It has recently been recognized that spatially inhomogeneous clouds and rain can substantially affect the height precision obtainable from a spaceborne radar altimeter system. Through computer simulation, it has been found that typical levels of cloud and rain intensities and associated spatial variabilities may degrade altimeter precision at 13.5 GHz and, in particular, cause severe degradation at 35 GHz. This degradation in precision is a result of radar signature distortion caused by variable attenuation over the beam limited altimeter footprint. Because attenuation effects increase with frequency, imprecision caused by them will significantly impact on the frequency selection of future altimeters. In this paper the degradation of altimeter precision introduced by idealized cloud and rain configurations as well as for a realistic rain configuration as measured with a ground based radar is examined

Goldhirsh, J.

Monaldo, F. M.

Walsh, E. J.

English

NASA Technical Reports Server

N8 4 27289 7
ALTIMETER HEIGHT MEASUREMENT ERRORS INTRODUCED BY THE
PRESENCE OF VARIABLE CLOUD AND RAIN ATTENUATION
Francis M. Monaldo and Julius Goldhirsh
The Johns Hopkins University/Applied Physics Laboratory
Johns Hopkins Road, Laurel, Maryland 20707
Edward J. Walsh
NASA/Goddard Space Flight Center
Wallops Flight Facility
Wallops Island, Virginia 23337
ABSTRACT
It has recently been recognized that spatially inhcmogeneous
clouds and rain can substantially affect the height precision obtain-
able from a spaceborne ::adar altimeter system (Walsh, et al., 1983).
Through computer simulation, it has been found that typical levels
of cloud and rain intensities and associated spatial variabilities
may degrade altimeter precision at 13.5 GHz and, in particular,
cause severe degradation at 35 GHz. T_is degradation in precision
is a result of radar signature distortion caused by variable atten-
uation over the beam limited altimeter footprint. Because attenua-
tion effects increase with frequency, imprecision caused by them
will significantly impact on the frequency selection of future al-
timeters.
In this paper we examine the degradation of altimeter precision
introduced by idealized cloud and rain configurations as well as for
a realistic rain configuration as measured with a ground based radar.
I. INTRODUCTION
As the requirements for precision in geodetic surveys grow more
stringent and as physical oceanographers begin to exploit altimeter
data to study ocean-wide circulation dynamics, the precision demands
on height measurements by future radar altimeters become more severe.
Hence, error sources that could previously be legitimately ignored
must now be considered. The precision degradation caused by spatial-
ly variable cloud and rain attenuation patterns is one such error
source.
When the narrow radar pulse transmitted from the altlmeter re-
flects from the ocean surface it is significantly spread by the ocean
surface roughness. This pulse broadening, while valuable in that it
provides an e£timate of ocean surface wave height, degrades the abil-
ity of the altimeter to measure the range between the satellite and
the surface. To reconstruct the position of the leading edge of the
pulse, the entire pulse waveform shape is processed in a tracking
_Igorlthm. Distortion of this waveform shape will necessarily de-
grade the precision with which the track point can be determined.
The beam-llmited surface footprints of spaceborne radar altlm-
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1984019194-289
https://ntrs.nasa.gov/search.jsp?R=19840019221 2020-03-22T09:22:20+00:00Z
eters of the Seasat class are on the order of 20 km. If the rain
a_d cloud attenuation is uniform over an altimeter Footprint, the
" total return signal power is reduced, the waveform shape remains
unchanged and the altimeter tracking _Igorithm height estimate is
_ unaffected. In this paper we focus on the situation where altimeter
_ precision is degraded because attenlation levels within the foot-
: print are laterally inhomogeneous, distorting the return waveform
shape.
2. RAIN CELL AND CLOUD ATTENUATION LEVELS AND SCALE S_ZES
Cloud liquid water content and rain intensity vary considerably
both spatially and temporally. As such, these quantities should be
- de_it with statistically. This section is designed to give the
reader a general appreciation of these quantities. Later we will
consider the computer simulation of the passage of an altimeter over
various plausible, idealized cloud and rain attenuation patterns as
well as the passage of such an altimeter over actual, measured rain
cells to determine the effect of these on altimeter measurement of
range to the sea surface.
2.1 Clouds
Cloud liquid water content, upon which attenuation depends, is
highly variable. Liquid water content may fluctuate between a small
fraction to sever_ gm/m 3 over a cloud width of 1 to 2 km (Ackerman,
1959). Ackerman i1967) has also measured liquid water contents
ranging from 0.5 to 2.5 gm/m 3 over distances exceeding 9 km. To the
authors' knowledge there are no statistics available relating cloud
size directly to liquid water content levels. However, Lopez (1977)
and Kuettner (1971) have determined typical scale dimensions for the
cumulus clouds and cloud streets based on either optical or refrac-
tive measurements to be on the order of several kilometers.
Interpolating the results of Gunn and East (1954), the attenua-
tion coefficient, normalized to cloud liquid water content, is ap-
proximately 0.17 (dB/km)/(gm/m 3) at 13.5 GHz and i.i (dB/km)/(gm/m 3)
at 35 GHz. Cole (1961) has provided average liquid water contents
for various common cloud types.
Table 1 summarizes and combines these results by estimating the
average two-way attenuation through a 1 km thick cloud for four com-
mon cloud types at both 13.5 and 35 GHz. Note that the total atten-
uation may vary between 0.034 and .85 dB at 13.5 GHz and 0.22 and 5.5
dB at 35 GHz.
2.2 Rain
Assuming a Marshall-Palmer (1948) drop size distribution, the
attenuation coefficient at 13.5 GHz is 0.06 dB/km at the small rain
rate of 2 mm/hr, 0.4 dB/km at the moderate rain rate of i0 mm/hr,
and 0.9 dB/km at the large rain rate of 20 mm/hr. At 35 GHz, the
attenuation coefficients are 0.5, 2.4, and 5.0 dB/km _r the rain !
rates, 2, 10, and 20 mm/hr, respectively (Goldhirsh d_,,_Rowland,
1982). Table 2 summarizes the results by providing th_ two-way
attenuation at 13.5 and 35 GHz, at various rain rates tot both a i
i
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1984019194-290
Table 1 Cloud Attenuation Levels
Normalized Liquid Total, Two-Way
Attenuation Water Attenuation Thru
Frequency Coefficlent Cloud Content a i km Thick
(GHz) (dB/km) / (gm/m 3) Type (gm/m 3) (dB)
13.5 0.17 Stratiform 0.1-0.2 0.034-0.068
Cumulus Humilis 1.0 0.34
Cumulus Congestus 2.0 0.68
Cumulonimbus 2.5 0.85
35 i.i Stratiform 0.1-0.2 0.22-0.44
Cumulus Humilus 1.0 2.2
Cumulus Congestus 2.0 4.4
Cumulonimbus 2.5 5.5
Table 2 Rain Attenuation Levels
" Totalr Two-Wa_ Attenuation (dB)
Attenuation 1 km 5 km
Frequency Rain Rate Coefficient Rain Cell Rain Cell
(GHz) (mm/hr) (dB/km) Height Height
13.5 2 0.06 0.12 0.6
i0 0.4 0.8 4.0
20 0.9 1.8 9.0
35 2 0.5 1.0 5.0
i0 2.4 4.8 24.0
20 5 I0. 50.0
Table 3 Track Point Error for Single Cloud Case (Cloud thickness -
1 km; Liquid water content - 1 gm/m 3)
Track Point Shift (cm)
Frequency SWH Maximum 1 Second 3 Secon_
(GHz) (m) Instantaneous Average Average
, l
13.5 2 3.9 2.2 0.6
13.5 4 8.0 4.0 1.2
35 2 17.6 6.3 2.9
35 4 41.5 20.4 7.2
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1984019194-291
1 km and 5 km rain cell height. Note that at 13.5 CHz and a 5 km i
rain cell height, the total attenuation varies between 0.6 and 9 dB
and at 35 GHz, it varies between 5 and 50 dB over the rain rate
range 2-20 mm/hr.
3. ALTIMETER PRECISION DEGRADATION
The effect cf clouds and rain on altimeter performance is depen-
dent upon two parameters: the spatial scales of attenuation varia-
bility relative to the altimeter beam-limited footprint and the mag-
nitude of the attenuation.
In this section we will model the effect on the altimeter esti-
:hate of the range to mean sea level as it passes over (i) plausible,
idealized cloud and rain attenuation patterns and (2) actually mea-
sured rain cell attenuation patterns.
3.1 Simulation of Altimeter Return Waveform Distortion
Figure 1 provides a schematic representation of the geometry of
• the simulations employed to estimate waveform shape distortions
caused by various attenuation patterns. Each annular region in the
altimeter footprint corresponds to a constant ocean surface area re-
sponsible for backscatter into a single range bin. An idealized,
cylindrical attenuation cell is sho_n to intersect the footprint.
This cell may represent either a cloud or a rain cell. It is clear
that different fractions of each annular region intersect with the
given cell. Hence, a different attenuation level may be associated
with each range bin. Construction of the return pulse shape was
performed for one annular region at a time. Fach annular region was
subdivided into 16 angular sections. For each one of these sections
the power return to the radar was calculated assuming no fading noise
present. The calculation included any attenuation. The angular
sections were integrated to obtain the power from an entire annular
region. This power was in turn weighted by the antenna pattern to
estimate the power return in the appropriate range bin. In this way,
the entire waveform shape was constructed, range-bin-by-range-bin.
t
The estimate of the position of the leading edge of the return
pulse is dependent upon the particular tracking algorithm used. The i
tracking algorithm used on Sea,at was chosen because its track point i
bias at high sea states is much lower than that of a threshold level
tracking algorithm (MacArthur, 1978). The Seasat algorithm used the i
: entire waveform shape to fashion its track point estimate. The sim-
ulations undertaken employed the Seasat tracking algorithm to deter-
mine track point position. I
!
1 In these simulations we examined altimeter operating at 13.5
and 35 GHz, with a 1 m dish at an altitude of 800 km with a ground I
track velocity of 7 km/s. i
3.2 Idealized Cloud and Rain Cell Attenuation Patterns i
i
Three idealized raln/cloud models were chosen to demonstrate i
the effect of rain and cloud attenuation on the altimeter measurement
of the range to mean sea level. Although these models are idealized,
t
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1984019194-292
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_'igure1 A!ti_meter-Attenuation C_II Configuration t
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1984019194-293
they were chosen tc represent plausible rain and cloud attenuation
• levels and scale sizes consistent with those discussed in Cection 2.
-_ The following rain/cloud models were considered in this analy-
sis: (i) A cylindrical cloud of 5 km diameter and 1 km thickness
with a liquid water content, M, of 1 gm/m 3. (2) A cylindrical rain
_ cell of 5 km diameter _nd 5 km thickness with a rain rate of i0
mm/hr. (3) A sinusoidally attenuating cloud medium with spatial
+. wavelengths of 5, 2.5, and 1.0 km. The maximum two-way attenuation
. . being 0.34 dB at 13.5 GHz and 2.2 dB at 35 GHz (M=I gm/m3). This
. type of cloud variation is representative of the periodic attenua-
tion associated with "cloud streets". For models 1 and 2 the altim-
_. eter is assumed to pass directly over the cloud or rain cell center.
In model 3, the altimeter ground track is assumed perpendicular to
the cloud street crests.
For the single cloud condition described above, the instantane-
ous track point shift can be quite significant, but when averaged
over a 1 or 3 s interval, the mean track point shift reduces substan-
tially (Table 3). For th_ 35 GHz case, the mean track point error
is still large compared tu the TOPEX requirement of a few centimeter
_+ precision (TOPEX Science Working Group Report, 1981)T
Table 4 presents the track point shift associated with cloud
" streets. Note that as the wavelength of the cloud streets decreases,
the track point shift gets smaller. This is because the attenuation
_ variations begin to occur at small enough scales that they are par-
.2 tially average_ over within each pulse. The table also indicates
that the maximum track point shift is much higher for 35 GHz than
for 13.5 GHz.
It is also important to note that track point errors generally
increase with significant wave height (SWH). At larger ocean wave
heights, the return pulse is spread out smearing the leading edge of
the pulse. This i_ further compounded by the introduction of a spa-
tially variable attenuation described here.
Consider now track point shifts for the case of the single cyl-
indrical rain cell of 5 km height and i0 mm/hr rain rate. It is
clear from Table 5 that the larger attenuation values associated _
with rain introduce substantially greater track point shifts. Even
after 1 and 3 s averages, the track point shifts at 13.5 GHz are
well outside the precision requirements of Seasat, GEOSAT and TOPEX.
< At 35 GHz the situation is worse.
_I 3.3 Effects Due to Measured Rain Cell Attenuation
I To augment the results obtainad for idealized rain patterns we
considered a sample of rain attenuation urcfiles obtained by a
! ground b8 ._d radar situated at Wallops Island, Virginia. The atten-
uation profile was constructed from a corresponding radar reflectiv-
ity profile employing a low elevation radar scan (Goldhirsh, 1979).
The radar reflectivity corresponding to each adjacent pulse volume
of resolution 15C m was converted to an equivalent attenuation coef-
cient employin_ an empirical relation derived from measured rain
drop size distribution data (Goldhirsh, 1979). The integrated
292 +++
1984019194-294
TaDle 4 Maximum instantaneou_ Track Point Shifts for the Cloud
Street Case (Maximum Liquid Water Content = 1 gm/m 3)
Track Point Shift at Various Cloud
Frequency SWH Street Wavelengths !cm)
(GHz) (m) 1.0 km 2.5 km 5.0 km
.... , ...
13.5 2 0.7 0.9 2.6
35 2 6.4 8.3 13.3
Table 5 Track Point Error for Rain Cell Case (Rain Height = 5 km;
Rain Rate = i0 mm/hr)
Track Point Shift (cm)
Frequency SWH Maximum ! Second 3 Second
(GHz) (m) Instantaneous Average Average
r"•
13.5 2 97.1 45.7 14.9
13.5 4 93.2 50.5 15.6
35 2 119.7 64.6 21.7
35 4 150.6 86.6 30.6
Table _ Track Point Shifts for a Measured Rain Attenuatio** Case.
Assumes 2 m SWH.
Track Point Shifts (cm)
Frequency Maximum " Maximum P_MS of " RMS of
(GHz) Attenuation Instant. 1 Secon4 3 Second
(dB) Averages Averages
13.5 9.7 25.3 3.5 1.1
35 47.4 124.7 14.7 10.2
l
293
"19840]9]94-295
attenuation with height was constr,_cted assuI_ing the r3in to be uni-
_° form with altitude over a 4 km cell height. Figure 2a shows the re-
su!tirg attenuation profile associated with an estimated maximum
_ rain rate of abcut 25 mm/hr. The actual attenuation at 13.5 CHz var-
ies fror_ 0 to 9 dB. In Figure 2b track point errors induced by this
attenuatlon are plotted for a SWH of 2 m. A similar simulation was
, derived at 35 GHz (not shown).
• Results of these simulations are given in Table 6. Instantane-
ous track point errors are many centimeters at both frequencies. By
averaging over 1 to 3 seconds the track point errors at 13.5 GHz are
reduced to 3.5 and I.i cm, respectively. At 35 CHz the instantane-
ous error can be many tens of centimeters and the averaged errors
still exceed 10 cm. Much larger track point errors at 35 GHz as
opposed 13.5 GHz are caused by both the larger attenuations at 35
GHz and the smaller footprint of the beam.
Two additional points are worthwhile noting. First, the track
point shift in Figure 2b shows no mean trend as the mean absorption
of Figure 2a increases. This emphasizes our earlier statement that
" only inhomogeneities of absorption cause track point shifts. Second,
the results of Table 6 for 35 GHz are somewhat academic because no
actual radar would have sufficient signal-to-noise margin to be able
, to tolerate a 47 dB attenuation and maintain track.
4. CONCLUSIONS
We have demonstrated for both idealized rain and cloud config-
urations as well as measured rain rate variabilities, significant
al_imeter degradation may occur at 13.5 and 35 GHz. Although av_r-
aging track points over several seconds may mitigate these errors,
they may still be unacceptably high.
At 13.5 GHz, the effect of clouds on the average track point
shift is generally small (approximately 1 cm for cylindrical model
and less than 3 cm for the cloud street model). On the other hand,
rain rates as high as i0 mm/hr may produce unacceptably high range
uncertainties (e.g., isolated rain cell case).
! At 35 GHz, both the effects of clouds and rain may, in general,
l seriously degrade the track point errors. Errors as high as 7 cm for
isolated clouds and 13 cm for cloud streets may occur. For rain
rates of i0 mm/hr, absorptions as high as 47 dB and track point er-
rors as high as 31 cm may be produced. The employment of future
conventional type altimeter systems operating at 35 GHz and higher
is not recommended.
Since track point errors at 13.5 GHz may seriously be degraded
by rain, it is recommended that future altimeters operating at this
frequency employ rain detecting capabilities to flag rain corrupted
data.
294
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1984019194-296
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*t
Ackerman, B., 1959, "The Variability of the Water Contents of Tropi-
cal Cumuli", J. of ApFi. Meteoro__q_q!, vol. 16, April, pp. 191-
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i
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"Seasat-A Radar Altimeter Desian Description",MacArthur, J.L., 1978, _ - _ I
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]
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1984019194-298


Altimeter height measurement errors introduced by the presence of variable cloud and rain attenuation

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