Satellites Observations

Temperature and albedo

What we need to do

• How do we get values of temperature and albedo (reflectance) using the instruments on the satellites?

Today: Emission and Temperature

• And homework

Emission

• Broadband emission

• Or blackbody emission

• All objects with temperatures above 0 K will emit radiation and the radiation that they emit is dependent upon the temperature.

Planck’s Law

• The energy emitted by an object is a function of its temperature

• The emitted spectrum is also a function of its temperature

From Wallace and Hobbs

Blackbodies

• Perfect emitters: give off the max energy for each wavelength at each temperature

• This is given by

1exp

2)(

52

kThchc

TB

Bλ = Radiance at wavelength λ, and temperature T (K) (in Wm-2sr-1μm-1)

C = speed of light

h = Planck’s constant (6.626 x 10-34Js)

k = Boltzmann’s constant (1.38 x 10-23 JK-1

Solid angles

• The solid angle is the proportion of the surface area of a sphere subtended by the 2 dimensional angle. (See picture drawn on board)

• It is measured in steradians – sr.

Planck’s function for different temps

From Kidder and Vonder Haar

Not a blackbody

Wien’s displacement law

• Differentiate Planck’s law to find maximum of function

• Where differential is 0

• Wien’s law relates temperature to wavelength at which maximum energy is emitted

• Wavelength at which maximum energy is emitted is ‘colour’ of emitting object

dB/dλ = 0

Total Energy Emitted

• Integrate Planck’s function

0

)( ddTBEBB

An exercise for the student!

EBB is total energy of blackbody in Wm-2

Stefan- Boltzmann Law

E = T4

is Stefan’s constant

5.67 x 10-8 Wm-2K-4

Emissivity

• Most objects are not blackbodies• They emit less than the maximum amount of

energy for their temperature• Emissivity ( - sometimes called emittance)

varies with wavelength

λ = emitted radiation at λ / Bλ (T)

For blackbodies = 1

Typical emissivities

From AMS – Weather Satellites

Quiz

• Where was the highest official temperature recorded?

Measuring temperature

• Step 1: Calculate radiance (the amount of energy received by the sensor)

• Step 2: Invert Planck’s equation to get temperature from energy emitted at a given wavelength

Step 1

dcIR I is byte integer value

c & d are constants (we calibrate the instrument to get this right)

Do not have to worry about incident solar radiation and correct for it as the reflected radiation at the wavelengths used is far smaller than that emitted (especially at night!)

Invert Planck’s equation

)1/ln(/ 312

RncncT

Where c1 and c2 are constants found from Planck’s equation and n is the central wavenumber of the IR channel (in μm-1)

(Students are invited to prove the validity of this conversion by messing with Planck’s equation.)

Important point 1

• What we get is a ‘radiation’ or ‘brightness’ temperature– This will not be the true temperature of the

object and needs correcting for emissivity (if we know that)

Important point 2

• What we get is a ‘skin’ temperature– This is the temperature of the surface rather

than the bulk of the object– The surroundings (energy transfers) are more

closely related to total energy content rather than surface temperature

Important Point 3

• Surface temperature is not surface air temperature (1.2m or 2m temperature)

• Think about how hot (cold) pavement is compared to the air above it

Errors in T

• Due to scattering and absorption in the atmosphere

• In IR this is substantially due to water vapour – which is variable

• Can be corrected for

Absorption

• Chemistry!!!

• EM radiation comes in photons which are indivisible (wave-particle duality is a useful thing)

• A photon can be absorbed if the energy it has equals that needed by the absorbing medium for some energy transition

Molecular absorption

• Most atmospheric gases are molecules (N2, O2, O3, CO2, H2O, etc)

• Molecules have energy levels related to the vibration of the bonds between atoms

• And they have rotational modes also

• These produce broader absorption bands

Windows

• An atmospheric window is a part of the spectrum which is transparent to EM radiation

• Windows are crucial for life and remote sensing as they allow us to see through the atmosphere

2 windows

• Visible: 0.3 - 0.8μm

• IR: 8 - 12μm

Not windows

• Specific wavebands that are absorbed (and emitted) by particular molecular species are also useful– Water vapour channel– Ozone measurements

Thin Ci

• This really screws things up – avoid if possible

• Other problems are caused by Complex surfaces (eg. Urban areas) and Cu that are smaller than the pixel

Albedo

• Albedo varies with wavelength

• Many substances have high albedo (reflectance) in the visible (e.g. snow), but low albedo in the microwave (e.g. snow)

• Can also have different albedo for different colours and therefore appear coloured (e.g. leaves)

Measuring Reflectance (albedo)

• Measure the energy impacting the sensor in the visible waveband channel

• In Wm-2sr-1μm-1

• Energy reflected per unit time per unit area: Normalised for width of waveband and solid angle view.

Energy transitions

• Electrons in atoms are constrained to certain energy levels

• When a photon is absorbed it must move an electron from one level to another (quantisation)

• But quantum physics is a wonderful thing and Heisenberg said that everything is uncertain so energy bands have width

Errors

• The measurement of albedo has errors due to the scattering and absorption of radiation in the atmosphere

• This is pretty constant and can be corrected for (unless a volcano has erupted)

Review 1: EM

• What we’ve done to date– Various parts of the EM spectrum (esp. those

used in RS)– What objects produce what types of EM (esp.

things on and around the Earth)– What happens to the light as it encounters

matter (esp. the atmosphere)– How wavelength is related to temperature