SEROPREVALENCIA DE LA RINOTRAQUEITIS INFECCIOSA BOVINA

In the case of meteorological targets, the returned signal from a pulse volume consists of a number of randomly distributed scatterers. As the position of these scatterers varies at every scan, successive echoes from the same pulse volume fluctuate. Therefore, a sufficiently large number of independent samples are required in order to estimate the true average of the precipitation within the pulse volume. The rate of signal fluctuation is directly related to the particle relative movement rate inside the pulse volume and its measurement must contain significant meteorological information. The absolute motion of the particles in the pulse can be measured through the Doppler spectrum of the returned signal.

In order to derive an expression for Doppler frequency offsets, a point target at a distance r from the radar is considered. The phase position of a stationary target relative to the radar is AKrjX. When the target is in motion with respect to the radar with a radial

velocity o f v = d r l d t , its phase position changes proportionally. The phase change with time represents angular frequency [Levanon, 1988], given by:

Hence, the resultant Doppler frequency offset can be expressed as:

f d = — Y

^

(19)

Horizontal winds may have significant velocity tangential components, especially at off-nadir pointing angles which can broaden the Doppler spectrum width by hundreds of Hz. The hydrometeors vertical motion may reach velocities in the range o f ±10 m/s which translate into Doppler shifts in the order of 1 kHz. Independently from the intrinsic motion of the backscatterers in the pulse volume, an extra Doppler frequency component is introduced by the spaceborne rain radar platform motion. Assuming without loss of generality satellite motion along the jc axis, the Doppler offset as a function o f elevation and azimuth is given by (a detailed calculation can be found in Appendix A):

f d ~ ~ — f ^ s i n 0 cos(/)

4 (20)

It must be pointed out that the Doppler frequency caused by the satellite motion is independent of slant range and is only dependent on the scanning angles. For nadir pointing, the Doppler spread over the antenna footprint is given by:

A / , = - ^ s i n f

4 2 (21)

Assuming typical parameters of the TRMM system, the Doppler spread at the edges of the footprint reaches a value of 8 kHz. A Doppler frequency map is shown in Figure 2.6, as a function of the surface jc and y coordinates. Geometrically, the iso- Doppler contours correspond to hyperbolas on the ground. For the TRMM system geometry, Doppler shifts caused by the platform motion can reach values as large as 300 kHz, which represent the main Doppler frequency component and may amount to a significant fraction of the signal bandwidth.

waveform range sidelobe level (Chapter 4). Therefore, an increase of the compressed pulse range sidelobe level is expected for off-nadir pointing angles. It has generally been assumed that the range sidelobe level requirement for spaceborne rain radars (-60 dB, Section 2.4.2) remains constant as a function of Doppler frequency. However, the surface return power is weaker for scanning angles departing off-nadir pointing, since its reflectivity decreases with incidence angle. Assuming typical parameters for the BEST Mission, the pulse illumination remains in the beamwidth limited region and no further power reduction due to pulse limited illumination is considered.

-5 0 0 . 5 0 0

Figure 2.6. Doppler frequency offset map as a function of ground coordinates.

In order to calculate the range sidelobe level specification as a function of Doppler frequency, the surface reflectivity variation as a function of incidence angle model assumed for the TRMM clutter evaluation [Manabe and Ihara, 1985] has been adopted. The reflectivity model for elevation angles below 20° [Valenzuela, 1978] is based on ocean surface radar cross section experimental data at 13.9 GHz [Schroeder et al., 1984]. The ocean surface reflectivity model is given by:

tan(0)^

cr^(0) = (T^(O)sec(0)^g 5^ ₍₂₂₎

where is the total variance of the surface slopes. The interference through range sidelobe (Eq. 17) has been evaluated at ground level as a function of Doppler frequency and rainfall rate, without considering attenuation in the precipitation field (Figure 2.7(a)).

It can be concluded that a limited range sidelobe level degradation in the compressed pulse due to Doppler frequency offsets is allowed without interfering rainfall detection and estimation. The range sidelobe interference as a function of minimum detectable rate can reduce the range sidelobe specification up to 11 dB for Doppler shifts up to 200 kHz. The range sidelobe level curves shown in Figure 2.7(b) represent an

effective limit for the envelope of the ambiguity function along the v axis for any pulse compression waveform candidate. It should be noted that the range sidelobe level specification results are strongly dependent on the surface reflectivity assumptions made.

30 m m /h 2 0 m m /h 10 m m /h -2 0 -

0.5 m m /h

d o p p ler freq u en cy (kHz) rainfall rate (mm/h)

d o p p le r fre q u e n c y (kHz)

Figure 2.7. Range sidelobe level specification as a function of; (a) Rainfall rate and Doppler frequency; (b) Doppler frequency and minimum detectable rainfall rate.