Radio Propagation and Remote Sensing of the Environment - Chapter 12

12 Atmospheric Research by Microwave Radio Methods Microwave radio methods are finding greater application for research of the atmo-sphere of Earth. As discussed previously, they are based on the interaction of radiowaves with the atmosphere. This interaction is apparent in the decrease in wave amplitude, change of phase, polarization, and other radiowave parameters. Thermal microwave radiation is also the result of this interaction. The main focus of this chapter is on the neutral part of the atmosphere of Earth — the troposphere. Inves-tigating the ionosphere is addressed in Chapter 13. The interaction itself depends on the atmospheric components (gases, hydrom-eteors, etc.) and on general atmospheric parameters such as temperature and pressure. It allows formulation of the two main problems in tropospheric study on the basis of remote sensing technology. One problem is how to obtain information about general atmospheric parameters and their spatial distribution and dynamics. Radio-wave interaction with constant atmospheric components provides the basis for solv-ing this problem, where radiowave absorption by atmospheric oxygen is the main feature. The second problem is related to determining changeable atmospheric com-ponents, their spatial concentration, and so on. Solving this problem requires con-sideration of water vapor concentration, liquid water content in clouds, concentra-tions of minor gaseous constituents, their dynamics, etc. Both problems are in one way or another connected with the inverse problem solution. Solving the second one, as we discussed in Chapter 10, requires a priori information. To some extent, parameters of an atmospheric model can play the role of this a priori information. 12.1 MAIN A PRIORI ATMOSPHERIC INFORMATION A standard cloudless atmosphere is characterized by such parameters as temperature, density, and pressure. The height temperature profile is described by the broken line function T0 −ah, T(h) = T(11km), T(11km)+h−20, 0 ≤ h ≤11km, 11km ≤ h ≤ 20km, (12.1) 20km ≤ h ≤ 32km. 335 © 2005 by CRC Press 336 Radio Propagation and Remote Sensing of the Environment Here, T0 is the temperature at sea level, and a is the temperature gradient. For the U.S. standard atmosphere, T0 = 288.15 K, and a = 6.5 K/km. For an approximate calculation, we can use the simplified formula: T(h) = T0e−h Ht , Ht = 44.3km. (12.2) For many preliminary calculations, we can also use the exponential altitude model of atmospheric pressure: P(h) = P e−h Hp , P =1013 mbar, Hp = 7.7 km. (12.3) The exponential model is used to describe the water vapor density: ρw(h) = ρ0e−h Hw . (12.4) Here, ρ0 is the water vapor density at sea level and depends on climate and the locality. On the average, it varies from 10–2 g/m3 for a cold and dry climate up to 30 g/m3 for a warm and damp climate. For moderate latitudes, the U.S. standard model assumes ρ0 = 7.72 g/m3. The height (Hω) is usually considered to be between 2 and 2.5 km. The refractive index of air is determined by the semi-empirical formula: (n−1)6 = 77.6P+ 4810e , (12.5) where e is the water vapor pressure (mbar). The first term of this formula is deter-mined by the induced polarization of air molecules (mainly nitrogen and oxygen), and the second one describes the orientation polarization of water molecules that have a large dipole moment. The procedure for choosing numerical constants can be found in Bean and Dutton.30 The partial water vapor pressure is associated with density ρw by the approximate formula: e =1.61p ρw , (12.6) air where ρair is the density of moist air. The standard value of ρair is 1.225 · 10 g/m3. The altitude distribution can be approximately represented by the exponential model: n(h) =1+(n0 −1)e−h Hn . (12.7) © 2005 by CRC Press Atmospheric Research by Microwave Radio Methods 337 The standard water vapor pressure at sea level for moderate latitudes is 10 mbar. So the standard value of the refractive index is n0 −1= 3.19⋅10−4 . The standard gradient near the surface of Earth is assumed to be: dn = − n0 −1 = −4⋅10−8m−1 . (12.8) h=0 n It is easy to determine from this that the standard value of height Hn is 8 km. Variation of the air humidity for different climatic zones leads to a variation mean value of n0 – 1 and height Hn. The surface value of the refractive index can be calculated from meteorological data. With regard to Hn, the following fact can be used. It was established by Bean and Dutton.30 that the value of the refractive index varies slightly at the tropopause altitude of h = 9 km and is practically independent of the geo-graphical place and period of year. The averaged value n(9 km)−1=1.05⋅10−4. Hence, the median value of the height can be estimated from the following equation: Hn = ln(n0 −1)104 1.05. (12.9) Now, we will turn our attention to radiowave absorption by atmospheric gases. The main absorptive components are water vapor and oxygen. Water vapor has absorptive lines at wavelengths 1.35 cm (f = 22.23515 GHz), 0.16 cm (f = 183.31012 GHz), 0.092 cm (f = 325.1538 GHz), and 0.079 cm (f = 380.1968 GHz), as well as many lines in the submillimetric waves region. The wings of the submillimetric lines influence the absorption at millimetric waves; therefore, they are taken into account for calculation of absorptive coefficients. The resulting computation is comparatively complicated, so we will provide only some examples of the calculation. Figure 12.1 gives attenuation coefficient values of water vapor at sea level vs. frequency. The maximum attenuation of γ ρ ≅ 2.2⋅10−2 dB/km/g/m3 is at the resonance wave- length λ = 1.35 cm. Thus, γ w ≅ 0.17 dB/km near the surface of Earth at moderate latitudes. The altitude dependence can be expressed as a first approach by the exponential model: γ w(h) = γ w0 exp− h  . (12.10) γw Hγw ≅ Hw at transparency windows and rather more at the resonance wavelength, because absorption by water vapor becomes independent of the air pressure. Some data show that this height varies with the season of the year and reaches a value of 5 km. Oxygen owns the paramagnetic moment and has many lines of absorption in the millimeter-wave region. A separated absorption line occurs at a frequency of © 2005 by CRC Press 338 Radio Propagation and Remote Sensing of the Environment 100 10 H2O 1 0.1 0.01 O2 0.001 0.0001 0 50 100 150 200 250 300 350 F, (GHz) FIGURE 12.1 Computed spectra of attenuation coefficient of oxygen and water vapor at sea level. TABLE 12.1 Oxygen Absorptive Lines Frequencies Frequency (f) (GHz) 48.4530 48.9582 49.4646 49.9618 50.4736 50.9873 51.5030 52.0212 52.5422 53.0668 53.5957 54.1300 54.6711 55.2214 55.7838 Wavelength (λ) (mm) 6.19 6.13 6.06 6.00 5.94 5.88 5.82 5.77 5.71 5.65 5.60 5.54 5.49 5.43 5.38 Frequency (f) (GHz) 56.2648 56.3634 56.9682 57.6125 58.3239 58.4466 59.1642 59.5910 60.3061 60.4348 61.1506 61.8002 62.4112 62.4863 62.9980 Wavelength (λ)mm 5.33 5.32 5.27 5.21 5.14 5.13 5.07 5.03 4.97 4.96 4.91 4.85 4.81 4.80 4.76 Frequency (f) (GHz) 63.5685 64.1278 64.6789 65.2241 65.7647 66.3020 66.8367 67.3694 67.9007 68.4308 68.9601 69.4887 70.0000 70.5249 71.0497 Wavelength (λ) (mm) 4.72 4.68 4.64 4.60 4.56 4.52 4.49 4.45 4.42 4.38 4.35 4.32 4.29 4.25 4.22 118.7503 GHz (λ = 2.53 mm) and an absorptive band at the 5- to 6-mm area. The absorptive line frequencies of this band are provided in Table 12.1. These lines overlap at the lower levels of the atmosphere of Earth, forming a practically continuous band of absorption. Line resolution begins only at altitudes higher than 30 km. Sometimes at this altitude, we have to take into account Zeeman’s © 2005 by CRC Press Atmospheric Research by Microwave Radio Methods 339 line splitting. The attenuation coefficient values produced by oxygen are shown in Figure 12.1. The exponential altitude model is also used to determine the altitude dependence of the oxygen absorption coefficient: γox(h) = γox0 exp− h  . (12.11) ox In transparent windows, the following empirical relation can be used for the specific height: Hox = 5.3+0.022(T0 −290)km. (12.12) This height varies from 8 to 21 kilometers at frequencies coinciding with the absorptive lines. A more detailed discussion of this problem can be found in Deir-mendjian.86 The total absorption of a cloudless atmosphere is described by the sum: γat = γox + γ w . (12.13) The main a priori information about hydrometeor formation is based on the state-ment that they consist of water drops or ice crystals. The drop sizes, their concen-tration, and the altitude distribution of these parameters are defined by the type of hydrometeor formation. The initial parameters of these formations (temperature, pressure, etc.) depend on their altitude and, initially, can be found using the standard atmospheric model. Very important characteristics of hydrometeors are their geo-metrical dimensions, motion velocity, and lifetime. The first point of interest in this discussion is describing the electrophysical properties of fresh water, particularly the water dielectric permittivity and its depen-dence on wavelength (frequency). This dependence of the real and imaginary parts of permittivity is defined by the Debye formulae, which have the form: ε′ = εo + 1 εs −εo )2 , ε′′ = λr 1 εs −εo )2 , (12.14) where εs is the so-called static dielectric constant. This value is reached at λ → ∞, from which we derive the label of static dielectric constant. The opposite term ( is often called the optical permittivity and is reached at λ → 0. The wavelength λ is related to the relaxation time of water by the equation λ = 2πcτ . ε = 5.5, and εs and λr depend on the water temperature and salinity. The details of these depen-dencies will be given in the next chapter; here, we shall give the values of these parameters for T = T0. Thus, εs = 83 and λr = 2.25 cm. © 2005 by CRC Press ... - tailieumienphi.vn