Basic Properties of Radiation, Atmospheres, and Oceans

Transcription

1 Basic Properties of Radiation, Atmospheres, and Oceans Jean-Sébastian Tempel Department of Physics and Technology University of Bergen 16. Mai 2007 phys264 - Environmental Optics and Transport of Light and Particles

2 Outline 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

3 Outline Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

4 Extraterrestrial Solar Flux Terrestrial IR flux S(ν)

5 Extraterrestrial Solar Flux Terrestrial IR flux Solar irradiance ( Total instantaneous radiant energy falling on a unit surface at distance 1au from the Sun ): S = dνs(ν)[w/m 2 ] 1368W/m 2. (1) Deviation from blackbody curve ( T sun = 5778 K) due to: non-isothermal atmosphere optical depth varies with frequency

6 Extraterrestrial Solar Flux Terrestrial IR flux maybe this slide should be in a presentation of Ladislav-part??? Fundamental rule: a radiating object emits energy most efficiently at wavelengths where τ(ν) 1. Where atmosphere is transparent, it neither absorbs nor emits. Where atmosphere is opaque, its radiative energy is prevented from leaving the atmosphere, because it is reabsorbed by the surrounding medium. If τ(ν) = 1, a balance is struck between these two opposing tendencies.

7 Outline Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

8 Extraterrestrial Solar Flux Terrestrial IR flux Deviations from blackbody! Regions of min. emission arise from upper cold regions of the atmosphere, where τ(ν) 1. Highest emission arises from the warm surface in transparent spectral regions. Figure 2: Thermal emission spectra of the Earth measured by the IRIS Mi

9 Comparing both... Extraterrestrial Solar Flux Terrestrial IR flux Solar spectrum: λ = 290-3,500 nm ( shortwave ). Terrestrial spectrum: λ > 3,500 nm ( thermal IR ). No overlap!

10 Outline Flux of Sun and Earth Hydrostatic and Ideal Gas laws 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

11 Hydrostatic and Ideal Gas laws Atmospheres are highly compressible, oceans nearly incompressible. Propagation of visible light along horizontal path almost without attenuation; strong attenuation in oceans. hydrostatic equilibrium requires the pressure p to support the weight of the fluid above it. Ideal gas law (good approx.) leads to: ( z ) p(z) = p(z 0 ) exp dz /H(z ) z 0 H(z ) is the atmospheric scale height, constant up to the homopause (95km): 29.3 T [m]. (2)

12 Hydrostatic and Ideal Gas laws Atmospheres and oceans have a tendency to form a vertically stratified, but horizontally homogeneous medium. Exceptions: clouds/aerosol. Responsible physical processes: Upward transport of heat expands air near the surface. Since pressure tends to remain constant, the air density decreases. Air is more buoyant than overlying cooler air: instability, air is set into small-scale turbulent motion. Rising air cools by expansion, and displaces cooler air. Upper cooler air sinks and compressively heats. In equilibrium: ( ) T = g. (3) z ad c p

13 Hydrostatic and Ideal Gas laws

14 Outline Flux of Sun and Earth Hydrostatic and Ideal Gas laws 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

15 Hydrostatic and Ideal Gas laws Interaction Processes in atmosphere Photoionization and -dissociation Absorption of UV-B by O 3 in the ozone layer Scattering of UV-A and visible radiation by clouds & aerosols Absorption of near-ir radiation (O 3, H 2 O, CO 2 ) Absorption/Emission of thermal IR radiation by surfaces and IR-active gases.

16 Hydrostatic and Ideal Gas laws Radiatively-active atmosph. constituent height profile

17 Energy Budget(1) Hydrostatic and Ideal Gas laws Let E be the total thermal energy, then we get the average column-integrated energy: E t E = E/4πR 2 (4) N = (1 ρ)f s F TOA. (5) Here, N is the net flux at the TOA. The mean outgoing IR radiation F TOA can be described by: F TOA T eff σ B T 4 s. (6) Climate sensitivity

18 Energy budget(2) Hydrostatic and Ideal Gas laws Averaging over several years shows: N 0. [ (1 ρ)f s ] 1/4 T e =. (7) σ B With ρ = 0.3 and F s = S/4 we get T e = 255K = 18 C. Difference to Earth s mean temperature T s = +15 C due to greenhouse effect.

19 Climate Sensitivity Hydrostatic and Ideal Gas laws Considering small pertubation N, the feedback or direct response Ts d can be calculated: N + N T s T s = 0 (8) Ts d = αn (9) [ ] 1 F with α = TOA (1 ρ)f s. (10) T s T s α is called the climate sensitivity. See net flux

20 Outline Flux of Sun and Earth Vertical Structure 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

21 Mixed Layer and Deep Ocean Vertical Structure Upper Mixed Layer About 50 to 200 m in depth, varies with season. nearly uniform temperature and salinity. maintained by turbulent transport caused by mechanical stirring (wind stress).

22 Mixed Layer and Deep Ocean Vertical Structure Upper Mixed Layer About 50 to 200 m in depth, varies with season. nearly uniform temperature and salinity. maintained by turbulent transport caused by mechanical stirring (wind stress). Deep Ocean, average depth: 4 km Transition to colder, denser bottom water marked by an abrupt decrease in temperature (thermocline), and an abrupt increase in salinity (pycnocline).

23 Vertical Structure Mean Temperature / Depth profiles Depth (m) Mixed Layer Main Thermocline Zone Temperature ( C) Upper Zone Deep Zone Winter Seasonal Thermocline (summer) Dicothermal Layer 2000 Low Latitudes Mid Latitudes High Latitudes Figure 10: Typical mean temperature/depth profiles for the open ocean. The dicothermal layer refers to a layer of cold water that often occurs in northern high latitudes between 50 and 100 m. Stability in this layer is maintained by an increase in salinity with depth.

24 Vertical Structure Seasonal Variability of Thermocline 0 Temperature ( C) March May July August September Depth (m) November January gure 11: Daily short-wave radiation received at the sea surface in the absence of clouds. Units are W m 2 ].

25 Outline Flux of Sun and Earth Vertical Structure 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

26 Vertical Structure The radiative energy budget of the ocean is important: intimate coupling of ocean s with atmosphere. Because of high IR absorptance, ocean must be an efficient emitter of thermal radiation (Kirchhoff s law). Water is very opaque in IR: skin temperature (daytime) may be appreciably different from that of water just below the surface. But usually impurities in oceans play a major role in absorption/scattering.

27 Vertical Structure Reflectance of light in pure water is 0.02, but ocean s reflectance is 7% (due to ocean particles). Transperancy window between 0.4 and 0.6 µm, coincides with atmospheric window and with peak in solar spectrum! Blue color is due to absorption & scattering processes (compare next figure). In more fertile waters, color can shift to green or red depending on type of phytoplankton and organic substances.

28 Vertical Structure Absorption Coefficient of Ocean 10,000 1,000 Infra-red Visible Ultra-violet Absorption Coefficient (cm -1 ) Wavelength (µm) Figure 13: Typical absorption coefficient of the ocean.

29 Outline Flux of Sun and Earth 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

30 Propagation of light described in geometrical terms, sharp pencil. Energy transport occurs along direction of the beam. Direction of beam determined by gradient of m = m r + m i i. In radiative transfer theory: m = const., ignoring dispersion & ray bending. Ray incident on atmosphere splits up into infinite number of incoherent beams (all directions).

31 Angular Beam n^ θ ^ Ω da dω r Figure 1: The flow of radiative energy carried by a beam in the direction ˆΩ through a transparent surface element da. The flow direction ˆΩ is at an angle θ with respect to the surface normal ˆn (cos θ = ˆn ˆΩ).

32 Net rate of radiative energy flow, spectral net flux: Basic State Variables F ν = d 3 Relationship between Flux and Intensity E dadtdν [Wm 2 (15) Hz 1 ]. (11) Combination Basic State of the half-range Variables fluxes yields Spectral the net Intensity flux: and its Integration overangular all solid angles Moments yields (12) the spectral net flux The angle between F ν = F ν + ˆn and Fν the = direction 4π dω cos of θi propagation ν [W m 2 ˆΩ ishz denoted 1 ]. by θ. The energy per unit area, unit solid angle, unit frequency, and unit time is: If the spectral The spectral intensity intensity I ν ( r, ˆΩ) at or a point radiance is independent I of the direction ˆΩ, ν defined as the ratio it is said to be isotropic. If it is independent of position, it is called homogeneous. d 4 E [ I ν = W m 2 sr 1 Hz 1]. cosθdadtdωdν The spectral intensity is both isotropic and homogeneous in the special case of thermodynamic equilibrium, when the net flux is zero everywhere in the medium. Note that, in addition to dividing by dωdνdt, we have divided by the factor This cos θ follows = ˆn ˆΩ. fromthis thefactor that multiplied even though by dathe is the hemispherical projectionfluxes of the aresurface finite, they element areonto of equal the plane magnitude normal and to opposite ˆΩ. direction. Therefore no net energy flow Note can also occur that in if ˆn this and equilibrium ˆΩ are directed case. into opposite hemispheres, then ˆn ˆΩ is

33 Outline Flux of Sun and Earth 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

34 24 Flux of Sun and Earth Some (23) Perhaps the most important property of the intensity is expressed in the following theorem (see Figure 2): Some (23) Perhaps the most important property Theorem of the intensity I: is expressed in the following theorem In a transparent (see Figure 2): medium, the intensity is constant along a ray. Theorem I may be generalized Theorem to applyi: to a beam which is reflected any number In a transparent of times by perfectly-reflecting medium, the intensity mirrors: is constant along a ray. Theorem II: Theorem I may be generalized to apply to a beam which is reflected any The number intensity of times remains by perfectly-reflecting constant along mirrors: a ray upon perfect reflection by any mirror or combination of mirrors. Theorem II: The intensity remains constant along a ray upon perfect reflection by any mirror or combination of mirrors. 24

35 Some (24) A third property of the intensity applies to refraction in a transparent medium of variable index of refraction. The theorem applies for discrete changes in m(ν) as long as reflection at the interfaces can be neglected: Theorem III: The quantity I ν /m 2 (ν) remains constant along a ray in a transparent medium, provided that the reflectance at each interface can be neglected. The quantity I ν /m 2 (ν) is called the basic radiance. Clearly, Theorem I is a special case of Theorem III. 25

36 Outline Flux of Sun and Earth 1 Flux of Sun and Earth Extraterrestrial Solar Flux Terrestrial IR flux 2 Hydrostatic and Ideal Gas laws 3 Vertical Structure 4

37 Beam passes through volume with optically active The (27) particles. Interaction: absorption & (multiple) scattering. It is found experimentally that the degree of weakening depends linearly upon both the incident intensity and the amount of optically active matter along the The beam beam direction is(proportional said to have to the suffered length ds): extinction. The (Differential Form) di ν I ν ds. We define the constant of proportionality to be the extinction coefficient k.

38 The Differential Equation of Radiative Transfer (35) Flux of Sun and Earth We first define in a formal way the emission of radiative energy by a differential volume element within the medium. We ignore any time-dependence of the radiation field. Consider again a slab of thickness ds, and cross sectional area da, filled with an optically active material giving rise to radiative energy of frequency ν in time dt. This energy emerges from the slab as an angular beam with directions within the solid angle dω around ˆΩ. The Differential Equation of Radiative Transfer (36) The emission coefficient is defined as the ratio: We now have general definitions for both the loss and the gain of radiative energy in aj ν beam, ( r, ˆΩ) and d 4 E = may therefore write da ds dt dν dω = thed 4 net E rate of change [W mof 3 the Hzintensity 1 sr 1 ]. along the beam direction. dv dt dν dω Combining the extinction law with the definition of emission, we have: where k(ν) = σ(ν) + α(ν). di ν = k(ν)i ν ds + j ν ds Dividing by k(ν)ds, the differential optical path dτ s, we find: di ν = I ν + j ν dτ s k(ν). The ratio j ν /k(ν) is given the special name of the source function: 38 S ν j ν k(ν) [W m 2 Hz 1 sr 1 ].

39 The Differential Equation of Radiative Transfer (37) Our fundamental equation may be written in three mathematically equivalent ways: The differential equation of radiative transfer: di ν dτ s = I ν + S ν ; di ν ds = k(ν)i ν + k(ν)s ν ; ˆΩ I ν = k(ν)i ν + k(ν)s ν. In the third form the gradient operator emphasizes that we are describing a rate of change of intensity along the beam in the direction ˆΩ. ˆΩ I ν is sometimes called the streaming term. In Example 2.6 a derivation is provided of an extra term (1/c) I ν / t, which must be added to the LHS of the equations above when time-dependence cannot be ignored.

40 Literature Flux of Sun and Earth G.E. Thomas, K. Stamnes: Radiative Transfer in the Atmosphere and Ocean. Cambridge University Press, Cambridge (1999).