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Understanding Scattering in Radiative Transfer for Meteorological Applications

Exploring the radiative transfer equation with a focus on scattering phenomena, including absorption, emission, and different scattering regimes such as Rayleigh, geometrical optics, and Mie scattering. Discussing the importance of scattering in meteorological studies, satellite observations, and radar applications, and how it helps in understanding and measuring cloud properties from backscattered solar radiation.

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Understanding Scattering in Radiative Transfer for Meteorological Applications

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  1. Scattering Radiative Transfer Ralf Bennartz Cooperative Institute for Meteorological Satellite Studies University of Wisconsin – Madison

  2. Outline • What we want to know and why do we need it? • The radiative transfer equation revisited. • Different scattering regimes • Molecules, aerosols, cloud droplets, rain, birds, planes, the moon. • Recap: What is important?

  3. Why is scattering important? • We see scattered radiation. • Clouds scatter radiation back to space (energy loss) • Meteorological applications • E.g. radar

  4. What does a satellite observe? • Detects number of photons per exposure time at a given wavelength (or wvl range)traveling from viewing direction into detector • No. of photons, direction, per time  RADIANCE • We need to physically and quantitatively understand the relation between observed radiance and state of the atmosphere • Radiative Transfer Equation

  5. What can happen to photons? • 1. Photons can be ABSORBED • 2. Photons can be EMITTED • 3. Photons can be SCATTERED Let’s now build a budget equation for a beam of photons I(θ, ϕ) traveling in a certain direction (θ, ϕ): dI ds= Sources - Sinks Done….. Theoretical physics is so great…

  6. What can happen to photons? • 1. Photons can be ABSORBED • 2. Photons can be EMITTED • 3. Photons can be SCATTERED Let’s now build a budget equation for a beam of photons I(θ, ϕ) traveling in a certain direction (θ, ϕ): dI ds= Sources - Sinks Done….. Theoretical physics is so great…

  7. Scattering into line of sight: SOURCE Scattering Scattering out of line of sight: SINK θS

  8. Radiative Transfer Equation including scattering Alright… mdI = -I Attenuation dt + (1-w0)B Thermal Source w0 4p W'ò + I(W')P(W',W)dW' Scattering Source This is the radiative transfer equation including scattering All the SINKS are in the First term (-I) Scattering Source is the last term Bad news: Can only be integrated numerically b/c of ugly integral in last term…

  9. Quantities we already know…. m = cos(QS) : Cosine of Zenith angle ¥ ò d(z)= bAdz : Optical Depth z t(z,m)= e-d(z)/m : Transmission W(z,m)= -dt : Weighting Function dz

  10. Couple of new quantities P(W,W') : Scattering Phase Function ¥ ò d(z)= bS+bAdz z : Total Optical Depth bS w0= : Single Scatter Albedo bS+bA • Scattering Phase Function determines where radiation gets scattered….. • Single Scatter Albedo gives importance of scattering.

  11. Scattering Regimes • Size parameter x=2πr/λ determines scattering regime • Rayleigh scattering: Object much smaller than wavelength • Geometrical Optics: Object much larger than wavelength • Mie Scattering: In between Figure from Petty (2006)

  12. Cloud or Smoke? From HP Roesli

  13. Cloud or Smoke? • To the right are the reflectances at 0.6, 0.8, and 1.6 microns in identical units. • How does the feature appear in the different bands? • What is the difference? • What does this tell you about the particles? • So, is it cloud or smoke? From HP Roesli

  14. What scattering regimes? Blue sky/red sunset? This is Rayleigh regime… Scattering efficiency depends x4 Rainbow? Geometrical Optics. Can be understood using Ray tracing Rain with radar? Rayleigh Clouds and sunlight? Mie scattering

  15. Recap • Scattering important for solar spectral range but also for various other application (e.g. radar) • Scattering redistributes energy. Phase function tells us how. • Scattering can be source or sink in radiative transfer equation. • Single scattering albedo tells us how important scattering is in a given situation. • Next: How can we measure cloud properties from backscattered solar radiation?

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