# Earth-to-Earth Microwave Rain Attenuation Measurements: A Survey On the Recent Literature
## 3 Theoretical and Experimental Framework  
### Physical Mechanism of Attenuation Due to Rain  
Electromagnetic waves consist of photons, with each of them carrying energy declared as \(E=\mathit{l}\mathit{v}\), where \(\mathit{h}\) is the Planck constant, while \(\mathit{v}\) corresponds to the frequency of the electromagnetic wave. The electromagnetic radiation interacts with matter during its propagation through it, according to two fundamental mechanisms of absorption and scattering. Absorption refers to the ability of atoms and molecules to absorb the energy which is carried by photons. The absorbed photons can be re-emitted in many different directions, with varying intensities. This spatial dispersion of photons is referred to as scattering. Reflection, refraction, and diffraction are some forms of scattering. These two mechanisms are the primary source of electromagnetic signal's attenuation due to rainfall. The total energy \(E_{M}(\Lambda,\mathit{v},\mathit{J})\) of a molecule is expressed as  
\[E_{M}(\Lambda,\mathit{v},\mathit{J})=E_{E}(\Lambda)+E_{VIB}(\mathit{v})+E_{ ROT}(\mathit{J})+E_{TR} \tag{1}\]  
Figure 1: The four SALSA steps. where \(E_{E}(\Lambda)\) is the energy of its electrons, \(E_{VIB}(v)\) is the atom's vibrational energy around the molecule's equilibrium position, \(E_{ROT}(J)\) is the rotational energy corresponding to the molecule's rotation about its axes of symmetry, and \(E_{TR}\) is the energy of the molecule's translational motion. Moreover, \(\Lambda,v\) and \(J\) are the quantum numbers defining the value of each energy. When a molecule absorbs a photon of energy \(E_{tr}\), it transitions from its initial quantum state to another, excited state. Considering that the initial state is described by the quantum numbers \(\Lambda,\ v\) and \(J\), and that the new numbers describe the excited state \(\Lambda^{\prime},\ v^{\prime}\) and \(J\prime\), then the energy difference between the two states is equal to the energy of the absorbed photon:  
\[ \begin{array}{c}E_{hv}=E_{M}(\Lambda,\
u,J)-E_{M}(\Lambda^{\prime},\
u^{ \prime},J^{\prime})\\ =\Delta E_{E}(\Lambda\rightarrow\Lambda^{\prime})+\Delta E_{VIB}(v\to v ^{\prime})+\Delta E_{ROT}(J\to J^{\prime})+\Delta E_{TR}\end{array}  \tag{2}\]  
In nature, the water molecules are found as parts of clusters. The intermolecular interactions increase many different energy states. The corresponding energy levels are so close to each other that they practically form a continuum. Consequently, the energies of the absorbed photons form a continuum too, as well as the frequencies and wavelengths of the absorbed electromagnetic radiation. The water absorbance relative to electromagnetic waves, of wavelengths in the region above but close to 2 cm, is strong. Such waves interact strongly with the dipoles formed between hydrogen and oxygen atoms, while the absorbed energy is consumed, shifting the dipoles in the electric field [20]. It is proven that the H\({}_{2}\)O dipoles absorb the energy of those frequencies that correspond to vibration periods close to the dipole's relaxation time [21]. As far as the scattering effect, it is categorized into three main types, the Rayleigh scattering, the Mie scattering, and the geometric scattering. The factor that determines this categorization is a non-dimensional parameter defined as \(a\equiv\frac{\pi D}{\lambda}\), where \(D\) is the diameter of a spherical volume (a droplet, a particle, a molecule, etc.) that the radiation of wavelength \(\lambda\) is incident to. Only Rayleigh or Mie scattering is observed during the propagation of an electromagnetic signal through rainfall. The scattering in both cases is elastic, in the sense that the wavelength of the scattered light is the same as that of the incident light. The Rayleigh approximation is used to describe the scattering when the size of the spherical volume is considerably smaller than the wavelength of the incident radiation, so that \(a\ll 1\).