scattering/reflectance. it is due to the passage of the e.m. wave from a medium to another of...
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Scattering/Reflectance.It is due to the passage of the e.m. wave from a medium to another of different speed of propagation (refractive index).It depends from:- composition (refractive index) of the medium- relative (to the e.m. wavelength) length of the path of the e.m. within the discontinuity: size, shape and orientation of the medium
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SCATTERING:
Huygens principle
How many wavelengthsthe wave is spending inside a medium with different propagation characteristics?
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Scattering: a geometric optics representation
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Yang et al., “Single-scattering properties of complex ice crystals in terrestrial Atmosphere”, Contr. Atmos. Phys., 71, 223-248, 1998.
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Scattering
Mie scattering & Geometric Optics: Depends from scattering particleamount, shape, dimension & relative orientation particle-wave
Rayleigh scattering: Depends from scattering particleamount
Negligible Scattering: independent from an particle property
&
non spheric
al partic
les methods
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LID
AR
CLO
UD
RA
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R
PR
EC
. R
AD
AR
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RF
. R
AD
AR
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SCATTERING: DEFINIZIONIScattering Singolo
Variabili ottiche di singola particella (SSOP Single scattering optical properties)
- cross sections
- ssa
- phase function
Variabili ottiche di polidispersione
Variabili ottiche di volume
Variabili macroscopiche di strato
Scattering Multiplo
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Proprieta’ fisiche delle singole molecole e Aerosols (composizione)
(p,T)Proprieta’ ottiche delle singole molecole e Aerosols (λ,Ω)
Proprieta’ ottiche del volume (λ,Ω)
Equazione del trasporto radiativo (λ,Ω)Proprieta’ ottiche della superficie/boundaries (λ,Ω)
Soluzione (∫ ∫ …dλdΩ)
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Proprieta’ fisiche delle singole molecole e Aerosols (composizione)
Proprieta’ ottiche delle singole molecole e Aerosols (λ,Ω)
Proprieta’ ottiche del volume (λ,Ω)
Equazione del trasporto radiativo (λ,Ω)
Soluzione (∫ ∫ …dλdΩ)
Processi radiativi d’interazione
Calcolo delle proprieta’ ottiche di volume:Spessore ottico, albedo di singolo scattering, proprieta’ angolari dello scattering (per es: g o matrice di diffusione) o T,R,A
Risoluzione numerica dell’eq. Del trasporto radiativo
Risoluzione numerica di eventuali integrazioni angolari e spettrali
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Scattering: numerical representation
Variabili ottiche di singola particella
- Cross Sections (Efficiencies)
- Single scattering albedo: ω
- Phase function: Scattering Matrix,Tavola P(γ), Coefficienti dei Polinomi di Legendre, Asymmetry factor (g), Approximations (e.g.: HG)
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Diffraction limit
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Scattering: Polarization
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http://www.astro.uva.nl/scatter/
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Source function (solar, plane parallel)
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Metodi numerici per il calcolo delle proprieta’ ottiche di singola particella
• Rayleigh scattering (particelle relativamente piccole)
• Mie scattering (particelle sferiche di dimensioni comparabili con la lunghezza d’onda)
• Metodi numerici per particelle non sferiche (particelle non-sferiche di dimensioni comparabili con la lunghezza d’onda)
• Ottica geometrica (particelle di forma qualsiasi di dimensioni relativamente grandi)
Casi particolari: pr es: coated spherical particles
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Esempi programma di simulazione per scattering Mie http://omlc.ogi.edu/calc/mie_calc.html
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Ottica Geometrica
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Discrete Dipole Approximation
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Parametri per la descrizione della dipendenza angolare
• Scattering matrix
• Phase function– Tabelle– Coefficienti dei polinomi di Legendre– Asymmetry factor – HG approximation
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Accorgimenti numerici: delta-Eddington
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Scattering: numerical representation
Definizione di polidispersioneVariabili di polidispersione -> effective radiusEsempi di forme funzionali di distribuzione
dimensionale:- Junge (power law) (aerosols)- Log-normal (aerosols) - Gamma distribution (clouds)- Marshall & Palmer (precipitation)
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Una distribuzione dimensionale è definita da:
Distribuzione dimensionale
Esempi di distribuzione dimensionale descritta dalla funzione in basso con 2 valori di a e 3 di b
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Calcolo delle proprieta’ di singolo scattering per una polidispersione
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Calcolo dei coefficienti di scattering per 2 specie: A, M.
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(p,T)
La radiazione scatterata da un generico volume dipende dalla intensita’ e distribuzione angolare della radiazione incidente sul volume che pero’ dipende, atraverso lo scattering dei volumi vicini a sua volta dalla radiazione scatterata
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Scattering MULTIPLO: METODI NUMERICI
• Ordini di scattering successivi• Doubling or Adding• Invariant imbedding• Funzioni X e Y• Discrete – Ordinate• Armoniche sferiche• Sviluppo in eigenfuction• Montecarlo• Soluzioni analitiche• Pseudo-assorbimento
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Accorgimenti numerici: delta-Eddington
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Doubling or adding method
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Si definisce per la trasmissione diffusa e per la riflessione:
Un prodotto R1R2 implica: