Satellite Data Analysis

Electro-Magnetic radiation

Remote sensing

Remote sensing means to:

• Observe matter characteristics and physical quantities
• Use faraway sensors (satellite-based)

EM radiation

The radiation emitted from the sun is reflected in a particular way based on what it hits.

EM radiation is made of an electric (E) and magnetic (M) fields.

Wavelength: λ = c / nf    c = 3.10⁸ km/h    n = refraction index

The atmosphere is transparent only at some ranges of λ:

• Near the visible light (OPT - optical sensing)
• Radio waves (MW - microwave sensing)

Spectral reflectance: an object creates a particular signature of light reflected.

EM spectrum:

• Ultraviolet λ visible 0,4 µm infrared λ > 0,7 µm up to a few µm
• Microwaves λ > than mm

The most important colors to keep in mind are:

• Blue → 0,45 µm
• Green → 0,55 µm
• Red → 0,65 µm

Peaks of water absorption:

• 1,5 µm
• 1,9 µm

Electro-Magnetic radiation

Remote sensing

Remote sensing means to:

• Observe matter characteristics and physical quantities
• Use faraway sensors (satellite-based)

EM radiation

The radiation emitted from the sun is reflected in a particular way based on what it hits.

EM radiation is made of an electric (E) and magnetic (M) fields.

Wavelength: λ = c / n f c = 3.10⁵ km/h n = refraction index

The atmosphere is transparent only at some ranges of λ:

• Near the visible light (OPT - optical sensing)
• Radio waves (MW - microwave sensing)

Spectral reflectance: an object creates a particular signature of light reflected.

EM spectrum:

• Ultraviolet λ ≤ 0,4 μm
• Visible 0,4 μm infrared λ > 0,7 μm up to a few μm
• Microwaves λ ≥ than mm

The most important colors to keep in mind are:

• Blue → 0,45 μm
• Green → 0,55 μm
• Red → 0,65 μm

Peaks of water absorption:

• 1,5 μm
• 1,9 μm

Measuring the EM radiation

Energy = capability to perform work (Joules J).

Radiant energy = energy of an EM wave.

Flux of radiant energy = energy carried by an EM wave in 1 time unit.

Power of the EM wave (Watts W).

Density of radiant flux = radiant flux emitted or absorbed per surface unit (W/m²).

Spectral reflectance: ρ(λ) = power leaving / power landing

The reflectance is computed at a particular wavelength.

Irradiance = RF of an incoming EM wave.

Emittance = RF of an outgoing EM wave.

Directionality

The measurement happens at a specific angle, so it doesn't really intercept the whole emittance. The spreading of the radiation could be uneven, so the direction of measuring should be taken into account.

Radiance = density of radiant flux emitted by a surface unit and seen through a solid angle.

Diffuse reflection — the radiation is reflected evenly (ideal scenario).

Specular reflection — the reflection happens only at a specific angle.

The real-world case is a mix of the two reflections.

The less rough it is, the more the reflection is concentrated in a narrow cone.

Rayleigh criterion

The reflection type depends on the roughness of the surface compared to the wavelength.

Critical height: h_c = λ / 8 cos θ

Reflection Type:

• H => rough => diffuse
• H smooth => mirror

In the case of visible light data acquisition, the material should be smooth at μm scale to have specular reflection (it is the case for water).

Emittance estimation

Existence = emittance associated to the EM radiation emitted by bodies [W/m²]

Planck law

Considering a black body (no reflection) (the Sun is well approximated by the BB)

Spectral emittance: M_λ(λ, T) = 2hc² / λ⁵ 1 / e^hc/λkT – 1

The general shape has a peak and then goes down.

If the peak goes into the visible range, the object starts to glow.

At around ~3 μm it's difficult to differentiate the radiation produced by the Sun (which is then reflected) and the radiation emitted by the Earth (it's a fuzzy boundary).

Below 0.4 μm the ultraviolet radiation is blocked by the atmosphere.

Reflection range: 0.4 μm ≤ λ ≤ ~3 μm (usually 2.4 μm)

Emission range: λ ≫ 3 μm

Thermal remote sensing

To estimate temperature it would be sufficient to l