Aerospace and Electronic Systems - June 2019 - 20

The NEFOCAST System for Detection and Estimation of Rainfall Fields by the Opportunistic Use of Broadcast Satellite Signals
Table 2.

Summary of the Main Parameters of the Satellite Link
Feature/Item

Name/Value

Latm

0:09 dB

Tm

275 K

Tc

2:78 K

Tg

45 K

Figure 4.

Trx

13:67 K

Left: Downlink geometry with stratiform rain. Right: Rain rate
(mm/h) versus vertical coordinate (km).

The algorithm for the estimation of the rain rate
requires knowledge of the rain attenuation Lrain ðtÞ on the
satellite downlink, which from manipulation of (1) and (2)
can be formally expressed as follows:
Lrain ðtÞ ¼

½ðEs =N0 ÞðtÞðdryÞ
½ðEs =N0 ÞðtÞðwetÞ

ð1 À  Þ þ 

(3)

where
D

T À Tc
À m
Á:
Latm Tm þ Tg þ Trx

(4)

Equation (3) represents the basic tool we use for
the evaluation of Lrain ðtÞ, and it requires in principle
the availability of both the dry and wet SNRs at any
instant t during a rain event. In practice, however, only
the wet SNR is available (measurable) during a precipitation, and therefore only a presumed, fictitious value
for the dry baseline SNR can in fact be used in (3).
Estimation of the dry baseline SNR in rainy conditions
is an open research issue and is currently being investigated by the authors. The results presented in this
paper are obtained by replacing the dry SNR in (3),
during rainy periods, with the last value of dry SNR
measured before the rain onset, and keeping this value
constant for the entire duration of the rainy event. Further details of this procedure are given in "Slow-Fast
Differential Kalman Tracker." The numerical values
used to compute (4) are recapped in Table 2.
The values are either taken from the literature [18] or
directly measured at the receive station ID NEFOCAST-ITA-PI-003X (Pisa, 43.7203 N, 10.3836 E,
elevation angle ue ﬃ 40 ) and lead to  ¼ 0:799.

LINK GEOMETRY AND MODEL FOR RAIN ATTENUATION
To evaluate the rain attenuation in a satellite link, we
make the simplified assumption of stratiform precipitation, characterized by a clear separation, at the height h0
of the 0  C isotherm, between the upper layer, named the
20

"ice particles layer" (IPL), made of frozen dry particles,
and the lower layers in which the ice particles melt into
raindrops. Significant excess attenuation of the signal
occurs only in the lower layers due to the presence of
liquid-phase precipitation. These layers are structured as
follows: the superior one is named "melting layer" (ML)
and contains a combination of ice and rain, while the inferior is named "liquid layer" (LL) and contains only rain.
Figure 4 illustrates the geometry of the radio link and
represents the various precipitation layers. To simplify the
notation in the upcoming equations, the reference system
has been chosen to set the zero quota at the level of 0  C
isotherm and the vertical coordinate is oriented to increase
in the direction of the ground, so that at the ground
antenna level the vertical coordinate is h ¼ h0 . In the
remainder of the paper, the vertical coordinate is
expressed in kilometers and all the variables expressing a
value of rain rate are in mm/h. In the LL, the time-varying
rainfall rate RLL ðtÞ is assumed independent of the vertical
coordinate, while in the ML we assume that the liquid rain
fraction varies linearly with height [19], passing from 0 at
the 0  C isotherm level to the full liquid rate RLL ðtÞ at the
lower edge of the ML. Therefore, denoting with Rðh; tÞ
the (liquid) rain rate as a function of both the time and the
vertical coordinate h, we have
(
D

Rðh; tÞ ¼

RLL ðtÞ
dML h;

RLL ðtÞ;

0 h dML
dML < h h0

(5)

where dML (km) is the vertical extension of the melting
layer, given by the difference between the 0  C isotherm
level and the full liquid rain height, [20] and we assume
dML < h0 . We also assume that the specific rain
attenuation kðh; tÞ in dB/km is a time-varying function
of the vertical coordinate h, related to the rainfall rate
Rðh; tÞ according to the customary k ¼ aRb power law.
By adapting the power law to our 2-layer (ML-LL) model,
one gets.
The coefficients in the LL are supposed to be
independent of h and, for the NEFOCAST FL frequency
(11.345 GHz), take on the values aLL ¼ 0:0153 and

IEEE A&E SYSTEMS MAGAZINE

JUNE 2019
Aerospace and Electronic Systems - June 2019

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