Absorption and scattering of light, Tworzenie gier, Resources, Water
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//-->10 Absorption and scattering of lightin natural watersVladimir I. Haltrin10.1 IntroductionIn this chapter we restrict ourselves to the problems of absorptionabsorption[1–13], elastic [1, 4, 5, 10, 14–22] and inelastic Raman [23–44] scattering of light,and fluorescence [45–62] in natural waters. Owing to the lack of clear and simplenumerical procedures that connect scattering with easily measurable environ-mental parameters, scattering by air bubbles in water [63–65], Brillouin scat-tering [37, 66–69], and amplification of forward scattering by water turbulence[70, 71] are omitted from consideration. All conclusions of this chapter will beobtained mostly from analysis of experimental data with some additions de-rived from theory and from analysis of numerical computations. We will discussin detail two basic inherent optical properties of natural water, the absorptioncoefficient,a,the angular scattering coefficient,β,and inelastic parameters ofRaman scattering and fluorescence that are included as input parameters in ascalar radiative transfer equation:1∂+n∇+c(λ,x)L(λ,x,Ω) =QE(λ,x,Ω) +QI(λ,x,Ω),v ∂t(10.1)hereL(λ,x,Ω) is a total radiance of light in water that depends on spatialcoordinatesrand timet(herex= (r,t)is a combination of spatial coordinatesand time), and solid angle Ω = Ω(θ,ϕ); vis the speed of light in water;nis aunit vector in the direction of propagation of light;λis a wavelength of light;c(λ,x)is an attenuation (or extinction) coefficient which is a sum of absorptionaand beam scatteringbcoefficients,c(λ,x)=a(λ,x)+b(λ,x),(10.2)with the scattering coefficient expressed through the angular elastic scatteringcoefficientβ(λ,x,cosϑ)as follows:πb(λ,x)=4πdΩβ(λ,x,cosϑ)≡2πβ(λ,x,cosϑ)sinϑdϑ,(10.3)446Vladimir I. Haltrinwhere cosϑ=nn,nis a unit vector in the direction of initial propagation oflight.The right part of eq. (10.1) consists of two source parts, elasticQEandinelasticQI.The elastic sourceQE(λ,r,Ω) =4πdΩβ(λ,r,cosϑ)L(λ,r,Ω ),(10.4)describes elastic scattering of light,i.e.scattering without change in wavelength.The inelastic sourceQI(λ,x,Ω) =j=R,C,Yλ <λdλ4πdΩσj(λ, λ,x,cosϑ)L(λ,x,Ω ),(10.5)describes an input of energy to wavelengthλfrom lower wavelengthsλdue toinelastic processes of Raman scattering, red fluorescence by chlorophyll, and bluefluorescence by yellow substance. Hereσj(j =R, C, Y) corresponds to Ramanscattering, and chlorophyll and yellow substance emission coefficients. We ignorehere anti–Stokes (blue–shifted) components that are significantly weaker thanStokes (red–shifted) components.The previous eqs (10.1)–(10.5) introduce the following basic inherent opticalproperties of water:a(λ,x)– absorption coefficient;β(λ,x,cosϑ)– elastic angular scattering coefficient (or volume scattering func-tion);Rσ(λ, λ,cosϑ)– Raman scattering differential emission coefficient;σC(λ, λ,x,cosϑ)– chlorophyll fluorescence differential emission coefficient;σY(λ, λ,x,cosϑ)– yellow substance fluorescence differential emission coeffi-cient.The dependence onxof all these inherent properties (except Raman scatter-ing emission coefficient) is due to their dependence on concentrations of dissolvedand suspended matter in water. Knowledge of these five basic inherent propertiesis enough to solve any scalar radiative transfer problem in a body of water.Let us introduce additional four auxiliary inherent optical properties that arewidely used in optics of natural waters:elastic light scattering phase function,p(λ,x,cosϑ)=πβ(λ,x,cosϑ),b(λ,x)(10.6)2πp(λ,x,cosϑ)sinϑdϑ = 1;(10.7)10 Absorption and scattering of light in natural waters447single–scattering albedo (= probability of elastic scattering),ω=backscattering coefficient,πbb≡;ca+b(10.8)bB(λ,x)= 2ππ/2β(λ,x,cosϑ)sinϑdϑ;(10.9)probability of backscattering, or ratio of backscattering to scatteringbB(λ,x)B(λ,x)== 2πb(λ,x)and Gordon’s parameter,xG=bBBω.≡a+bB1−ω+Bω(10.11)πp(λ,xcosϑ)sinϑdϑ;π/2(10.10)Parametersω,B,andxGare dimensionless and vary in the following rangefor any possible type of absorbing and scattering media in natural water:≤ω≤1,≤B≤0.5,≤xG≤1.(10.12)Solutions to eq. (10.1) are the basis of deriving various apparent opticalproperties such as diffuse attenuation coefficient, diffuse reflection coefficient,remote sensing reflection coefficient, average cosines over radiance distributionL,lidar equation, and others. In the following sections we consider inherentoptical properties of natural, and mostly oceanic, water, in detail.10.2 Absorption of light in natural waterNatural oceanic, marine or lake water consists of water molecules and impuritiesdissolved and suspended in water. Absorption of light occurs in water molecules,molecules of yellow substance, also known as ‘Gelbstoff’, dissolved organic matter(DOM), or colored dissolved organic matter (CDOM), and different kinds ofchlorophyll molecules that present in phytoplankton cells that grow in naturalwaters. The composition of natural water is very complex and varies from regionto region. In this section we restrict ourselves to a simplistic model that takesinto account four major ingredients of absorption: pure water, two componentsof yellow substance and an average type of chlorophyll. In this approximationthe absorption coefficient of natural water at wavelength of lightλat any fixeddepth can be written as:a(λ)=aW(λ) + 0.06a(λ)C0.65+aCFexp(−kFλ)+aCHexp(−kHλ),CFH(10.13)−1hereaWis an absorption coefficient of pure water in m ;aCis a specific ab-sorption coefficient of chlorophyll in 1/m, andCis dimensionless concentra-448Vladimir I. Haltrintion of chlorophyll,C=CC/C, whereCCis a concentration of chlorophyll inmg/m3, andC= 1 mg/m3. The absorption by yellow substance or DOM issplit into two parts: absorption by fulvic acid and absorption by humic acid.Both components of DOM, fulvic and humic acids, have similar optical prop-erties with different absorption and fluorescence coefficients. For typical marinewater the composition of fulvic and humic acids is, approximately, constant withζ=CH/(CF+CH) = 0.1. By introducing the total concentration of DOMCY=CF+CH,we can rewrite eq. (10.13) in the following simplified form:a(λ)=aW(λ) + 0.06a(λ)C0.65+aCYexp(−kYλ).CY(10.15)(10.14)The numerical values ofaWandaare given in Table 10.1, and coefficientsCaandkjforj=F, H, Yare given in Table 10.2. The spectral behavior of alljabsorption components is shown in Fig. 10.1.1.61.41.2ChlorophyllPure Water1"Gelbstoff" or DOM0.80.6Humic Acid0.40.2Fulvic Acid350400450500550600650700750Wavelength of Light, nmFig. 10.1.The components of absorption of light in natural water10 Absorption and scattering of light in natural waters449Table 10.1.Spectral absorption coefficient of pure water and specific spectral absorp-tion coefficient of chlorophyll [8, 9]λ,nmaw, m−1,a, m−1C380.0382.5385.0387.5390.0392.5395.0397.5400.0402.5405.0407.5410.0412.5415.0417.5420.0422.5425.0427.5430.0432.5435.0437.5440.0442.5445.0447.5450.0452.5455.0457.5460.0462.5465.0467.5470.0472.5475.0477.5480.0482.5485.0487.5490.0492.5495.00.011370.010440.009410.009170.008510.008290.008130.007750.006630.005790.005300.005030.004730.004520.004440.004420.004540.004740.004780.004820.004950.005040.005300.005800.006350.006960.007510.008300.009220.009690.009620.009570.009790.010050.010110.010200.010600.010900.011400.012100.012700.013100.013600.014400.015000.016200.017300.5380.5570.5760.5970.6180.6390.6620.6850.6870.7340.7810.8040.8280.8550.8830.8980.9130.9260.9390.9560.9730.9871.0011.0001.0000.9860.9710.9580.9440.9360.9280.9230.9170.9090.9020.8860.8700.8550.8390.8190.7980.7860.7730.7620.7500.7340.717λ,nmaw, m−1a, m−1C497.5500.0502.5505.0507.5510.0512.5515.0517.5520.0522.5525.0527.5530.0532.5535.0537.5540.0542.5545.0547.5550.0552.5555.0557.5560.0562.5565.0567.5570.0572.5575.0577.5580.0582.5585.0587.5590.0592.5595.0597.5600.0602.5605.0607.5610.0612.50.019100.020400.022800.025600.028000.032500.037200.039600.039900.040900.041600.041700.042800.043400.044700.045200.046600.047400.048900.051100.053700.056500.059300.059600.060600.061900.064000.064200.067200.069500.073300.077200.083600.089600.098900.110000.122000.135100.151600.167200.192500.222400.247000.257700.262900.264400.266500.6930.6680.6570.6450.6310.6180.6000.5820.5550.5280.5160.5040.4890.4740.4590.4440.4300.4160.4000.3840.3700.3570.3390.3210.3070.2940.2830.2730.2750.2760.2720.2680.2790.2910.2820.2740.2780.2820.2650.2490.2420.2360.2580.2790.2660.2520.260λ,nmaw, m−1a, m−1C615.0617.5620.0622.5625.0627.5630.0632.5635.0637.5640.0642.5645.0647.5650.0652.5655.0657.5660.0662.5665.0667.5670.0672.5675.0677.5680.0682.5685.0687.5690.0692.5695.0697.5700.0702.5705.0707.5710.0712.5715.0717.5720.0722.5725.0727.50.267800.270700.275500.281000.283400.290400.291600.299500.301200.307700.310800.322000.325000.335000.340000.358000.371000.393000.410000.424000.429000.436000.439000.448000.448000.461000.465000.478000.486000.502000.516000.538000.559000.592000.624000.663000.704000.756000.827000.914001.007001.119001.231001.356001.489001.678000.2680.2720.2760.2870.2990.3080.3170.3250.3330.3340.3340.3300.3260.3410.3560.3720.3890.4150.4410.4880.5340.5650.5950.5700.5440.5230.5020.4610.4200.3740.3290.2950.2620.2380.2150.2080.1900.1740.1600.1460.1340.1230.1120.1030.0940.086
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