Radiative Transfer

Christian Mätzler & Jaro Ricka

Institute of Applied Physics

Spring Semester 2009

Advanced Lecture Course S7149 U Bern

Contents

• Introduction • The Radiative Transfer Equation• Solutions Without Volume Scattering• A Simple Case With Scattering• Random Walk and Diffusion (under construction)• Single and Multiple Scattering (under construction)• Monte Carlo Methods (under construction)• Lorenz-Mie Scattering on Spheres• Polarised Radiative Transfer (under construction)• Special Interests ???

1 Introduction: 1.1 Historical Overview

Radiative transfer is a tool for

- astronomy and astrophysics,

- remote sensing of the earth surface atmosphere and ocean,

- assessment of the light and heat transport in the natural (climate, hydrosphere, meteorology, biosphere)

- technical (paint, paper, textile, architecture, imaging, medicine)

- cognitive human environment (e.g. in art).

Radiative transfer describes the emission, propagation, scattering and absorption of (thermal) radiation.

Almost everything we know about the universe and a lot about our environment has been brought to men by radiation. Thus radiative transfer is as old as vision.

Introduction: Historical OverviewToday's knowledge on (thermal) radiation is based - among others - onWillebrod Snell (1591-1626)Friedrich Wilhelm Herschel (1738-1822)Josef von Fraunhofer (1787-1826)Augustin Fresnel (1788-1827) Robert Bunsen (1811-1899)Gustav Robert Kirchhoff (1824-1887): Application of the first and

second laws of thermodynamics let Kirchhoff formulate a law on radiation in 1860, stating that under local thermodynamic equilibrium the emissivity of a given object is equal to its absorptivity.

James Clark Maxwell (1831-1879) stated that magnetism, electricity, and light are different manifestations of the same fundamental laws.

Max Planck (1858-1947) found a function that describes the spectral shape of thermal radiation, giving a key to a new area of physics, quantum theory, by the introduction of the constant h.

Albert Einstein (1879-1955) first understood the Planck function as a photon signature.

Introduction: Historical Overview

One of Herschel's experiments to investigate the different heating powers of the colours of sunlight led todiscover “dark” infrared rays

Introduction: Historical Overview

Experimental rules of Bunsen revealed properties of low and high optical thickness:

Rule 1 : A hot and opaque solid, liquid or highly compressed gas emits a continuous spectrum.Rule 2 : A hot, transparent gas produces an emission spectrum with bright lines. The number and colours of these lines depends on which elements are present in the gas, constituting signatures of these elements.Rule 3 : If a continuous spectrum passes through a transparent gas at a lower temperature, the gas generates dark absorption lines, whose number and colours depend on the elements in the gas.

Missing was the understanding of line positions, strengths and widths. The driving questions in spectroscopy led to the fast and successful development of

quantum theory in the early 20th Century.

Introduction: Historical Overview

Gustav Kirchhoff Max Planck

Introduction: Historical Overview

Fathers of Radiative Transfer

Introduction: Historical Overview

Early publications on the transport of radiation, i.e. radiative transfer, in dilute media were bySir Arthur Schuster (1851-1934) and Sir Arthur Eddington (1882-1944) in astrophysics, andKubelka and Munk (1931) for the paper industry.The topic was deepened by collected papers and textbooks of Subrahmanyan Chandrasekhar (1910-1995) and Hendrik Christoffel van de Hulst (1918-2000). That the situation is different in dense media (refractive) was already noted by Kirchhoff, and first insight was given by David Hilbert (1862-1943) in 1912. The effects can be expressed by the Fundamental Theorem of Radiometry (Wyatt, 1978) as used in radiation transfer in natural waters (Mobley, 1994), and with more complications in anisotropic plasmas as described by George Bekefi (1925-1995) in his book of 1966.

Introduction: Historical Overview

The concept of radiance I

A characteristic figure from Bekefi's book on radiation processes in plasmas with inhomogeneities and

anisotropic behaviour.

Introduction: Historical Overview

Artists recognised radiative transfer effects, too.

Canale Grande in Venice by William Turner, painted in 1835

Introduction: Historical OverviewNature laboratory

Introduction: Historical Overview

Introduction: Historical Overview

Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“

benötigt.

Introduction: Historical Overview

Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“

benötigt.

Introduction: Historical Overview

Introduction: Historical OverviewGlory above clouds in Greenland

Introduction: Historical OverviewRainbows near sunset

Introduction: Historical Overview

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Introduction: Historical OverviewCircum zenithal arc

Introduction: Historical OverviewCircum zenithal arc