ESA Training Course Oceanography from Space. Introduction into Hydro Optics

Transcription

1 ESA Training Course Oceanography from Space Introduction into Hydro Optics Roland Doerffer GKSS Institute for Coastal Research September 26, 26 The penetration of light in the sea Source: Batfish in the Maledives 1

2 First Exercise: Determine the 1% depth Problem: you have an irradiance meter, which measures the downwelling irradiance at a wavelength of 44 nm. Your cable has a length that you can operate the instruments to a depth of only 2 m. However, you want to determine the depth with 1% of the surface irradiance (=~ depth of euphotic zone). Plot the irradiance profile on the linear paper, then on the log paper m, 4.2 V 2 m, 3.46 V Downwelling irradiance Ed Linear paper for calculating the penetration depth

3 Log paper for calculating of penetration depth Result of exercise Water depth z (m) rel. downwelling irradiance Ed 3

4 result of exercise, log scale Water depth z (m) rel. downwelling irradiance Ed The pioneers of hydro - optics Secchi, 1865, white disk to measure penetration of light into the sea Fol and Sarasin (1885), photographic plates in the Mediterranean Sea Knudsen (1922) Penetration of light into the sea, used submerged spectrograph with photgraphic plates for recording Shelford and Gail (1922) first use of photoelectric cells for marine observations Shouleikin, 1923: On the colour of the sea Atkins and Poole, 1933, Clarke 1933, Utterback and Boyle, 1933) Design and use of rdadiance and irradiance meters Pettersson, 1934: beam transmittance and scattering meter Hulbert, 1934: The polarization of light at sea Gershun, 1936: The light field Kalle (1938) Problem of the colour of the sea Wattenberg, 1938: Transparency and Colour of Sea Water Whitney, 1938: Transmission and scattering of solar energy by suspension in lake waters 4

5 Pioneers II Takenouti, 194: angular distribution o fof submarine solar radiation, effect of altitude of the sun upon the vertical extinction coefficient Sauberer and Ruttner, 1941: Radiation in inland waters Lauscher, 1947: Radiation theory of the Hydrosphere Kalle (1949) Fluorescence and Gelbstoff Duntley, 1948: Underwater visibility Joseph (1949, 195): vertical attenuation in the visible and UV spectral range, upand downwelling irradiance, reflectance, influence of bottom, used Selen photocells and absorption filters Chandrasekhar, 195: Radiative Transfer Jerlov, 1951: optical studies of ocean waters Timofeeva, 1951: Scattering in the sea Absorption, scattering and beam attenuation Attenuation of a beam by absorption and scattering consider a beam of photons which collide with particles The beam is attenuated by photons, which are absorbed and photons, which are scattered into another direction and, thus, do not reach the detector c = a + b [m -1] 5

6 Beam attenuation Absorption coefficient: a [m-1]loss of radiant flux froam a beam by means of absorption through an infinitesimally thin layer Scattering coefficient: b [m-1]loss of radiant flux froam a beam by means of absorption through an infinitesimally thin layer Beam attenuation: c=a+b, Transmittance T = Ft/F, c= -lnt volume scattering function: β(θ), m-1 sr-1 π b = 2π β ( θ )sinθdθ Scattering function of pure water b [m-1] scattering angle [degree] 6

7 Phase function of particles b(theta)/b [m-1] scattering angle [degree] Radiance Basic radiometric quantities Radiant flux: the time rate of flow of radiant energy F = Q / t, [W] Irradiance: the ratio of the radiant flux incident on an infinitesimal element of surface to the area of that element E (S) = df / ds, Ê = (S) E(S) ds / (S) ds = F / S, [Ω m -2 ] dω Radiance: Radiant flux per unit solid angle per unit projected area of a surface L = d 2 F / dω ds cosθ, [Wm -2 sr -1 ] θ ds 7

8 The cosine law θ= da for cos()=1 de(θ,ϕ) = L(θ, ϕ) cosθ dω θ=45 ο da =da/cos θ for cos(45) = For cos(45) the irradiance has decreased by The irrdiance decreases with the cosine of the solar zenith angle Because the illuminated area per solid angle radiance increases with the cosine Note also the consequence for irradiance measurements: an irradiance sensor has always to be levelled Radiometry Radiant arclength / radius [rad] Circle: 36 deg = 2.pi.r / r = 2.r.pi 1 sr= 36/(2.pi) = 57.3 deg r Steradiant Ω: Sphere surface: 4.pi.r 2 area / radius 2 [sr] sphere: 4.pi.r 2 / r 2 = 4.pi sr r a Irradiance: E [W m -2 µm -1 ], downwelling, upwelling irradiance E d, E u Radiance: L [W m -2 sr -1 µm -1 ] Absorption coefficient: a [m -1 ]Loss of radiant flux froam a beam by means of absorption through an infinitesimally thin layer Scattering coefficient: b [m -1 ]Loss of radiant flux froam a beam by means of absorption through an infinitesimally thin layer volume scattering function: β(θ), m -1 sr -1 π b = 2π β ( θ )sinθdθ Beam attenuation: c=a+b, Transmittance T = F t /F, c= -lnt 8

9 Radiance and Irradiance The radiance at a given point in the spherical co-ordinate system is a function of the polar angle θ and the azimuth angle ϕ de(θ,ϕ) = L(θ, ϕ) cosθ dω; E = 2π L(θ, ϕ) cosθ dω Irradiance, like radiance, is characterized by a value and a direction (which is defined by a normal to the considered surface). Along with the vector irradiance, we can consider the scalar irradiance. Scalar irradiance is the integral of the radiance distribution over all directions about the considered point E o = 4π L(θ, ϕ) dω, [W m -2 ] Transmission and Attenuation Note: for the underwater light field the irradiance attenuation coefficient is only constant, if the angular radiance distribution is constant. Since this is not the case, the k value is only an approximation of the true attenuation. Furthermore, the attenuation coefficient is defined for monochromatic light T= E(z2) /E(z1) Transmission K= -ln(t) Attenuation K k=k/dz [m-1] attenuation coefficient m -1 dz z1 z2 Ed(z) T=exp(-k*dz) 9

10 Relationships between transmission and attenuation Transmission T = Ed(z2)/Ed(z1) for delta z dz = z2-z1 Attenuation K = -ln(t) = -ln(ed(z2)/ed(z1)) for delta z dz = z2-z1 Attenuation coefficient (per meter) : k= -ln(ed(z2)/ed(z1))/(z2-z1) dimension is 1/m or m -1 Transmission per meter: t = exp(-k) = exp(-k/(z2-z1)) Transmission: T = exp(-k*dz) 1% depth: ln(.1)/k, Signal depth z9 = 1/k Characteristics of underwater light field Downwelling irradiance: Upwelling irradiance: Downwelling scalar irradiance: Upwelling scalar irradiance: Diffuse attenuation coefficient: de d, u, od, ou = - K d, u, od, ou de d, u, od, ou dz; K = - de / Ε dz = - d lne / dz; K d K u K od K ou.; 2π π / 2 E d = dϕ L( θ, ϕ)cosθ sinθdθ 2π π E u = dϕ L( θ, ϕ)cosθ sinθdθ π / 2 2π π / 2 E od = dϕ L( θ, ϕ)sinθdθ 2π π E ou = dϕ L( θ, ϕ)sinθdθ π / 2 Optical depth: ζ = K d z or τ = c z 1

11 transmission air-water Snell s Law sinθ a sinθ w n = n w a n w = 1.34 Specular reflectance Fresnel s Equation for unpolarized light sin ( θ a θ w) tan ( θ a θ w) r = sin 2 ( θ + ) ( + ) a θ w tan θ a θ w 11

12 Remote Sensing Reflectance For comparison with the satellite-sensed signal, it is needed to consider the above-surface remote-sensing reflectance which is the ratio of the upwelling radiance to the downwelling irradiance just above the sea surface R RS (λ, θ, ϕ, + ) = L u (λ, θ, ϕ, + ) / E d (λ, + ). The subsurface upwelling radiance L u ( - ) passing through the sea surface decreases due to reflection and refraction; the above-surface downwelling irradiance passing through the sea surface decreases due to reflection but it is augmented due to internal reflection of the subsurface upward flux from the sea surface dω L u ( + ) = (t - /n 2 ) L u ( - ); E d ( - ) = t + Ed ( + )/(1- γr) R RS = (t - t + /n 2 ) r RS /(1- γr); R RS = ζ r RS /(1- Γ r RS ); dω/n 2 ζ= t - t + /n 2 ; Γ = γq. For nadir viewing: ζ.518, Γ 1.562, (Lee et al. 1998). Spectral Colour and wavelength in Nanometer (nm) nm = 1 billion of a Meter = or million part of a millimeters 12

13 Spectral characteristics of upwelling radiant flux Irradiance reflectance: the ratio of the upwelling irradiance to the downwelling irradiance R(λ, z) = E u (λ, z) / E d (λ, z). The irradiance reflectance just beneath the sea surface ( subsurface irradiance reflectance ) is a characteristic of true ocean color R(λ, - ) = E u (λ, - ) / E d (λ, - ). Because the light collectors with a narrow field of-view are used for remote sensing (for example, SeaWiFS field-of-view is less than three angular minutes), it is common to deal with remote sensing reflectance. Subsurface remote-sensing reflectance: r RS (λ, θ, ϕ, - ) = L u (λ, θ, ϕ, - ) / E d (λ, - ), [sr -1 ]; r RS (λ, θ, ϕ, - ) = R (λ, - ) / Q (λ, θ, ϕ, - ), Q (λ, θ, ϕ, - ) = E u (λ, - ) / L u (λ, θ, ϕ, - ), [sr]; In the case of the isotropic angular distribution of L u (θ,ϕ): Q(θ,ϕ) = π; in the real cases Q(θ,ϕ) = Angles 13