1. SIO 210: Light and Optics Oct. 12, 2009 Uwe Send (usend@ucsd.edu, x26710)usend@ucsd.edu Reading: DPO chapter 3 J.R. Apel, Principles of Ocean Physics, Academic Press N.G.Jerlov, Marine Optics, Elsevier Publishing Optical properties and availability of light are important for physical, chemical, and biological processes, and for the useage of optical methods (like satellite remote sensing).

2. The ocean is transparent to sound All about this spectral window today

3. In order to correctly interpret subsequent figures, we need understand the various terms in optics: (careful, always look at units, terms like “flux” and “intensity” are NOT used like elsewhere in physics, where those are per area for example) Need concept of “solid angle”: The solid angle Ω gives the area of angles where light is coming from (or going to). Unit is “steradian” [sr]. Gives the area cut out on a unit sphere. Or : Ω r gives the area cut out on a sphere of radius r. The solid angle covering ALL DIRECTIONS (total area of unit sphere) is 4π.

4. Solid angle element dΩ dΩ=sinθ dθ dφ ∫∫∫ dΩ =sin θ dθ dφ = 4π π2π2π θ,φθ,φ00 Integration over whole sphere gives

5. “radiant flux” or “radiant power” Φ : The measure of radiant energy that is emitted, received, absorbed in a time interval, unit Watts [W] “radiance” L: The radiant flux in/from a certain direction PER perpendicular area and PER solid angle, unit Watts per square meter per steradian [W m -2 sr -1 ] Side view of irradiated area A Perpendicular (projected) area, A p = A cosθ Solid angle, Ω Flux Φ θ Surface normal ΔΦ(θ,φ) A p ΔΩ L = ΔΦ(θ,φ) A cosθ ΔΩ = = d2Φ(θ,φ)d2Φ(θ,φ) dA cosθ dΩ L = or

6. “Irradiance” E : The total radiant power hitting (or leaving) a specifically oriented area that is emitted, received, absorbed in a time interval, unit Watts per square meter [W m -2 ] Need to sum over radiation from ALL directions, but oblique (non-perpendicular) radiation gets diluted (weakened) by factor cos(θ). Side view of irradiated area A Perpendicular (projected) area, A p = A cosθ Radiance L 2 θ Radiance L 1 Total power received by A is L 1 ΔΩ A + L 2 ΔΩ A p = L 1 ΔΩ A + L 2 ΔΩ A cosθ Power per area then is E =L 1 ΔΩ + L 2 ΔΩ cosθ π2π2π ∫∫ L cosθ sin θ dθ dφ 00 E = ∫ L cosθ dΩ = E d is downward part, E u is upward part This is the quantity which describes energy hitting e.g. the sea surface, or a flat surface under water !

7. Note that Irradiance depends on orientation of the area and does not give equal weight to radiation from high above vs. from an oblique angle. A measure for total radiation independent of direction is “Scalar Irradiance” E 0 : E 0 = ∫ L dΩ 4π4π Hard to measure and less practical significance…. NOTE: a sphere is equally sensitive to all directions, but measures irradiance (received power per surface area) of ¼ E 0 (since capture area is πr 2 but surface area is 4πr 2 )

8. Caution/complication at sea surface: Irradiance E gives only total power HITTING a piece of sea surface (adding up all directions). But what happens with it depends on direction again (degree of reflection, scattering, refraction)  at sea surface often need to integrate over all directions anyway (or use average reflectivity, scattering, etc)… see subsequent figures.

9. Main light source: incident solar radiation Approx 30% albedo as seen from space albedo at sea surface

10. Solar radiation reaching the sea surface: sun atmosphere

11. Remaining wavelengths at different depths (clear seawater):

12. Reflection at the surface: 98% 2% ΦiΦi ΦrΦr ΦtΦt vertical incidence Reflection coefficient r = Φ r / Φ i Depends on angle θ and roughness (wind). This is NOT the albedo (albedo is larger since also contribution from ocean interior) !!!

13. Surface reflection coefficient vs. incident angle for different wind speeds Direction of wind in plane of incidence/reflection

14. Refraction when entering the water: θiθi θtθt sin θ i / sin θ t = n ≈ 4/3, n is function of T, S, λ ! no surface light from here Looking up, all surface light is compressed into angle +/-48.3°

15. Refraction coefficient as fn of T,S, λ  digits after the 1.3

16. Effects on radiation within the ocean: absorption (by dissolved substances and pigments) removal of energy from a beam of light (makes heat, chemical energy, fluorescence, etc) a = - 1/Φ dΦ a /dr (beam absorption coeff, unit m -1 ) Φ ΦtΦt ΦbΦb ΦaΦa These are true water properties, independent of light incidence, angle distribution, etc ! scattering (by particles, inhomogeneities) only redistributes direction of radiation total energy removed from beam by scattering in all directions b = - 1/Φ dΦ b /dr (beam scattering coeff, unit m -1 ) attenuation c = a + b (beam attenuation coeff, unit m -1 )

17. Scattering within the ocean: Effect on propagation of radiation Scattering process by particles

18. Typical log distributions of particle sizes

19. Absorption coefficient for pure seawater

20. yellow substance Particulate substances Chlorophyll A Wavelength distribution of absorption coeff. a for some sea water substances

21. Absorption coefficient for various photosynthetically active pigments

22. Beam attenuation c was simple: absorption and scattering REMOVES energy from beam. Real light is diffuse, from all directions  scattering from other directions thus also ADDS energy into a given direction absorption in a layer of thickness dz is larger for oblique angles Therefore, irradiances E (E, E u, E d, E net, E 0 ) have a different vertical attenuation coefficient K, which also depends on distribution of light ! K = -1/E dE/dz

23. Diffuse attenuation coefficient for some typical chlorophyll-like pigment concentrations

24. Albedo:  E out E in Albedo = E out /E in (only shortwave, no thermal radiation) Albedo is 4.5% for clear smooth seawater if all radiation comes vertically from above (θ=0°), 13.5% for θ=70°. For diffuse light it depends on the distribution over angles.

25. Albedo for smooth and rough sea surface, vs angle Albedo for smooth sea surface Albedo with wind roughness

26. Minimum albedo (i.e. without clouds) from space (i.e. also includes atmospheric reflection/scattering). Shows much higher values at high lat since sun at lower angles there

27. Net available radiation at depth, relative comparisons. Result of reflection, albedo, refraction, scattering, absorption

28. Net available radiation at depth, in real irradiance units (2 extreme cases)

29. Photosynthetically available radiation (PAR): The available power per area in 400-700nm range. Usually in units of light quanta (Einstein [E]), 1 Wm -2 ≈ 2.5 x 10 18 E s -1 m -2 Conversion of 1mol of CO 2 into organic form via photosynthesis requires approx. 10 E.

30. Jerlov water type classification (I-III open ocean, 1-9 coastal)

32. θ φ dθdθ sinθ dφ dΩdΩ