Pat Arnott, ATMS 749, UNR

HOW DO WE TALK ABOUT RADIATION IN THE

ATMOSPHERE?

Pat Arnott, ATMS 749, UNR

Relationship between Spherical and Cartesian Coordinates

Pat Arnott, ATMS 749, UNR

Solid Angle Definition

Pat Arnott, ATMS 749, UNR

Irradiance Definition

F = Irradiance, (also called flux or flux density), is the electromagnetic energy per unit time, per unit area, transported through dA, or deposited on dA. SI units are Watts/m2 when integrated over a distribution function F. (Example: solar flux at the TOA is 1360 W/m2.)

FMonochromatic Irradiance, SI units are W/m3.

Pat Arnott, ATMS 749, UNR

Monochromatic Radiance Definition

I = Monochromatic radiance, is the monochromatic irradiance (measured on a surface normal to the beam) per unit solid angle traveling in a particular direction.

This is the most fundamental measure we can use for radiation in the atmosphere.

Pat Arnott, ATMS 749, UNR

Irradiance - Radiance Relations

Upward irradiance.Note ESPECIALLY the cos term (that gets the normal component of radiance) and the sin term (that helps define the solid angle.)

Pat Arnott, ATMS 749, UNR

Irradiance - Radiance Relations

Special case: I isotropic, same in all directions, like black body radiation from a surface.

Pat Arnott, ATMS 749, UNR

BLACK BODY RADIATION AGAIN: RADIANCE

Note especially the units of radiance on the left.

Pat Arnott, ATMS 749, UNR

ASIDE: EMISSIVITY OF VARIOUS SUBSTANCES

Pat Arnott, ATMS 749, UNR

Irradiance - Radiance Relations

Downward irradiance

Pat Arnott, ATMS 749, UNR

THE BIG PICTURE: Radiation Heating of the Atmosphere

From Oort and Peixoto

Pat Arnott, ATMS 749, UNR

ATMOSPHERE HEATING BY RADIATION: The heating rate is the divergence of the net irradiance (or net flux if you prefer).

From Oort and Peixoto

Pat Arnott, ATMS 749, UNR

ATMOSPHERE HEATING BY RADIATION: The heating rate is the divergence of the net irradiance (or net flux if you prefer).

From Oort and Peixoto

Pat Arnott, ATMS 749, UNR

ATMOSPHERE HEATING BY RADIATION: The heating rate is the divergence of the net irradiance (or net flux if you prefer). This is

the figure caption for the heating rate calculation, and the reference.

2 problems:

1. Is the assumption of stratosphere radiative equilibrium good?

2. Is it correct to separate out the LW emission from components?

From Oort and Peixoto

Pat Arnott, ATMS 749, UNR

Sun and Satellite Perspective: How do the properties of the surface affect what we see?

Pat Arnott, ATMS 749, UNR

Radiance and Irradiance: How do we define radiation?

Types of reflection: Can also think of the reflected light as emitted light from different types of surfaces.

Pat Arnott, ATMS 749, UNR

Geometry for the BDRF (bidirectional reflection function)

ρ(θi,φi;θ f ,φ f ) ≡ BDRF =S0 cos(θi )

I ↑ (θr ,φr )for a clear day.

I ↑ (Ωru ruu) = ρ(

2π∫ Ωi

u ruu,Ωru ruu) I ↓ (Ωr

u ruu)n∑• Ωi dωi for a cloudy day.

S is solar irradiance coming in.

I is the reflected radiance.

Pat Arnott, ATMS 749, UNR

ENERGY BUDGET: 100% in, 100% out. What does it do along the way?

Pat Arnott, ATMS 749, UNR

ASIDE:COMPLEX

REFRACTIVE INDICES OF WATER AND

ICE.

Note that the author DID

NOT show that the real part of the refractive

index for ice at 2.85 microns is

less than 1!

n =c / vphase

vphase =c / n

c=light speed