Rain Attenuation Retrieval Using Surface Reference Technique and
the NASA ER-2 Doppler Radar Data
E. Verónica Morales-Irizarry
Graduate Student, University of Puerto Rico at Mayagüez
Jessenia Merced-González
Undergraduate Student, University of Puerto Rico at Mayagüez
Sandra Cruz-Pol
University of Puerto Rico at Mayagüez
Abstract
1. Introduction
caused by rain. We will use the surface
reference technique (SRT) to correct the
For years airborne weather radar attenuation. The SRT estimate the path
systems have been used to study integrated attenuation (PIA) through rain
mesoscale convective systems (MCS) and from the decrease in the surface return
other
mesoscale
and
cloud-scale (Iguchi et el. 1994). PIA denotes the twophenomena. These radars have provided way attenuation to the surface expressed
an important tool to help understand the in units of decibels (Iguchi et al. 2000).
kinematic and dynamical aspects of
In the following sections we are
MCSs, such as the importance of the rear going to describe in details the data used,
inflow jet, mesoscale up- and downdrafts, the EDOP radar system, the surface
the sustenance of anvil precipitation, etc. reference technique, and the results
(Heymsfield et al. 1996). The Doppler obtained.
radar is an instrument that can detect
tracers of wind and measure their radial 2. Description
velocities in clear and inside heavy rainfall
regions. In this paper we are going to
The data was taken during the
describe information recollected by the Cirrus Regional Study of Tropical Anvils
NASA ER-2 Doppler radar (EDOP). It is and Cirrus Layers - Florida Area Cirrus
mounted on the high altitude NASA ER-2 Experiment (CRYSTAL-FACE) on July 29,
aircraft, and makes use of a nadir pointed 2002 with the EDOP radar system. This
radar beam and a radar beam pointed experiment is a measurement campaign
approximately 33.5º forward of nadir. that investigates the physical properties of
Reflectivity and Doppler information are the tropical cirrus cloud and their formation
received from both antennas, the nadir processes. The understanding of the
and the forward.
production of upper tropospheric cirrus
In this paper we used the reflectivity taken clouds is very important because is
by the nadir antenna.
essential for the modeling of the Earth’s
Reflectivity
is
the
expected climate.
backscattering cross section per unit
The EDOP radar is an X-band
volume. Using the reflectivity measured in radar with two fixed radar beams: one
the storm we can retrieve the attenuation
Fig. 1 EDOP measurement concept
in the observed surface cross section from
pointed at nadir and the other pointed the reference value is assumed to be a
approximately 33.5º forward of nadir result of the two-way attenuation along the
(Fig.1)
(Heymsfield
et
al.
1996). propagation path (PIA).
Reflectivity and Doppler information is The PIA for each beam is then used as a
received from both antennas, but for this limiting condition in an attenuation
paper we are going to use the data taken correction algorithm (Iguchi and Meneghini
by the nadir pointed antenna. It have an 1994).
antenna beam width of 3º in the vertical
The SRT development has focused
and horizontal directions. For an altitude of over the ocean because it has a well20 km, which is the flight altitude of the known, and relatively constant, microwave
ER-2, the footprint of EDOP at the surface reflection. Only few studies have been
is approximately 1 km. The ER-2 has a developed over land because at incidence
ground speed of 210 m/s and the data angles near-nadir the radar cross-section
system uses an integration period of 0.5 s. of land surface can be highly variable. In a
The transmit pulse is 0.5 µs and the gate cloud free region over the ocean the
spacing is over sampled at intervals of surface echo at nadir incidence has
37.5 m. The general specifications of the fluctuations of 1 dB while the nadir echo
EDOP radar system are given in Table 1 over land becomes highly variable with a
(Heymsfield et al. 1996).
standard deviation of 4 dB. The
The SRT algorithm uses the radar variability
of surface echo along a flight

cross section of the ocean surface as a track limits the minimum PIA that can be
means of estimating the path integrated observed.

attenuation. In the SRT an initial value is
determined for the radar cross section of a 3. Process
rain-free area in relatively close proximity
The data was taken on July 29,
to the rain cloud. During subsequent 2002 beginning at 18:01 and finishing at
observations of precipitation any decrease 18:11 UTC. The flight track is from
longitude -82.49, latitude 26.51 to
longitude -81.65, latitude 26.32. In Fig. 2
shows the flight track of the ER-2 and
flight tracks of other aircrafts during that
date.
Table 1. EDOP System Specifications
Fig.2 Flight tracks on July 29, 2002.
C | K |2
Pr ( r ) 
Z m (r)
r2
(1)
where Zm(r) is the apparent measured
radar reflectivity factor and is given by

r


Zm (r)  Z(r)exp0.2 ln 10  k(s) ds


0
(2)
and

When there is attenuation, the radar
equation becomes

K 
m 2 1
m 2  2 .
(3)
Where pr is the received power, r is the
range
 from the radar, C is the radar
constant, m is the complex index of
refraction of the precipitating particles.
r
k(s) ds

0
K(s) is the attenuation rate and
is the total attenuation from range 0 to r.
The “path integrated attenuation” (PIA) in
the attenuation to the surface, given by

rs
0 k(s) ds where rs is the range to the
surface (Iguchi and Meneghini 1994).
When the attenuation is negligible,
Z(r)=Zm(r) and the rainfall rate can be
estimated by using the relationship Z-R. If
the objective is to attain a reasonable
beamwidth with a small antenna, the

wavelength used in an airborne radar must
Z (r )
C1   m s   qSrs 
be short and, therefore, the rain will
 Zrs  
attenuate the signal. In that case is
(9)
S
(
r
)
needed to solve equation (2) for the where
s is defined by
rs
unknowns Z(r) and k(r) for a given function

Zm(r) (Iguchi and Meneghini 1994).
S(rs)   Z m (s) ds

0
(10)
3.1 Surface Reference Technique (SRT)
 Substituting (9) into (5), we get
PIA can be estimated by the
1/ 

surface reference technique by the


Zm (rs) 


decrease in the surface return. If k(r) is
Zt  Z m r
  q[Srs   Sr]
Z
r
k  Z  ( r )






s

 .
related to Z(r) by
and  is
constant in range, equation (2) can be
written as follows:
(11)
As

Defining
as

du
d
rs
ln Z m ( r )  q   0
 u 


dr
dr
As  exp 0.2 ln 10  k ds
(4)

0
,
(12)
 

u  Z ( r )
where
and q=0.2ln10. A then
Z (r )
 general solution for this can be
A s  m s
Z rs 

,
(13)
1 / 
Z ( r )  Z m ( r ) C1  qS ( r ) 
Z rs 

(5) where
is a constant and the solution
can be written as
C
1 / 


where 1 is an arbitrary constant, and
Z t  Z m r  A
 s  q[ S rs   S r ] 
S
(
r
)
. (14)

is defined by

r
(Iguchi and Meneghini 1994).

S(r)   Z m (s) ds
This method can be called as “final value

0
(6)
method and it uses the PIA as the single
r 0
If is given that the initial condition at
condition to choose the solution.
is
Z ( r)  Z m ( r)
.
(7) 3.2 Path Integrated Attenuation (PIA)

C1

Then
becomes 1. This corresponds
to
Let PIA denote the two way
the Hitschfeld-Bordan solution:
r r
attenuation to the surface (  s )

1 / 
expressed in units of decibels, that is
Z HB ( r )  Z m ( r ) 1  qS ( r ) 

.
(8)
Z (r )
PIA  10 log 10 m s  10 log10 A s

 Zrs 
(Hitschfeld-Bordan 1954)
, (15)
If the final condition on Z(r) is given at (Iguchi et al. 2000).
(align these symbols with other text as The SRT gives an independent estimate of
r r
C
r=rs)  s , then 1 (should be as C1, also PIA. This PIA is denoted by PIAsr. This

check similar cases in the paper) must technique assumes that the decrease of
satisfy the following condition:
the apparent surface cross section is
caused by the propagation loss of radar


signal by rain (Meneghini et al. 2000):
0
0
PIA SR   0   no
 rain
 rain

.
(16)
0
no  rain
In the later equation
indicates the
average of the surface cross section in
 rain-free conditions for a given incidence
angle. This 
decrease of the surface cross
0
section is denoted by  and expressed
in decibels.
We want to obtain the best estimate
0
PIA e
of PIA, denoted
, from  and  .
 by
Then introduce an attenuation correction
Fig. 3 Reflectivity
factor . With this attenuation correction
Z
factor, e 
(the attenuation-corrected),
can


be calculated at all ranges by (Iguchi and
 Meneghini 1994)
Z m r 

Ze r 
1/ 
r
1 q   Z m s ds
0
. (17)
0
If the surface reference  is
taken to be exact and if we set



PIA e  PIA SR   0
,
the
correction factor is given by

  s 

1 10 

where  is defined as
0
attenuation
/10
,
  q  0 Zm s ds
(18)
rs

.
Fig. 4 Reflectivity vs altitude over the
ocean no precipitation
(19)


4. Discussion and Conclusion
The flight track of the NASA ER-2
starts over the ocean and finishes over
land. There is no rain over ocean until 20
km Fig. 4, that is why there is no
reflectivity profile, because there is no rain
to reflect. After 20 km begins a high
precipitation region.
The following figures show the profile of
the reflectivity from the data. Fig. Shows Fig. 5 Reflectivity vs. altitude over the
the reflectivity profile over the ocean ocean with precipitation
without precipitation. This is the region
Li, L., S. M. Sekelsky, S. C. Reising, C. T.
Swift, S. L. Durden, G. A. Sadowy,
S. J. Dinardo, F. K. Li, A. Huffman,
G. Stephens, D. M. Babb, H. W.
Rosenberger, 2001: Retrieval of
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ground-based
and
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Skofronick, G., J. Wang, G. Heymsfield,
Fig. 6 Reflectivity vs altitude over land with
R. Hood, W. Manning, R.
precipitation
Meneghini, and J. Weinman, 2003:
Combined
radiometer-radar
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