RA-2 Rain Mode: Full Deramp Formulation

The RA-2 rain mode has been designed to have transmitted and LO reference pulses o f different lengths in order to configure the range window, allowing the acquisition o f the maximum number of independent samples per scan. Conventional altimetry full deramp formulation has been modified along in order to incorporate the previous condition. A preliminary study o f surface return interference shows that severe range sidelobe reduction schemes need to be applied to the deramped signal in order to minimise the ground clutter interference.

7.4.1 Full Deramp Formulation of Signals of Different Lengths

The use of a longer reference signal implies that successive rain echoes are deramped by different sections o f the LO signal (Figure 7.14). Therefore, it is necessary to introduce some modifications to the RA-2 altimeter mode formulation.

(a)

<

F igure 7.14. Diagram of RA-2 rain mode full deramp of signals of different length.

The linear FM received echo is formulated as:

Sr(t) = rect t - T cos V

f

r

rect LO t - ^LO V COS B (16)

A detailed calculation o f the full-deramp formulation o f linear FM signals o f different lengths can be found in Appendix D.2. The in-phase component o f the com plex envelope o f the deramped echo (after filtering the spectrum component centred at 2 /q ) is given by:

( f t - 3kf(f)== rect ktyj + r cos r . "rb ^ v " “ 2 ytdt + tj) (17)

Notice that the new full deramp formulation only differs from the conventional one by a factor o f which equals zero when the echo and the LO reference signal are o f the same length. The previous term repositions the deramped echoes in the range window. The RA-2 rain mode power spectrum point target response is given by:

2

T,_LO r

sine B_{f * - ^ l}

\ I 2 J J ₍₁₈₎

7.4.2 Ground Clutter Range Sidelobe Interference

In order to validate the performance o f any sidelobe reduction processing to minimise surface interference, it is indispensable to assess the impact o f the technique on both the precipitation signal and surface return spectrums.

(a) (b)

I

I

Z - Z m a x (dB Z) ((h)

Figure 7.15. Precipitation model: (a) Radar reflectivity as a function of altitude; (b) Altitude variation of rainfall rate. Reproduced from [Amayenc et al., 1994].

Amayenc et al. [Amayenc et al., 1994] derived a rainfall reflectivity model as a function o f height, established from radar precipitation measurements. The radar reflectivity obtained at S-Band for a given rain rate is about constant on average up to 4 km above the ground, decreasing with altitude above at a rate o f 5 dBZ/km (Figure 7.15). The same model can be extended to the Ku-Band with the appropriate attenuation

coefficients. Such^model can be employed as a correction factor for the rain power levels calculated in section 7.2.2.

In order to ease the calculation, a uniform precipitation field over a height o f 4 km above the ground is considered. The rain return spectrum is simulated according to the its power level as a function of rain rate (Eq. 9) with the appropriate attenuation coefficients, and disregarding at the moment any waveform or statistical considerations. The simulation does not consider attenuation o f the bright band which could be rather significant (3 to 4 dB) for large rainfall rates [Awaka, 1992]. Bright band attenuation could be incorporated to the model by simply scaling the rain and ground power curves. The surface return is simulated as the power spectrum o f the superposition o f a deramped echo in each range bin, weighted with appropriate power and attenuation coefficients.

(a) (b) I - 1 0 S ^-110 (c) ^-110 r a n g e w in d o w (km) r a n g e w in d o w (km) (d) m in im u m d e te c ta b le h e ig h t (km ) r a n g e w in d o w (km)

Figure 7.16. Ground clutter range sidelobe interference (4 km precipitation field) for low, medium and high rainfall rates: (a) 5 mm/h; (b) 20 mm/h; (c) 50 mm/h; (d) Minimum detectable height as a function of rain rate.

Three different rain rates are considered, (i) 5 mm/h (low detectable rate), (ii) 20 mm/h (medium detectable rate) and (iii) 50 mm/h (high detectable rate). The results of the simulation are shown in Figure 7.16(a-c) and are considered to be representative for each rainfall rate range (low, medium and high). Figure 7.16(d) shows the minimum

detectable height (below a storm top of 4 km) as a function o f rain rate. The rain detectability region corresponds to the area between the storm top and the minimum detectable height curve for each rain rate.

Two factors restrict the performance o f the RA-2 rain mode^fidj^ deramp alternative. Severe ground clutter interference does not allow j«r^etec1j[the minimum required rainfall rate (only rates above 13 mm/h are free o f surface interference). Medium rainfall rates producejsufficient signal-to-noise ratio but are interfered^in the lower part of the range window. High rainfall rates attenuate the ground clutter return, reducing the interference, but the rain signal falls below the system noise floor at low altitudes. Detectability benefits of any range sidelobe reduction technique will be assessed with respect to the previous considerations.