© 2005 by CRC Press 335 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- 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 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 (12.1) Th Tah h Th T () , ,= −≤≤ () ≤≤ 0 011 11 11 11 km, km km 20km, kkm 20km km. () + −≤≤        hh20 32, TF1710_book.fm Page 335 Thursday, September 30, 2004 1:43 PM tigating the ionosphere is addressed in Chapter 13. one, as we discussed in Chapter 10, requires a priori information. To some extent, © 2005 by CRC Press 336 Radio Propagation and Remote Sensing of the Environment Here, T 0 is the temperature at sea level, and a is the temperature gradient. For the U.S. standard atmosphere, T 0 = 288.15 K, and a = 6.5 K/km. For an approximate calculation, we can use the simplified formula: (12.2) For many preliminary calculations, we can also use the exponential altitude model of atmospheric pressure: , (12.3) The exponential model is used to describe the water vapor density: . (12.4) Here, ρ 0 is the water vapor density at sea level and depends on climate and the locality. On the average, it varies from 10 –2 g/m 3 for a cold and dry climate up to 30 g/m 3 for a warm and damp climate. For moderate latitudes, the U.S. standard model assumes ρ 0 = 7.72 g/m 3 . The height ( H ω ) is usually considered to be between 2 and 2.5 km. The refractive index of air is determined by the semi-empirical formula: , (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 ρ w by the approximate formula: , (12.6) where ρ air is the density of moist air. The standard value of ρ air is 1.225 · 10 3 g/m 3 . The altitude distribution can be approximately represented by the exponential model: . (12.7) Th Te H hH t t () , .== − 0 44 3 km. Ph Pe hH p ()= − 0 P 0 1013= mbar , H p = 77.km. ρρ w ()he hH w = − 0 n T P e T − () =+       1 77 6 4810 6 . ep= 161. ρ ρ w air nh n e hH n ()=+ − () − 11 0 TF1710_book.fm Page 336 Thursday, September 30, 2004 1:43 PM © 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 . The standard gradient near the surface of Earth is assumed to be: . (12.8) It is easy to determine from this that the standard value of height H n is 8 km. Variation of the air humidity for different climatic zones leads to a variation mean value of n 0 – 1 and height H n . The surface value of the refractive index can be calculated from meteorological data. With regard to H n , 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 . Hence, the median value of the height can be estimated from the following equation: (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 gives attenuation coefficient values of water vapor at sea level vs. frequency. The maximum attenuation of dB/km/g/m 3 is at the resonance wave- length λ = 1.35 cm. Thus, dB/km near the surface of Earth at moderate latitudes. The altitude dependence can be expressed as a first approach by the exponential model: . (12.10) 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 n 0 4 131910− = ⋅ − . dn dh n H h= −− = − − = −⋅ 0 0 81 1 410 n m n() .9110510 4 km − = ⋅ − H n n = − ()     9 110 105 0 4 ln . . γρ ww ≅⋅ − 22 10 2 . γ w ≅ 017. γγ γ ww w () exph h H = −       0 HH γww ≅ TF1710_book.fm Page 337 Thursday, September 30, 2004 1:43 PM complicated, so we will provide only some examples of the calculation. Figure 12.1 © 2005 by CRC Press 338 Radio Propagation and Remote Sensing of the Environment 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 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) Wavelength ( λλ λλ ) (mm) Frequency (f) (GHz) Wavelength ( λλ λλ ) mm Frequency (f) (GHz) Wavelength ( λλ λλ ) (mm) 48.4530 6.19 56.2648 5.33 63.5685 4.72 48.9582 6.13 56.3634 5.32 64.1278 4.68 49.4646 6.06 56.9682 5.27 64.6789 4.64 49.9618 6.00 57.6125 5.21 65.2241 4.60 50.4736 5.94 58.3239 5.14 65.7647 4.56 50.9873 5.88 58.4466 5.13 66.3020 4.52 51.5030 5.82 59.1642 5.07 66.8367 4.49 52.0212 5.77 59.5910 5.03 67.3694 4.45 52.5422 5.71 60.3061 4.97 67.9007 4.42 53.0668 5.65 60.4348 4.96 68.4308 4.38 53.5957 5.60 61.1506 4.91 68.9601 4.35 54.1300 5.54 61.8002 4.85 69.4887 4.32 54.6711 5.49 62.4112 4.81 70.0000 4.29 55.2214 5.43 62.4863 4.80 70.5249 4.25 55.7838 5.38 62.9980 4.76 71.0497 4.22 F, (GHz) K, (dB/km) 0.0001 0.001 0.01 0.1 1 10 100 050100 150 200 250 300 H 2 O O 2 350 TF1710_book.fm Page 338 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press Atmospheric Research by Microwave Radio Methods 339 line splitting. The attenuation coefficient values produced by oxygen are shown in dependence of the oxygen absorption coefficient: . (12.11) In transparent windows, the following empirical relation can be used for the specific height: 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: . (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: (12.14) where ε s 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 ( ε o) is often called the optical permittivity and is reached at λ → 0. The wavelength λ r is related to the relaxation time of water by the equation . ε o = 5.5, and ε s and λ r 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 = T 0 . Thus, ε s = 83 and λ r = 2.25 cm. γγ ox ox0 ox () exph h H = −       HT ox =+ − () 53 0022 290 0 γγγ at ox w =+ ′ =+ − + () ′′ = − + () εε εε λλ ε λ λ εε λλ o so r r 11 22 r so ,, λπτ rr = 2 c TF1710_book.fm Page 339 Thursday, September 30, 2004 1:43 PM Figure 12.1. The exponential altitude model is also used to determine the altitude © 2005 by CRC Press 340 Radio Propagation and Remote Sensing of the Environment To estimate hydrometeor reflectivity (see Equation (11.15)), we need to calculate the parameter: . (12.15) For fresh water: (12.16) It is easy to see that the frequency dependence of this parameter begins devel- oping for the wavelength (i.e., for wavelengths shorter than 2 mm). For longer wavelengths, (12.17) and now depends on temperature only. Usually, K = 0.8 to 0.93 for water. The ice permittivity is about 3.2 at these wavelengths, and K ≅ 0.2. The other parameter of our interest is: (12.18) which is associated with absorption in hydrometeors (see Equation (5.46)). For water, . (12.19) The absorption coefficient in clouds is: (12.20) K = − + ε ε 1 2 2 K so so r = − () + − () + () ++ () = εεχ εεχ χ λ λ 11 22 22 2 22 2 ,. λλε ε λ<++≅ ro s r ()().2201 K = − +       ε ε s s 1 2 2 L = ′′ + ε ε 2 2 L = − () + () ++ () εεχ εεχ so so 22 22 2 γ π λ εεχ εεχ π λ = − () + () ++ () = 24 22 18 23 2 22 2 Na w r so so rrw so so  ρ εεχ εεχ − () + () ++ () 2 22 2 22 . TF1710_book.fm Page 340 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press Atmospheric Research by Microwave Radio Methods 341 Here, w is the cloud liquid water concentration, and is the water density. For waves longer than 2 mm: . (12.21) The water content here is expressed in g/m 3 and wavelength in cm. For freshwater ice, we can assume to obtain: , (12.22) where I is the ice concentration and ρ I is its density. 12.2 ATMOSPHERIC RESEARCH USING RADAR (WR), which will be covered in greater detail here. The main areas of concern include: • Measurement of the radio echo power from meteorological targets, with the echo being selected against a background of interfering reflection from the top beacons • Detection and identification of meteorological objects by their reflectivity • Definition of the horizontal and vertical extent of meteorological forma- tions and determination of their velocity and the displacement direction • Determination of the upper and lower boundary definitions for clouds • Detection of hail centers in clouds, determining their coordinates, and defining their physical characteristics Weather radar operates at centimeter and millimeter wavelengths; some of them are dual frequency. Specific requirements for weather radar depend upon the particular type of meteorological object and include the following: • Exceptionally wide-scattering cross-section variations of atmospheric for- mations reaching values of around 100 dB • Considerable horizontal and vertical sizes of the atmospheric objects relative to the antenna footprint and spatial extent of the radio pulse • Rather low velocity of moving targets • Large time–spatial changeability of radio-reflecting and -attenuating char- acteristics of atmospheric formations  ρ w γ πλ λρ εε ε λ = − + () ≅⋅   − 18 2 136 10 22 6 2 ww r  w so s 1 cm .     =       059 2 . w λ dB km ′′ ≈⋅ − ε 510 3 γ λρ ≅ 001. I I TF1710_book.fm Page 341 Thursday, September 30, 2004 1:43 PM We briefly examined this problem in Chapter 11 when we discussed weather radar © 2005 by CRC Press 342 Radio Propagation and Remote Sensing of the Environment The primary WR value measured is the backward scattering cross section: . (12.23) Here, the reflectivity is expressed in cubic centimeters. In some cases, the reflectivity is expressed via the diameter of drops, in which case Equation (12.23) must be increased by a factor of 2 6 = 64. As we can see, the drop radius must be known to determine the reflectivity. Various distribution functions are used to calculate . 39 One of the most com- 86 The gamma-distribution (or Pearson’s distribution), which has wide application, is a particular case of Deirmendjian’s distribution when γ = 1: . (12.24) Finally, with regard to α = 0, we obtain the following exponential distribution: . (12.25) In the future, we will most commonly use the gamma-distribution, as this distribution describes well the atomized component of clouds. As shown in Aivazjan, 39 the processing of experimental data to determine coefficient α gives us values of 2 to 6 within the drop radius interval (1.0 to 45.0) · 10 –4 cm, depending on the type of cloud. The radius a 0 value varies in the range (1.333 to 3.500) · 10 –4 , and the drop concentration N attains values of 188 to 1987 cm –3 . For the mean model (referred to as the Medi model by the author), we can assume that α = 2, a 0 = 1.5 · 10 –4 cm, N = 472 cm –3 , a min = 1.0 · 10 –4 , and a max = 20.0 · 10 –4 cm. Calculations based on this model give us values of W = 0.4 g/m 3 , and Θ = 9.9 · 10 –17 cm 3 . Aivazjan 39 recommends use of the distribution: (12.26) to describe large-drop components of clouds within the radius range (20 to 200)· 10 –4 cm. The value of µ varies from 4 to 10 for different cloud types. Variations in concentration N for this radius interval are 2.0 ⋅ 10 –5 cm –3 to 20 cm –3 . The Medi model parameters are µ = 6, a min = 2.0 ⋅ 10 –3 cm, a max = 8.5 ⋅ 10 –3 cm, and σπ π λλ d 0 4 4 3 4 16 1 45 10 () . = ≅ ⋅ KΘΘ a 6 fa a a a a a a () exp= ()       −       = () α β α β α α βΓΓ mm 00 0 0 1 β βα α exp , ,−       =+ = a a a a m fa a a a () exp= −       1 00 fa aa a a () min max min = − − () − − µ µ µ µ 1 1 1 1 TF1710_book.fm Page 342 Thursday, September 30, 2004 1:43 PM monly used (as noted in Chapter 11), is the distribution proposed by Deirmendjian. © 2005 by CRC Press Atmospheric Research by Microwave Radio Methods 343 N = 1.54 cm –3 . The results of calculations give us W = 0.12 g/m 3 and Θ = 1.6 ⋅ 10 –15 cm 3 . Comparison reveals that cloud water content and radiowave absorption are primarily determined by the atomized component. By contrast, large drops dominate in cloud reflectivity formation. Sometimes super-large drops with radii up to 0.15 cm influence the radar echo of clouds even though their concentration is extremely low. In particular, calculations made on the data given in Aivazjan 39 give us Θ = 1.4 ⋅ 10 –14 cm 3 for the main conditions, with concentration N = 2.0 ⋅ 10 –3 cm –3 . Such drops are often generated in rain clouds. The variety of cloud reflectivity allows us to distinguish the type of clouds by radar data. In meteorology, the reflectivity is often determined relative to drop diameter (expressed in mm 6 /m 3 ). This value is equal to Z = (6.4 ⋅ 10 13 )Θ. The average values Good spatial resolution, achieved by use of a pencil-beam antenna and wideband signals, allows us to study the inner cloud structure and to detect local motions due to the Doppler effect. Reflectivity changes with altitude and has a maximum at the altitude of the zero-isotherm (h ≅ 1.5 to 2 km for moderate latitudes in summer). A second maximum at a height of 8 km typically belongs to thunderclouds. For ordinary clouds, the value of Θ decreases smoothly from the lower boundary to the upper one. Cumulus clouds have maximal reflectivity in the middle. The extent of the reflected signal and its change in shape depend on the type of cloud. All of these data are used to identify and classify cloud cover. The process of radiowave reflection by rain is more complicated compared to the case of clouds. To begin, the theoretical description must include consideration of the velocity of drop fall, which depends on the radius of the drop. The sizes of rain drops are larger then water drops in clouds. For example, the median value of drop radius is: (12.27) according to the formula proposed by Laws and Parsons. 88 Here, J is the rain intensity (expressed in mm/hr); a med ≅ 0.1 cm for rain of strong intensity (J = 12.5 mm/hr). When J = 100 mm/hr, the drop radius will be of the order of 2.5 mm. The Rayleigh approximation is not correct for calculation of the cross sections of drops in the millimeter-wave region. The Mie formulae must be used instead because of the TABLE 12.2 Average Cloud Reflectivity Values (Z, mm 6 /m 3 ) Type of Clouds St Sc Cu Cong Ac As Ci Ns Cb Cb with Thunder 0.83 17.61 55.17 1.31 0.78 0.87 350.7 2432.2 19,234 Source: Data from Stepanenko. 87 aJ med = 0 069 0 182 . . TF1710_book.fm Page 343 Thursday, September 30, 2004 1:43 PM of reflectivity for some types of clouds are shown in Table 12.2. © 2005 by CRC Press 344 Radio Propagation and Remote Sensing of the Environment necessity to sum the slow convergent series. These calculations for different situa- tions were done (see, for example, Aivazjan 39 ). The complexity of the calculations is made greater by the need to know the distribution function. The Marshall–Palmer function, a result of experimental data approximation, is commonly used for first estimations; this function is a variant of the exponential distribution (Equation (12.25)), and the parameters depend on the rain intensity. The Marshall–Palmer distribution describes well the distribution of drop sizes for radii a > 0.05 cm. A more accurate picture is given by the Best distribution, which is a gamma-distribution variant. In any case, the dependence of distribution parameters on the rain intensity has to be taken into account. As a result, we cannot express analytically the depen- dence of the rain reflectivity on its intensity J; therefore, the empirical dependence of the type given by Equation (13.26) is commonly applied. Another circumstance that must be taken into account is wave attenuation in rain which becomes particularly noticeable in the millimeter-wave region. This means that the radar equation has to be developed by taking into account radiowave extinction inside the rain. So, Equation (11.18) is reduced to: . (12.28) Here, scattering has to be added to the absorption by the drops. In other words, the total cross section must be used for the extinction coefficient calculation. Equation (12.28) is simplified based on the assumption of spatial homogeneity of the rain. The extinction coefficient also depends on the rain intensity. The empirical formula is similar to Equation (11.22) and has the form: dB/km. (12.29) The parameters ν and µ depend on the radiowave frequency. Their empirical value can be found in Ulaby et al. 90 and Atlas et al. 91 The data given in Ulaby et al. 90 allow us to determine an approximation in the region of 2.8 to 60 GHz: , (12.30) We can assume that parameter µ is equal to unity for the first approximation. Frequently, qualitative assessment for description of the rain is realized by the value of parameter: , (12.31) where H is the target height (km), and Θ i is the reflectivity at a level 2 km higher than the maximal reflectivity Θ max zone. A steady downpour takes place at Y i < 2 for WL PA l L LL() () ()exp( )= − + − 801 2 2 4 42 2 π λ ε ε γ e Θ γν µ = J ν = ⋅ − 397 10 52377 . . f YH ii = − () lg lg lg max max ΘΘΘ TF1710_book.fm Page 344 Thursday, September 30, 2004 1:43 PM [...]... the first Russian experimental radiometry systems used on the Cosmos-243, Cosmos-384, and Cosmos-1151 missions The chosen frequencies of 3.5, 8.8, 22, 35, and 37 GHz provided information about the thermal radiation of the surface of the Earth, atmospheric water vapor, and clouds The radiometry information at the frequencies of 3.5 and 8.8 GHz were appropriate for defining emissions from the surface of. .. shows that the brightness temperature grows with an increase of the rain rate and reaches saturation.90 The experimental data generally verify these results The second problem of rain intensity measurement is the poor spatial resolution of the microwave radiometry system The ordinary footprint of the spaceborne radiometer antenna is of the order of tens of kilometers The horizontal size of the rain can... Radio Propagation and Remote Sensing of the Environment differs from Equation (12. 72) Equation (9.89) shows this difference for the rather simple case of particles with an isotropic scattering indicatrix filling up the halfspace In reality, the analytical result has to be more complicated because drop albedo is a function of the radii of the drops This leads us to the conclusion that the albedo of the. .. Propagation and Remote Sensing of the Environment C E ϕ1 ξ ϕ2 D A B d ϕ1 r P r1 R2 R1 θ 0 FIGURE 12. 2 Researching the atmosphere of Earth by means of radio- occultation and communication links for the measurement of data transmission to the ground terminal This method was shown to be efficient when used for Mars and Venus atmospheric research32 and is being developed further for use within the atmosphere of the. .. be smaller, and the fraction of FOV covered by the rain is unknown beforehand This is one of the reasons for using spaceborne weather radar for the detection of rain areas and the rain rate definition, as was done in the TRMM mission Spaceborne radiometry can be used for the retrieval of a vertical temperature profile The emission at the oxygen band of 50 to 60 GHz is of primary interest The weighting... on the basis of the approximate relation p 0 = v ⊥ t 0 If the question is one of receiver thermal noise, then the correlation time is associated with the filter bandwidth t 0 ≅ 1 ∆f 0 , and the fluctuations of the refraction angle can be defined via the frequency fluctuations: ( ) © 2005 by CRC Press TF1710_book.fm Page 354 Thursday, September 30, 2004 1:43 PM 354 Radio Propagation and Remote Sensing of. .. Equation (12. 58), reaching maximum at the height where ν 2 (h max ) = ( f − f res ) 2 In such a way, the height of the maximum is a function of chosen frequency f; that is, h max = h max ( f ) On the other hand, the weight of the © 2005 by CRC Press TF1710_book.fm Page 356 Thursday, September 30, 2004 1:43 PM 356 Radio Propagation and Remote Sensing of the Environment integration areas in Equation (12. 58)... L ≅ − R r cosθ is the distance from the turn point to the point of radiowave reception, where θ is the central angle between the satellites (θ > π/2) by radio occultation and Rr is the distance from the receiving satellite to the center of the Earth The refraction attenuation of the radiowave amplitude is described by the formula: ( V= © 2005 by CRC Press 1 1 − d ξ dp R r cos θ ) (12. 41) TF1710_book.fm... dξ ∫ dp arch R dp p (12. 43) R Knowledge of the altitude distribution of air permittivity opens the way for determining the air temperature height profile The equation for air pressure P has the form: ( ) R ∫ P( R) = P R 0 − m g(h) N (h)dh , (12. 44) R0 where m is the average mass of the air molecules, N is their concentration, and g is the free-fall acceleration On the other hand, the gas state equation... value and, correspondingly, the value of the relative tropospheric frequency shift are weakly dependent on the internal details of the air permittivity altitude profile (see Chapter 4) because of the small troposphere thickness relative to the radius of Earth, which leads to the small role of tropospheric sphericity As a result, the key parameters for these effects are the ground and integral values of the . examples of the calculation. Figure 12. 1 © 2005 by CRC Press 338 Radio Propagation and Remote Sensing of the Environment 118.7503 GHz ( λ = 2.53 mm) and an absorptive band at the 5- to 6-mm. 2004 1:43 PM Chapter 4) because of the small troposphere thickness relative to the radius of Earth, © 2005 by CRC Press 348 Radio Propagation and Remote Sensing of the Environment and communication. Press 354 Radio Propagation and Remote Sensing of the Environment . (12. 55) Equation (12. 55) is determined by many factors, particularly, by the signal-to-noise ratio. We must say that the given