Radio Propagation and Remote Sensing of the Environment - Chapter 12 ppt

Atmospheric Research by Microwave Radio Methods 337The standard water vapor pressure at sea level for moderate latitudes is 10 mbar.. Atmospheric Research by Microwave Radio Methods 339l

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by Microwave Radio Methods

Microwave radio methods are finding greater application for research of the sphere of Earth As discussed previously, they are based on the interaction ofradiowaves with the atmosphere This interaction is apparent in the decrease in waveamplitude, change of phase, polarization, and other radiowave parameters Thermalmicrowave radiation is also the result of this interaction The main focus of thischapter 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

atmo-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 aboutgeneral 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 mainfeature 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 oneway 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

A standard cloudless atmosphere is characterized by such parameters as temperature,density, and pressure The height temperature profile is described by the broken linefunction

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,

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336 Radio Propagation and Remote Sensing of the Environment

Here, T0 is the temperature at sea level, and a is the temperature gradient For theU.S standard atmosphere, T0 = 288.15 K, and a = 6.5 K/km For an approximatecalculation, we can use the simplified formula:

deter-be found in Bean and Dutton.30 The partial water vapor pressure is associated withdensity ρw by the approximate formula:

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Atmospheric Research by Microwave Radio Methods 337

The standard water vapor pressure at sea level for moderate latitudes is 10 mbar Sothe standard value of the refractive index is The standard gradientnear the surface of Earth is assumed to be:

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 calculatedfrom meteorological data With regard to Hn, the following fact can be used It wasestablished 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 graphical place and period of year The averaged value Hence, the median value of the height can be estimated from the following equation:

geo-(12.9)

Now, we will turn our attention to radiowave absorption by atmospheric gases Themain absorptive components are water vapor and oxygen Water vapor has absorptivelines 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 manylines in the submillimetric waves region The wings of the submillimetric linesinfluence the absorption at millimetric waves; therefore, they are taken into accountfor calculation of absorptive coefficients The resulting computation is comparativelygives attenuation coefficient values of water vapor at sea level vs frequency Themaximum attenuation of dB/km/g/m3 is at the resonance wave-length λ = 1.35 cm Thus, dB/km near the surface of Earth at moderatelatitudes The altitude dependence can be expressed as a first approach by theexponential model:

at transparency windows and rather more at the resonance wavelength,because absorption by water vapor becomes independent of the air pressure Somedata show that this height varies with the season of the year and reaches a value of

n H

complicated, so we will provide only some examples of the calculation Figure 12.1

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118.7503 GHz (λ = 2.53 mm) and an absorptive band at the 5- to 6-mm area Theabsorptive line frequencies of this band are provided in Table 12.1

These lines overlap at the lower levels of the atmosphere of Earth, forming apractically continuous band of absorption Line resolution begins only at altitudeshigher 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.

λλλλ) (mm)

Frequency (f) (GHz)

Wavelength (

350 TF1710_book.fm Page 338 Thursday, September 30, 2004 1:43 PM

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line splitting The attenuation coefficient values produced by oxygen are shown independence of the oxygen absorption coefficient:

The total absorption of a cloudless atmosphere is described by the sum:

The main a priori information about hydrometeor formation is based on the 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 ofhydrometeor formation The initial parameters of these formations (temperature,pressure, etc.) depend on their altitude and, initially, can be found using the standardatmospheric model Very important characteristics of hydrometeors are their geo-metrical dimensions, motion velocity, and lifetime

state-The first point of interest in this discussion is describing the electrophysicalproperties 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 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 (εo)

is often called the optical permittivity and is reached at λ→ 0 The wavelength λr

is related to the relaxation time of water by the equation εo = 5.5, and

εs and λr depend on the water temperature and salinity The details of these dencies will be given in the next chapter; here, we shall give the values of theseparameters for T = T0 Thus, εs = 83 and λr = 2.25 cm

Figure 12.1 The exponential altitude model is also used to determine the altitude

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To estimate hydrometeor reflectivity (see Equation (11.15)), we need to calculatethe parameter:

12

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Here, w is the cloud liquid water concentration, and is the water density Forwaves longer than 2 mm:

(12.21)

The water content here is expressed in g/m3 and wavelength in cm For freshwaterice, we can assume to obtain:

where I is the ice concentration and ρI is its density

12.2 ATMOSPHERIC RESEARCH USING RADAR

(WR), which will be covered in greater detail here The main areas of concerninclude:

• Measurement of the radio echo power from meteorological targets, withthe echo being selected against a background of interfering reflection fromthe top beacons

• Detection and identification of meteorological objects by their reflectivity

• Definition of the horizontal and vertical extent of meteorological tions and determination of their velocity and the displacement direction

forma-• Determination of the upper and lower boundary definitions for clouds

• Detection of hail centers in clouds, determining their coordinates, anddefining their physical characteristics

Weather radar operates at centimeter and millimeter wavelengths; some of them aredual frequency Specific requirements for weather radar depend upon the particulartype of meteorological object and include the following:

• Exceptionally wide-scattering cross-section variations of atmospheric mations reaching values of around 100 dB

for-• Considerable horizontal and vertical sizes of the atmospheric objectsrelative 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 acteristics of atmospheric formations

2

1 36 10

6 2

s

1cm

dBkm

We briefly examined this problem in Chapter 11 when we discussed weather radar

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The primary WR value measured is the backward scattering cross section:

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 26 = 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:

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 a0 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, a0 = 1.5 · 10–4 cm,

N = 472 cm–3, amin = 1.0 · 10–4, and amax = 20.0 · 10–4 cm Calculations based on

this model give us values of W = 0.4 g/m3, and Θ = 9.9 · 10–17 cm3 Aivazjan39

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, amin = 2.0 ⋅ 10–3 cm, amax = 8.5 ⋅ 10–3 cm, and

a a

µ

µ µ1

1

monly used (as noted in Chapter 11), is the distribution proposed by Deirmendjian

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N = 1.54 cm–3 The results of calculations give us W = 0.12 g/m3 and Θ = 1.6 ⋅ 10–15

cm3 Comparison reveals that cloud water content and radiowave absorption areprimarily 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 extremelylow In particular, calculations made on the data given in Aivazjan39 give us Θ = 1.4

⋅ 10–14 cm3 for the main conditions, with concentration N = 2.0 ⋅ 10–3 cm–3 Suchdrops 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 mm6/m3) This value is equal to Z = (6.4 ⋅ 1013)Θ The average valuesGood spatial resolution, achieved by use of a pencil-beam antenna and widebandsignals, 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) Asecond maximum at a height of 8 km typically belongs to thunderclouds Forordinary clouds, the value of Θ decreases smoothly from the lower boundary to theupper one Cumulus clouds have maximal reflectivity in the middle The extent ofthe reflected signal and its change in shape depend on the type of cloud All of thesedata are used to identify and classify cloud cover

The process of radiowave reflection by rain is more complicated compared tothe 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 ofrain drops are larger then water drops in clouds For example, the median value ofdrop radius is:

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necessity to sum the slow convergent series These calculations for different tions were done (see, for example, Aivazjan39) The complexity of the calculations

situa-is made greater by the need to know the dsitua-istribution function The Marshall–Palmerfunction, a result of experimental data approximation, is commonly used for firstestimations; 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-distributionvariant In any case, the dependence of distribution parameters on the rain intensityhas 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 inrain which becomes particularly noticeable in the millimeter-wave region Thismeans that the radar equation has to be developed by taking into account radiowaveextinction inside the rain So, Equation (11.18) is reduced to:

Here, scattering has to be added to the absorption by the drops In other words, thetotal 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:

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80% of cases For the remaining 20% of cases, a shower occurs At 2 < Yi < 8,

showers occur 75% of the time; a steady downpour, 20% of the time; and

thunder-storms, 5% of the time When Yi > 8, probability of a storm is high (95%), andshowers occur only 5% of the time

We must say a few words about radar detection of hail Small, as compared withthe wavelength, ice particles scatter much more weakly than water drops of similar

size because, as we already pointed out, K ≅ 0.18 for ice; however, ice particles ofradius comparable to the wavelength can scatter significantly more than similar waterdrops because of the transparency of ice particles for radiowaves Some resonance

up to 10 to 15 dB in comparison with water spheres A simple explanation of thiseffect is based on the supposition that radio beams are focused on the back wall of

an ice particle and reflected backward to the radar.91,92 In reality, hail particles areoften covered by a water film created, for example, during their fall due to an increase

in air temperature and decrease of altitude The thickness of this film forming in themelting regime is of the order of 0.01 cm The scattering cross section becomessmaller in this case During the wet growth of hail, this film can have a thickness

of the order of 0 to 0.2 cm.92 In this case, the hail particle behaves as an absorptivesphere, and Equation (5.97) can be used to calculate the cross section in the firstapproximation, especially in the case of waves in the millimeter range In light ofthe relatively large size of hailstones, we can come to some conclusions with regard

to the strong reflectivity of hail clouds and hail precipitation The backward tering cross section of hail precipitation varies within the range 10–8 to 10–6 cm–1

scat-at the X-band and (5 ⋅ 10–10) to (5 ⋅ 10–6) cm–1 for the S-band.92 These cross sectionsare comparable to those for rain This similarity of cross sections makes it difficult

to distinguish reflection from hail and reflection from rain by one frequency; ever, the specific cross-section spectral dependencies for rain and hail are differentwhich allows us to use the two-frequency radar technique This idea is also used inother areas of weather radar applications In particular, a high probability of almostall precipitation detection is achieved by the simultaneous use of the X-band andmillimeter-wave bands

how-Rain drops and ice and snow particles have a non-spherical form which leads

to depolarization of the scattered radiowaves This depolarization can be assessed

by the depolarization factor , where σm is the cross section of thematched polarization (for transmission and reception), and σc corresponds to the

cross-polarization component At the X-band, m ≅ –1.8 dB for dry snow, –4 dB formoist snow, –16.5 dB for a steady downpour, and –19.5 dB for showers The degree

of polarization allows us to identify the type of precipitation

It is necessary to note that reflection by rain, clouds, etc., has a stochasticcharacter The scattered field is described by the Gaussian function which leads tothe Rayleigh law for amplitude distribution and exponential function of the proba-bility distribution for the scattered signal intensity:

m= σ σc m

P I I

I I

can take place (see Chapter 5) which leads to growth of the scattering cross section,

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The stochastic character of reflection means that all relations between reflectivityand hydrometeor parameters are statistical For example, Equation (12.29) reflects

a correlative connection but not a deterministic one Due to the multiplicity of thehydrometeor structures and their dynamics, etc., the accuracy of the calculationscompared to experimental data is not very high and has very often the value of tenspercents

Particle movement changes the frequency of backward-scattered waves due tothe Doppler effect This regular motion causes a frequency shift that helps define aparticular regular transition In such a way, we can measure the velocity of the fall

of a drop, wind speed, etc This particle motion results in signal spectrum expansion,which is described by Equation (5.188) Let us assume that the velocity distribution

is a Gaussian one:

(12.33)

Here, v0z is the velocity of the deterministic motion (wind, for example) The standarddeviation characterizes the velocity pulsation because of, for example, tur-bulent processes The maximum of the spectral curve defines the regular motionspeed, and its width permits us to obtain the amplitude of the turbulent pulsation

In particular, the spectrum width of the signal reflected by a tornado allows us toestimate the angular velocity of its rotation, which is one of the distinguishing signs

of a tornado

Weather radar is used sometimes to observe lightning The short lifetime oflightning (0.2 to 1.3 sec) is a problem with regard to their observation Very often,the reflection from lightning is masked by signals scattered from the rainy zones

We have stated already that modern radar is able to detect radiowave scattering

by weak inhomogeneities of the troposphere Sometimes these inhomogeneities

behave as a point target moving in space and are regarded as the so-called angels

type.91 For the first approximation, these “angels” can be assumed to be dielectricspheres for which the dielectric constant differs slightly from the permittivity of thesurrounding medium For these spheres, the cross section of the backward-scattering

is expressed in the form:

(12.34)

in accordance with Equation (5.51) It was supposed in the process of simplification

that 2ka >> 1, and cos2(2ka) was averaged Assuming that a = 100 m = 104 cm, and

, we obtain cm2 Such high values are observed duringsome summer conditions;87 however, the assumption about sharp spherical wallsappears to be too artificial More reasonable is an assumption about a smooth change

of permittivity To take this fact into account, let us note Equation (12.34) can berewritten as:

2

0 2 2

0 2

2

ε − = ⋅ −

1 2 10 5 σ πd( )≅ 10

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In order to consider a smooth permittivity change, we can use Equation (3.108).The cross section will depend on wavelength in this case It has been reported thattwo-frequency radar allows us to estimate the values of the temperature or airhumidity gradients within a spherical layer bounded by an atmospheric inhomoge-neity.88 Sometimes, the concentration of dielectric inhomogeneities is so high thatreflection from them has a diffusive character, and the amplitude of the reflectedsignal experiences intense fluctuations This radio echo is referred to as an incoherentone, in contrast to the echo generated by point targets An incoherent echo isfrequently connected with the precloud state

Other types of “angel”-like reflection are caused by atmospheric formations Inparticular, tropospheric layers with high vertical gradients of air permittivity lead to

a horizontally stretched echo with a scattering-specific cross section of the order of 10–16

to 10–15 cm–1.87

Zones of high turbulence are also the subject of radar observation Usually, theKolmogorov–Obukhov approximation is applied to describe a radar echo Equation(11.23) is reduced to:

where C n is the so-called structure constant Its value in the troposphere varies withinthe interval of (2 ⋅ 10–8) to (2 ⋅ 10–7) cm–1/3 We can easily see that, in this case, thespecific cross section has a value of 10–16 to 10–14 cm–1 at a wavelength of 10 cm

12.3 ATMOSPHERIC RESEARCH USING RADIO RAYS

The various atmospheric effects (e.g., radio ray bending, phase delay, frequencyshift, intensity attenuation) can provide the basis for determining atmospheric param-eters through the processing of radio signals Airborne platforms (aircraft, balloons,satellites) and the Sun can be sources of the radiowaves The reception platform, as

a rule, is ground based The refraction angle and relative Doppler shift are frequentlyindependent, and the angular position of the radiation source is the only parameterfor which observation data are accumulated However, the refraction angle valueand, correspondingly, the value of the relative tropospheric frequency shift areweakly dependent on the internal details of the air permittivity altitude profile (seewhich leads to the small role of tropospheric sphericity As a result, the key param-eters for these effects are the ground and integral values of the air dielectric constant Tropospheric sphericity is important for the occultation technique of observationand gives more reliable results for height profiles based on radio data This method

is rather simple in terms of the basic idea and in interpretation of the data; however,

it is comparatively complicated in practice because it requires at least two satellites

11

Chapter 4) because of the small troposphere thickness relative to the radius of Earth,

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and communication links for the measurement of data transmission to the groundterminal This method was shown to be efficient when used for Mars and Venusatmospheric research32 and is being developed further for use within the atmosphere

of the Earth.35

The idea behind the method is very simple Let us imagine that high-orbit satellite

A (i.e., a satellite in an orbit above the atmosphere) radiates the radiowaves, andsatellite B receives them (Figure 12.2) The radio beam connecting the satellites willsink into the atmosphere during their mutual movement At least two effects willtake place during the sinking of the radio beam that are applicable for interpretation

of these measurement data The first effect relates to the amplitude change due todifferential refraction (Equation (4.39)) The second one is the frequency change as

a consequence of the Doppler effect In this case, the corresponding frequencychange is described by Equation (4.61), which, strictly speaking, is correct for thecase of an infinitely distant transmitter (receiver) In practice, this situation occurswhen, for example, the transmitter is onboard a geostationary satellite and thereceiver is onboard a satellite rotating around the Earth, which is the simplest case.Measurement of the frequency shifts of the received waves during the satellitemotion allows us to note the refraction angle value as a function of the sighting(tangent) distance We then obtain the integral equation on the basis

of Equation (4.44) The variable change by the formula transformsthe equation:

which can be reduced to a known Abel equation, which we will carry out here as

it is simpler to state the method of its solution Let us multiply Equation (12.37) by

and integrate with respect to p within the limit from R to ∞ Later,taking into account the change of integration order,

FIGURE 12.2 Researching the atmosphere of Earth by means of radio-occultation.

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Let us now consider how to define atmospheric permittivity based on refractionattenuation We have described it before, and the effect itself is estimated by simpleconcepts Let us assume a parallel radiowave beam and study the change of this

beam area inside an interval of sighting distances (p, p + dp) The incident beam energy is proportional to the differential dp at this altitude Due to refraction, the

beam turns through an angle ξ(p) at altitude p, and through an angle

at altitude p + dp As a result, the beam is divergent, and its area is

at the place of reception Here, is the distance from the turn point tothe 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 tothe center of the Earth The refraction attenuation of the radiowave amplitude isdescribed by the formula:

F

R R

1 ξ rcosθ

Tiêu đề	Atmospheric Research by Microwave Radio Methods
Trường học	CRC Press
Chuyên ngành	Atmospheric Research
Thể loại	Chapter
Năm xuất bản	2005
Thành phố	Boca Raton

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