2. OBJETIVO GENERAL
4.3. RELACIONAR LOS CONOCIMIENTOS, ACTITUDES Y PRÁCTICAS DE
Although there is sufficient rainfall returned power to make the signal detectable, it is very low compared to the returned power from the Earth's surface, especially for small cloud and rain reflectivities. The dynamic range o f the measurements can easily achieve a figure o f 60 dB. The ground clutter can easily be rejected by gating in the unmodulated pulse system alternative. However, for pulse compression systems, the ground point target response is overlapped with those o f the rain, and can interfere and obscure the measurement (linear FM signal theory is developed in Chapter 3).
Pulse compression systems are characterised by the modulation o f the carrier frequency o f the radar pulse, so that it is possible to attain better range resolutions with a less demanding peak power requirement, increasing the number o f available independent samples (section 2.5). However, when the returned echoes are processed in the receiver, range sidelobes appear on both sides of the pulse main peak response, being a source of self-clutter interference. On the other hand, the sidelobes o f the antenna radiation pattern must also be under a certain level to prevent surface interference.
In order to characterise the specifications imposed on the radar waveform and the antenna radiation pattern by the ground clutter return, the spaceborne surface radar equation is derived and compared to the levels of rainfall return power in this Section.
2.4.1 Earth Surface Radar Equation
In order to calculate the surface radar equation, equal steps are followed as for the calculation o f the meteorological radar equation (Section 2.2), but considering now the surface integration over the antenna footprint (the area intercepted by the antenna beamwidth on the ground). The radar cross section o f the surface is defined as the backscattering coefficient per unit area, A particular case o f a sideways looking radar and an antenna radiation pattern which has symmetric Gaussian distribution along the two principal directions are assumed. Thus, the surface return power, according to the system geometry shown in Figure 2.3, is given by:
hsecO n —0.2 In 10 \ ocjfdr
P,=- --- ^
-
0' ^ - - - -a°(e)e
where h is the satellite altitude and the storm top height.
storm top
rain cell
antenna footprint
Figure 2.3. Spaceborne meteorological radar target scenario and geometry.
The surface radar cross section
cj®
depends on the type of surface (land orsea),
its roughness, the transmitted frequency and the angle of incidence. In the following sections, surface power calculations are assumed to be over the sea surface, with a scattering model described in the TRMM design proposal [Manabe and Ihara, 1988].2.4.2 Interference through Range Sidelobe
When the pulse compression technique is implemented by frequency modulating the radar waveform, range sidelobes appear on both sides of the filtered pulse in reception. Since there is a very significant difference between the backscattered power from the precipitation and the Earth's surface, the compressed pulse range sidelobes must be kept at a very low level. Otherwise, ground clutter range sidelobes could mask the precipitation return, in particular at low heights and low rainfall rates or cloud reflectivities. The rainfall to surface power ratio gives a good estimate of the range sidelobe level which needs to be achieved in order to prevent Earth's surface clutter interference. The rain to surface power ratio is given by (Eq. 8 and Eq. 16):
P ^ _ _ _ cT V___________
Ps ~ 2(/!-z)^sec(0)cT°(0)
rj{R) 0.21nl0a/^ — sec(0)
e
(17)
where z is the pulse volume altitude.
TRMM Mission rain to surface power ratio contour maps are displayed in Figure 2.4, considering a compressed pulse range sidelobe level factor of 50 dB. Hence, it
should be noted that the 0 dB contour shown in the plots represent a power level 50 dB below the ground power level.
1 i> C i c it
100 1000
I o 3 0 0 If) t i n
i r = M L L f f A T E f 1
R f j f M F m . L l U U E ( M M . / H I
Figure 2.4. Pr/Ps ratio contour maps (in dB) for sea clutter through range sidelobe at 13.8 GHz: (a) Scan angle 6= 0°; (b) Scan angle 6= 15°. Reproduced from [Manabe et al., 1988].
In order to prevent the Earth's surface return interfering the rainfall signal through range sidelobe, the compressed pulse sidelobe level must be at least 60 dB below the main peak. Such a stringent specification has not yet been achieved with the current state of technology. Due to the difficulty of generating a FM waveform giving the required compressed pulse range sidelobe level of -60 dB, TRMM designers ruled out the implementation of the pulse compression technique. Hence, the specified range resolution of 250 m is obtained by transmitting an unmodulated short pulse (1.67 |is). Pulse compression range sidelobe level considerations in terms of Doppler frequency are developed in section 2.5.
2.4.3 Interference through Antenna Sidelobe
The ground backscattered power received through antenna sidelobes can also interfere with cloud/rain rate measurements. For off-nadir angles, the ground clutter which interferes a particular pulse volume at a range r from the satellite consists of an annular area on the ground at the same range r [Manabe and Ihara, 1988]. The width of this annular area is determined by the extent of the transmit pulse width ( r ± c T / 2 ) .
Therefore, power from the pulse volume (through antenna main lobe) is received simultaneously with power from that particular area of ground clutter (through antenna sidelobes).
Manabe and Ihara calculated the Pf/P^ ratio for an antenna with an isotropic sidelobe pattern of -35 dB. Some contour maps of the P^/P^ ratio are shown in Figure
2.5. They concluded that there is a critical altitude below which light rainfall rates are interfered with by ground clutter through the antenna sidelobes. However, if the sidelobes of the antenna radiation pattern are kept below -30 dB, the interference has no significant impact on most measurable rainfall rates. A different study [Hanado and Ihara, 1992] considered a more realistic antenna radiation pattern (a phased array fed with a Taylor distribution). They showed that for a sidelobe level of -30 dB, the critical interference height (depending on the scan angle) extends to 1.2 km over the sea surface for an incidence angle of 17°. (a) (b) 5 n 2 I 0 I 00 RO [NFAl.L HOTc ( MM/H 1 -I a o z> 2 I •VIUIJ" I'-I-riirjTiT- J 1 i n i o n l o n n im I nrALL rrtl imh/hj
Figure 2.5. Pr/Ps ratio contour maps (in dB) for sea clutter through antenna sidelobe at 13.8 GHz. (a) Scan angle d= 0°; (b) Scan angle 0= 15°. Reproduced from [Manabe et al., 1988].