[GRL]
Supporting Information for
Effects of the passage of Comet C/2013 A1 (Siding Spring) observed by the Shallow
Radar (SHARAD) on Mars Reconnaissance Orbiter
Authors: Marco Restano1, Jeffrey J. Plaut2, Bruce A. Campbell3, Yonggyu Gim2, Daniel
Nunes2, Fabrizio Bernardini1, Anthony Egan4, Roberto Seu1, Roger J. Phillips5
Affiliations:
Dipartimento DIET, Università di Roma “La Sapienza,” I-00184 Rome, Italy.
1,*
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA.
3
Smithsonian Institution, Washington, DC 20013–7012, USA.
4
Space Operations Department, Southwest Research Institute, Boulder, CO 80302, USA.
5
Planetary Science Directorate, Southwest Research Institute, Boulder, CO 80302, USA.
Corresponding author: M. Restano, Dipartimento DIET, Università di Roma “La Sapienza,” Via
Eudossiana, 18 - 00184 Rome, Italy. (marco.res@inwind.it)
1
Contents of this file
Text S1 to S3
Figures S1 to S5
Tables S1
TEXT S1
TEC measurements obtained by the Italian Team/DIET Dept. Sapienza University of
Rome:
The Italian team obtained the results reported in the paper by adopting the approach
described in Restano et al., [2014] in which the ionosphere is modeled according to the
Chapman model, which depicts the ionosphere electron density as a single-peak function
having a Gaussian shape. The phase distortion ∆𝜑(𝑓) associated with the ionosphere
propagation affects the phase spectrum of the received signal:
∆𝜑(𝑓) =
4𝜋𝑓
𝑐
𝐿
𝑓𝑝 (𝑧) 2
∫0 [√1 − (
𝑓
) − 1] 𝑑𝑧
(E1)
where f is the frequency, c is the speed of light and 𝑓𝑝 (𝑧) is the distribution of the plasma
frequency versus height 𝑧. Since the model presented in (E1) requires both the plasma
frequency distribution along the height 𝑓𝑝 (𝑧) and the ionosphere layer thickness 𝐿, a
simpler version can be introduced for correcting data. This model [Cartacci et al., 2013;
2
Restano et al., 2011; Picardi et al., 2008] called the Uniform Model considers a constant
plasma frequency value along the height 𝑓𝑝,𝐸𝑄 and a layer thickness equal to 𝐿𝐸𝑄 . This
simplifies the previous relation to:
∆𝜑,𝐸𝑄 (𝑓) =
4𝜋𝑓𝐿𝐸𝑄
𝑐
𝑓𝑝,𝐸𝑄 2
(√1 − (
𝑓
2
) − 1) = 2𝜋𝜏0 (√𝑓 2 − 𝑓𝑝,𝐸𝑄
− 𝑓)
(E2)
The ionosphere equivalent thickness [Cartacci et al., 2013; Restano et al., 2011; Picardi
et al., 2008] is usually fixed to an average value 𝐿𝐸𝑄 = 80 km (o = 533 sec). The
ionosphere phase distortion can be written as Taylor series, which allows clear
identification of terms related to the additional time delay (𝑎1 ) and to the phase distortion
(𝑎2 ) induced by the propagation through the ionosphere [Cartacci et al., 2013; Picardi et
al., 2008]:
2
∆𝜑,𝐸𝑄 (𝑓) = 2𝜇𝜏0 (√𝑓 2 − 𝑓𝑝,𝐸𝑄
− 𝑓) = 𝑎0 + 𝑎1 (𝑓 − 𝑓0 ) + 𝑎2 (𝑓 − 𝑓0 )2 + ⋯
2 − 𝑓 ) [𝑟𝑎𝑑]
𝑎0 = 2𝜋𝜏0 (√𝑓02 − 𝑓𝑝,𝑒𝑞
0
𝑎1 = 2𝜋𝜏0 (
𝑓0
2
√𝑓02 −𝑓𝑝,𝑒𝑞
𝑎2 = −2𝜋𝜏0 (
(E3)
(E3.1)
− 1) [𝑟𝑎𝑑/𝐻𝑧]
(E3.2)
) [𝑟𝑎𝑑/𝐻𝑧 2 ]
(E3.3)
2
𝑓𝑝,𝑒𝑞
3
2 )2
2(𝑓02 −𝑓𝑝,𝑒𝑞
3
The other terms of the series are not needed [Cartacci et al., 2013]. 𝑓0 is the SHARAD
central frequency, equal to 20MHz. The SHARAD radar transmits chirp signals. The
received distorted signal can be expressed at baseband in the frequency domain as [Restano
et al., 2014]:
𝑆𝑅𝑋 (𝑓) = 𝐹𝐹𝑇 {𝑟𝑒𝑐𝑡(
𝑡−𝑡0
𝑇
)𝑒𝑥𝑝[𝑗𝜋𝐾(𝑡 − 𝑡0 )2 ]} ∙ 𝑒𝑥𝑝{𝑗∆𝜑,𝐸𝑄 (𝑓)}
(E4)
Where 𝑡0 is the receiving time, T is pulse length, K is the chirp rate and ∆𝜑,𝐸𝑄 (𝑓) is the
distortion associated with ionosphere propagation in (E2). Ionosphere-compensated
radargrams are obtained by correcting the phase distortion ∆𝜑,𝐸𝑄 (𝑓) during the matched
filtering processing. This processing performs the convolution between the received signal
and the matched filter and is known as range compression. The matched filter ℎ(𝑡) is the
time-reversed, complex conjugate of the transmitted signal [Cumming and Wong, 2005]:
𝑡
𝑡
ℎ(𝑡) = 𝑟𝑒𝑐𝑡 (𝑇) 𝑒𝑥𝑝{−𝑗𝜋𝐾(−𝑡)2 } = 𝑟𝑒𝑐𝑡(𝑇)𝑒𝑥𝑝{−𝑗𝜋𝐾𝑡 2 }
(E5)
The range compression can be then expressed in both domains as [Cumming and Wong,
2005]:
𝑆𝑅𝐺 (𝑡) = 𝑆𝑅𝑋 (𝑡) ∗ ℎ(𝑡)
𝑜𝑟
𝑆𝑅𝐺 (𝑓) = 𝑆𝑅𝑋 (𝑓) ∙ 𝐻(𝑓)
(E6)
4
Where operator “∗” indicates convolution that corresponds to a multiplication in the
frequency domain. The azimuth processing is implemented after the range compression of
the individual echoes. It follows that it is not necessary to implement it when the study of
the ionosphere is considered. Ionosphere parameters 𝑎1 and 𝑎2 are retrieved by maximizing
the output of the matched filtering (E6). This involves the compensation of ∆𝜑,𝐸𝑄 (𝑓) in
(E4) adopting a pre-distorted 𝐻(𝑓) which includes a suitable 𝑒𝑥𝑝{−𝑗∆𝜑,𝐸𝑄 (𝑓)} term. Since
∆𝜑,𝐸𝑄 (𝑓) is unknown, a series of pre-distorted matched filters having different ∆𝜑,𝐸𝑄 (𝑓)
terms has been considered to correct each individual echo. When the 𝐻(𝑓) maximizing the
output of the matched filter is found, the related ∆𝜑,𝐸𝑄 (𝑓) is directly associated with an
ionosphere having a certain plasma frequency. The total electron content is obtained from
the 𝑎1 value by inverting [Garner et al., 2008]:
𝑎1 = 2𝜋 ∙
1.345×10−7
𝑓0 2
𝑇𝐸𝐶
(E7)
Figure S1 reports the matched filter output improvement after the correction of the phase
distortion due to the ionosphere. Table S1 summarizes the results reported in the paper in
TECU units. TEC is often reported in multiples of the so-called TEC unit, defined as
TECU=1016·m-2. We evaluated the overall mean and the ‘accuracy‘ as the standard error
by dividing the standard deviation by the square root of the number of individual echoes.
In conclusion, the TEC is five times higher with respect to the typical case (GROUP SZA
∼115°) for the first observation 38583_01. For the second observation 38586_05, an
enhancing factor of 1.6 has been estimated with respect to the typical case (GROUP SZA
5
∼93°). GROUP SZA ∼93° and GROUP SZA ∼115° belong to observations planned for
this event. Results in Table S1 are reported in the main manuscript (Figure 2 - TEC values).
Figure S1. Example of echo compensation.
Observation/ Group of
Measured TECU
Evaluated over
Duration
Observations
Num. of individual
Info
echoes
38583_01 (SZA ∼115°)
0.25±0.0042
1 observation
300s
52173
Comet effects
GROUP SZA ∼115°
0.05±0.0034
35 observations
120s each
21008
Reference group
38586_05 (SZA∼93°))
0.42±0.0072
1 observation
60s
10070
Comet effects
GROUP SZA ∼93°
0.27±0.006
7 observations
60s each
10070
Reference group
Table S1. Results summary
TEXT S2
TEC measurements obtained by the US Team
6
The method adopted to obtain the TEC values for the orbits 38583_01 and 38586_05 is
described in [Campbell et al., 2011, 2014]. Radargrams are shown in Figure S2. By
reporting the TEC in multiples of the so-called TEC unit, defined as TECU=1016 m-2, the
mean TECU values are 0.20 for the observation 38583_01 and 0.4 for the observation
38586_05. The minimum sensitivity of the technique to steps in the TEC is about 0.006
TECU. It is worth noticing that for the observation 38583_01 the estimated TECU (Figure
S2, right panel) increases to a maximum TECU of ∼0.3 as the SZA decreases from 117°
to 114°, then is observed to decline abruptly as the track ends its coverage near a SZA of
about 109°.
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Figure S2. Left: Radargrams of the two night-side observations in which the comet’s
presence was detected. Right: TEC variation versus SZA. Observations acquired at night
usually do not require any compensation of the ionosphere.
8
TEXT S3
TEC measurements obtained by the US Team/ JPL
To estimate the total electron content, N/m2, we have the corrected the phase distortion by
using the same model presented in Text S1 and monitored the strength of surface returns.
Similarly to Text S1, the maximum surface return is expected when a correct ionosphere
model is used. Pulse pre-summing and synthetic aperture radar (SAR) processing were
applied in our approach. The Pulse-by-pulse optimization shows the statistical variation in
the total electron density (Figure S3). For more than half of 26086 pulses in the observation
38583_01, the surface return is maximized for TECU values between 0.2 and 0.4. The
mean value is equal to 0.31 TECU and the accuracy, evaluated as in Text S1, is 0.0013.
We have also compared radargrams with different electron density parameters. Unlike the
pulse-by-pulse comparison, we have applied a constant total electron density for all the
pulses of each radargram. Figure S4 shows radargrams of the observation 38583_01 for
TECU values from 0.0 (no correction) to 0.4 at an interval of 0.1 TECU. The sharpness of
the surface returns is peaked around TECU values of 0.2 and 0.3, consistent with the pulseby-pulse analysis. For the observation 38586_05, the surface return is maximized for
TECU values between 0.4 and 0.5 (Figure S5). The mean value is equal to 0.48 TECU and
the accuracy, evaluated as in Text S1, is 0.0030 for a total number of 5035 pulses.
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Figure S3. Histogram of the pulse-by-pulse optimization. The majority of the pulses in the
observation 38583_01 is optimized when the total electron density is between 0.2 and 0.4
TECU (=10^16 /m^2). TECU step is 0.01.
Figure S4. Radargrams of the observation 38583_01. From TECU=0 (uncorrected) to
TECU=0.4 with a TECU step of 0.1. The surface return is dispersed without the
ionospheric correction (TECU=0). As TECU increases, the surface return is better focused
(TECU=0.2 and 0.3) and overcorrected at TECU=0.4.
10
Figure S5. Histogram of the pulse-by-pulse optimization. The majority of the pulses in the
observation 38586_05 is optimized when the total electron density is between 0.4 and 0.5
TECU (=10^16 /m^2). TECU step is 0.01.
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