the two models,the dataset was used to carry out error analysis.The mean absolute percentage errors
(MAPE,
Fig.3.The linear correlation of b p (532)/OSM (i.e.b p measured at 532nm divided by OSM)with
ISM/OSM.
Fig.4.The relationship between the mass-speci fic scattering coef ficient at 532nm
(b p *(532)and the ISM/TSM
ratio.
Fig.5.The single-scattering albedo spectra (ratio,b p (λ)/c pg (λ),of scattering to attenuation coef ficients in Lakes Taihu (a),Chaohu (b),and Dianchi (c).
312K.Shi et al./Journal of Great Lakes Research 40(2014)308–316
Eq.(8))between the modeled and measured scattering values were cal-culated using Eq.(8).We used the scattering coef ficient at four wave-lengths (440,675,710,and 750nm)to assess the precision of the simulated power-law model (Table 5).The four wavelengths were selected because re flectance at these wavelengths is generally used for remotely estimating water quality.The model (Eq.(5))with high preci-sion was suitable for simulating the scattering coef ficients at Lake Taihu and Lake Chaohu.However,the model (Eq.(7))failed to simulate the scattering coef ficient at wavelengths where the phytoplankton absorp-tion is strong.This poor performance can be attributed to the organic particle absorption.The relative error of Eq.(7)is greater than 10%at 675nm for Lake Dianchi.Doxaran et al.(2009)discussed the effects of organic particle absorption on the scattering coef ficients and gave a new model by taking into account the particulate absorption coef ficient when simulating the spectral scattering coef ficient (Eq.(9)):b p λðÞ¼b p 532ðÞÃλ532
γ−1−tanh 0:5Ãγ2
h i Ãap λðÞ:
ð9Þ
The value of γis estimated using Eq.(5)and scattering coef ficients in the near-IR,and a p (λ)is the particle absorption coef ficient.According to Eq.(9),we can obtain a new model (Eq.(10))for Lake Dianchi:b p λðÞ¼b p 532ðÞÃλ532
0:45−1−tanh 0:5Ã0:45
2
h i Ãap λðÞ:ð10Þ
We calculated the mean absolute percentage errors (MAPE,Eq.(8))of the two models to compare the two scattering models for Lake Dianchi.As shown in Fig.6,in the spectral range of approximately 450–606nm,the simulation error of the common power law model (Eq.(7))is lower than the model that considers the effect of particulate absorption;in the spectrum range of approximately 606–750nm,the simulation error of the common power law model (Eq.(7))is higher than that in the model (Eq.(10))that takes into account the effect of the particulate absorption.The simulation error of the common power law model (Eq.(7))has a relatively high error peak at approximately 675nm with a MAPE value of 8%because of the effect of the organic par-ticulate absorption.The model (Eq.(10))has a relatively low error at that wavelength with a MAPE of 2%.
Discussion
The size distribution of particles in lake waters is often assumed to be well described by a power law function of the particle diameter (Boss et al.,2001a;Morel,1973).For non-absorbing spherical particles with a constant refractive index,this distribution follows a power law between zero and in finite diameter.The scattering spectral slope (γ)is related to the differential slope (j)through (Astoreca et al.,2012;Babin et al.,2003;Morel,1973;Twardowski et al.,2001):j ¼γþ3:
ð11Þ
Eq.(11)is not valid when the imaginary refractive index is signif-icantly larger than zero.To test the scattering spectral slope,γ,we obtained the scattering spectral slope γ(420–690nm)at visible wavelengths and γ(700–750nm)at near-IR wavelengths,separate-ly.The relationships between the γ(700–750nm)and γ(420–690nm)are shown in Fig.7for Lake Taihu and Lake Chaohu and in Fig.8for Lake Dianchi.In Lake Taihu and Lake Chaohu,the relation-ship between γ(700–750nm)and γ(420–690nm)is linear with a slope close to 1.The observed relative difference between the near-IR and visible scattering spectral slopes remains limited in the case of high mineral particle content.However,in Lake Dianchi,the most striking result is the signi ficant difference between the visible and near-IR scattering spectral slopes.No correlation (Fig.8)be-tween γ(700–750nm)and γ(420–690nm)was found in Lake Dianchi.Thus,we could extract the slope of the particle distribution from γ(420–750nm)in Lake Taihu and Lake Chaohu.The γis only derived from scattering coef ficients at wavelengths from 700to 750nm,where the phytoplankton absorption is weak,which could be used for estimating the particle size in Lake Dianchi.
As shown in Fig.2,in Lake Taihu (both autumn and spring)and Lake Chaohu,the spectral shape of b p (λ)is spectrally dependent on λ−γ,from the visible to the near-infrared,but for Lake Dianchi,the story is quite different.The λ−γlaw is only valid for a population of particles with a high inorganic particle content (Ahn et al.,1992;Bricaud and Morel,1986;Bricaud et al.,1998;Doxaran et al.,2009;Morel,1988;Morel and Bricaud,1981).In Lake Taihu and Lake Chaohu,the particle content is dominated by inorganic particles (Fig.9).The average slopes of the particle distribution (average j:3.92in autumn Lake Taihu,3.8in spring Lake Taihu,and 3.9in Lake Chaohu)are close to 4in Lake Taihu and Lake Chaohu.This spectral scattering coef ficient is similar to that of pure minerals.Therefore,a simple power law could simulate the var-iations in the spectral scattering coef ficient with low error.However,the spectral scattering coef ficient in Lake Dianchi is obviously affected by the particulate absorption.Such scattering reduction is typical for particle populations dominated by phytoplankton (Doxaran et al.,2009).The decrease in b p (λ)at short,visible wavelengths is highly pronounced at Lake Dianchi,where a discontinuity is systematically
Table 5
The forecast precision of the scattering coef ficient spectral model (Eq.(5))at four wavelengths in Lake Taihu and Lake Chaohu but not Lake Dianchi.
440nm
675nm 710nm 750nm Lake Taihu (autumn)0.010.050.040.07Lake Taihu (spring)0.020.030.050.05Lake Chaohu
0.02
0.05
0.04
0.04
Fig.6.The mean relative error (MAPE)of the two models for b p (λ
).
Fig.7.Plot of the visible (420–690nm)scattering coef ficient slopes as a function of the near-IR (700–750nm)slopes in Lake Taihu and Lake Chaohu.
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K.Shi et al./Journal of Great Lakes Research 40(2014)308–316。