Solar light interaction with the atmosphere

Extracted from Chimot, J., Global mapping of atmospheric composition from space – Retrieving aerosol height and tropospheric NO2 from OMI, PhD book, Delft University of Technology (TU Delft), The Royal Netherlands Meteorological Institute (KNMI), July 2018.

 

The sunlight can be modeled as an ensemble of electromagnetic radiation (i.e. group of photons) covering a specific spectral wavelength λ / frequency range. The Sun approximately radiates as a black body at a temperature of 5700 K. According to the Plank’s law, solar radiation peaks in the visible spectral range from λ =400–700 nm, with a maximum in the green spectrum domain at λ = 500 nm. Earth itself radiates with a lower average temperature (about 255 K) having a radiation peak in the thermal infrared (λ = 10 μm).

Solar_spectrum_en_svg.png
The spectrum of sunlight (light yellow) compared with a theoretical black body curve at 5778 K, and the solar radiation at sea level (Source: wikimedia).

The Earth atmosphere is not completely transparent: depending on the wave- lengths, the Sun light is absorbed, remitted, reflected and/or scattered. An example of such interaction is the blue sky “visible” during daylight, which is the result of the molecular light scattering by N2 and oxygen in all the directions (i.e. Rayleigh scattering), especially very strong for shorter wavelengths. Another example is the red sunset that can be observed sometimes. This remaining red light in the sunlight is due to the filtering of the blue part by Rayleigh scattering. In absence of atmosphere, there would be no Rayleigh scattering and our sky would be like that of the moon: dark with only some bright stars. Aerosol and cloud particles are responsible for scattering, which is wavelength and particle type dependent. Its intensity strongly varies with the scattering angle. The specific Mie scattering (i.e. valid for spherical particles) is said to be elastic: i.e. molecules remain unchanged and the scattered photon keeps the same energy and wavelength. On the contrary, Raman scattering (weak interaction with matter) is inelastic. The outcome photon has then a different energy and wavelength.

Trace gas molecules interact with light via absorption (Einstein, 1917). Since they consist of chemical bound groups of atoms, they are driven by quantum me- chanical principles. This means one can quantify their internal energy and their energy states are discrete (Burrows et al., 2011). In presence of incident solar radiation, the molecule in a lower energy state becomes excited. Incoming photon with the right energy, i.e. wavelength, is then absorbed, and the molecule undergoes to an higher energy state. Depending on the energy / frequency, the molecule stimulation is characterized by rotation of the entire molecule, vibration of the atoms or electronic transition of the energy states. The resulting spectrum contains discrete absorption lines corresponding to the discrete molecule energy states.

To be able to observe trace gas absorption, it is required to measure a light spectrum over a large enough spectral range and with a sufficient spectral resolution to identify the so-called absorption spectral lines. For that purpose, the designed UV-visible-shortwave infrared passive satellite instrument looking downward (nadir point of view) are usually spectrometers: a device that measures the upwelling radiance corresponding to the backscattered sunlight at the top of the atmosphere (TOA). The individual photons striking the instrument’s detector is converted into electrons. The detected signal is then decomposed into a series of energy intensity as a function of wavelength: the radiance spectrum (Duncan et al., 2014).

Overall, a critical aspect in satellite observations of atmospheric constituents is the light path, or more precisely the average length of the ensemble of all possible light paths due to all possible scattering and absorption processes occurring in the atmosphere and at the surface. This is likely the key uncertainty in the quantification of atmospheric trace gases such as NO2 – Nitrogen dioxide.

Radiative transfer models (RTMs) simulate the propagation of the light through the atmosphere and at the surface. They can then help to investigate how the satellite spectrum measurements are affected by the state of the atmosphere and identify the most important parameters. These models are central to quantify the green- house magnitude, climate change effect, efficiency of photochemical reactions in the Earth atmosphere and trace gas retrievals. Several types of RTMs exist: e.g. discrete ordinate which numerically solve the radiative transfer equation (Spurr, 2008), backward Monte-Carlo based on statistical techniques applied to a large ensemble of paths for each photon (Deutschmann and Wagner, 2008), and the doubbling adding principles (de Haan et al., 1987; Stammes et al., 1989) as implemented in the DISAMAR KNMI software (de Haan, 2011). When applied to UV and visible wavelengths (in the absence of thermal emission), the central equation in the RTMs is written as:

Screen Shot 2018-07-24 at 21.16.21

with dI(λ,θ,φ) / ds the spectrum change of incoming radiation moving through an infinitesimal thin layer with a thickness ds, εa(λ) and εs(λ) the absorption and scattering coefficients respectively, θ the zenith angle, φ the azimuth angle, and S(θ,φ)the dimensionless scattering phase function (i.e. the angular dependency of the scattering effect).

For practical reasons, in the UV-vis, we generally focus on the reflectance spec- trum R in which the extraterrestrial solar irradiance features are removed (leaving then mostly the atmospheric absorption lines of interest):

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with μ0 the solar zenith angle.