Abstract
Basic knowledge on the theory of electromagnetic wave scattering, radar measurements, and methods of estimating the scatterer parameters are the theme of this chapter. The main scatterers concerned are water and ice particles, and Bragg scatterers generated by perturbations of radar refractive index due to turbulence of the atmosphere. First, basics of radar are discussed, where system parameters of pulse radars and characteristics of scatterers are discussed. Second, radar observation of isolated scatterers, radar equation for an isolated scatterers, and characteristics of scattering are shown. Then, radar theory for hard scatterers are discussed, where scattering by dielectric spheres, radar equation for distributed hard scatterers, Mie scattering, the Rayleigh approximation, and radar reflectivity factor are discussed. Following, radar theory for soft scatterers are discussed, where backscattering mechanisms by refractive index perturbations, partial reflection from a stratified atmosphere, and scattering by linear scatterers are covered.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-4-431-54334-3_13
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Notes
- 1.
- 2.
Among the refractive index perturbations, only those which have a wavelength equal to one half the radar wavelength contribute substantially to the backscatter. These perturbations are defined as the Bragg scatterers as will be discussed in Sect. 3.4.
- 3.
Here we assume that the efficiency of the antenna η 1 = 1 and power gain g is equal to directivity g D. Refer to Sects. 2.1.4 and 8.2.1. The lower case g denotes the value in a pure number (in linear unit), whereas the upper case G denotes it in decibel.
- 4.
Bistatic radars which will be discussed later in Sect. 4.2.3 utilizes the side scattered signals.
- 5.
- 6.
Doviak and Zrnić (2006, p. 35) define the Rayleigh region as \(\pi D/\lambda <\pi /16 \simeq 0.2\).
- 7.
The distinction between the incident vector wave number \(\boldsymbol{k}_{\mathrm{0}}\) and scattering vector wave number \(\boldsymbol{k}_{\mathrm{s}}\) is the direction of two vectors.
- 8.
Thus, the following discussion leads to the same result as the Rayleigh approximation that will be discussed in Sect. 3.3.4.
- 9.
If B 6 τ is 1.0, the integral of | W(r) | 2 normalized by c τ ∕ 2 becomes 1.17.
- 10.
The values \(\sigma _{\vartheta }\) and \(\sigma _{\varphi }\) correspond to the standard deviations of the Gaussian distribution.
- 11.
This value (i.e., cross section per unit volume) is equal to a radar the reflectivity factor of 6.6 dBZ as will be obtained by (3.67).
- 12.
The unit of dBm is the logarithmic expression of the power in regard to 1 mW. \(1\ \mathrm{mW} = 0\ \mathrm{dBm}\), hence \(8.85 \times 1{0}^{-14}\ \mathrm{W} = 8.85 \times 1{0}^{-11}\ \mathrm{mW} = -100.5\ \mathrm{dBm}\).
- 13.
The attenuation is a complicated function of m, but in the special case that the radar wavelength is long compared to diameter of scatterers, i.e., in the Rayleigh region, it can be expressed simply as will be discussed in Sects. 3.3.4 and 6.3.3.
- 14.
Usually, \([\mathrm{{mm}}^{6}\mathrm{{m}}^{-3}]\) is more frequently used for the unit of Z than \([\mathrm{{m}}^{6}\mathrm{{m}}^{-3}]\). In this case, the coefficient 10 − 18 which comes from the unit conversion should be multiplied to the original Z. Thus (3.67) becomes
$$\displaystyle\begin{array}{rcl} \eta \ [{\mathrm{m}}^{-1}] = \frac{{\pi }^{5}} {{(\lambda [\mathrm{m}])}^{4}}\vert K{\vert }^{2}Z[{\mathrm{mm}}^{6}{\mathrm{m}}^{-3}] \times 1{0}^{-18}.& & {}\\ \end{array}$$ - 15.
As will be discussed in Sect. 6.4, hydrometeor classifications (e.g., distinguishing ice crystals from rain drop) applying polarimetric parameters have become possible.
- 16.
Ordinary radars that share a single antenna for transmission and reception are called monostatic radars. On the other hand, the radars equipped with a pair of antennas that are separated, typically by large distances, where one antenna is used for transmitting and the other is used for receiving, are called bistatic radars as will be discussed in Sect. 4.2.3.
- 17.
From Gossard and Strauch (1983, p. 259). The nomenclature of \(\Phi _{n}(\kappa )\) is not necessarily unique. It is either called the space spectrum or spatial power-spectral density (Ottersten 1969a), the space spectrum (Battan 1973, p. 256), or the spectral density (Doviak and Zrnić 2006, p. 390).
- 18.
- 19.
The spatial scale and characteristics of the inertial subrange will be discussed in Sect. 7.3.2
- 20.
See Sect. 7.3.3 for energy dissipation rate.
- 21.
The horizontal distance over which the scattered waves have a strong correlation is called the horizontal correlation distance.
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Fukao, S., Hamazu, K. (2014). Radar Measurements and Scatterer Parameters. In: Radar for Meteorological and Atmospheric Observations. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54334-3_3
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