# Geoinformatics & IT

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geoinformatics:thermal-infrared

# Thermal Infra-red Remote Sensing

Using special sensors and the thermal radiation properties of physical bodies, we can measure surface temperature from a distance. In this project, we'll be using thermal infra-red (TIR) techniques to estimate surface temperatures of an iceberg using thermal camera ground measurements and a land parcel using satellite sensors.

## Theoretical foundation

Some basic notes on blackbody radiation:

• All bodies with temperature above 0 K emit radiation.
• 0 K = ‒273,15 °C
• A blackbody is a theoretical object that completely absorbs all wavelengths of electromagnetic radiation incident on it.
• When a blackbody is heated to a temperature above 0 K, it emits radiation.
• Blackbody radiation at temperatures comparable to the temperature of the earth’s surface (~300 K) is the thermal infrared (TIR)
• “Good absorbers are good emitters”, meaning that a blackbody emits 100% of the radiation it absorbs (so the absorbed radiation has no effect on the blackbody’s temperature)

Basic principles:

PrincipleDescription
Planck’s Law of blackbody radiationDescribes the electromagnetic radiation of a blackbody of a defined temperature
Stefan-Boltzmann LawCalculates the total electromagnetic radiation as function of a blackbody’s temperature
Wien’s Displacement LawCalculates the wavelength at which maximum spectral radiant exitance (emitted radiation) occurs
Kirchhoff’s Law• Emittance at a given wavelength = absorbance at the same wavelength
• Blackbodies are theoretical; the behaviour of real objects can be described based on how close to being a blackbody they are.
• Emissivity (ε):
ε = 1 ⇒ blackbody
ε < 1 ⇒ real-life material

### Plank's law

This law describes how blackbody radiation can be calculated by the object’s (absolute) temperature:

$$M_\lambda=\frac{2\pi hc^2}{\lambda^5\left(e^{\displaystyle\frac{hc}{\lambda kT}}-1\right)}$$

Where: $M_λ$ = radiation, $λ$ = wavelength, $T$ = absolute temperature.

Therefore, at any given wavelength, we can have a spectral radiant exitance curve (“radiation”) according to the absolute temperature:

### Stefan-Boltzmann Law

Describes the total electromagnetic radiation as a function of the absolute temperature:

$$T_\mathrm{RadBB}=\sigma T{}_\mathrm{kin}^4$$

where $T_\mathrm{RadBB}$ is the radiant flux, and $T_\mathrm{kin}$ the kinetic temperature.

If kinetic temperature is measured in degrees Kelvin, then the temperature value is directly proportional to the average kinetic energy of the molecules in the substance.

### Wien's Law

Describes the wavelength at which maximum spectral radiant exitance occurs.

$$\lambda_\max=\frac AT$$

In Figure 1, the dotted line connects the peak radiances of the temperature curves.

Therefore, hot lava is red because it radiates the red wavelengths more than other wavelengths.

For example:

### Kirchhoff’s Law & Relevance of Emissivity

• Perfect blackbodies are nowhere in this world!
• For a given wavelength, the emittance is equal to the absorbance

$$\varepsilon_{\left(\lambda\right)}=\alpha_{\left\{\lambda\right\}}$$

• Conservation of energy: [absorption] + [reflection] + [transmission] = 1 (for a given wavelength)

$$\varepsilon_{\left(\lambda\right)}+\rho_{\left(\lambda\right)}+\tau_{\left(\lambda\right)}=1$$

• For opaque objects that do not transmit radiation: [absorption] + [reflection] = 1

$$\varepsilon_{\left(\lambda\right)}+\rho_{\left(\lambda\right)}=1$$

• It is therefore calculated that:

$$T_{\mathrm{rad}}=\varepsilon^{\left(\frac14\right)}\cdot T_{\mathrm{\kappa\iota\nu}}$$

For real materials, ε < 1, so the radiance temperature will always be lower than the actual kinetic temperature on the surface of the material! 