Temporal Decorrelation and Topographic Layover Impact on Ka-band

Temporal Decorrelation and Topographic Layover Impact on Ka-band

Temporal Decorrelation and Topographic Layover Impact on Ka-band Swath
Altimetry for Surface Water Hydrology
Delwyn Moller, Remote Sensing Solutions
Ernesto Rodriguez, Jet Propulsion Laboratory, California Institute of Technology
Overview:
Traditional radar altimetry has demonstrated the ability to retrieve surface water heights with decimeter accuracies along the
nadir path. However, a profiling sensor is insufficient to provide global monitoring of fresh water bodies. In response, to
address both hydrologic and oceanographic needs, the NRC Decadal Survey has recommended the Surface Water Ocean
Topography (SWOT) mission. During this mission a swath-based imaging altimeter (shown at right in Figure 1) will provide
the key hydrologic variables needed for comprehensive river discharge and storage observations, specifically temporal height
change, slope and spatial extent [1]. In addition, key imaging capabilities provide classification masks and data for
topographic corrections.
As part of a virtual mission, we have developed a high-fidelity instrument simulator capable of predicting the radar response
and error characteristics over dynamically modeled study regions [2]. In this poster we specifically address two error
sources:
1. The effects of water decorrelation on the SAR image formation.
2. Predictions of layover contamination in the high relief topography.

Figure 1: SWOTs swath-based imaging altimeter.

Coherence Time Characterization and Effects:
To provide proof-of-concept validating data for the SWOT concept, a Ka-band radar breadboard (see Figure 2), developed for the Mars Science Laboratory project, was fielded to three diverse locations in Ohio (consisting of a small
fast-flowing river, a reservoir, and a large slow-flowing river). Measurements of backscatter as a function of incidence angle and Doppler measurements were collected at each site. In situ measurements of wind and current were
taken. Temporal coherence was derived from the phase variability of the cross-correlated pulse-pair returns. This quantity is important because, for a synthetic aperture system, the scene must remain correlated over the aperture
synthesis time in order to achieve full resolution.
The Ka-band radar was not able to directly measure coherence times of the surface, but does measure the complex pulse-pair product, the phase statistics of which can be used to estimate coherence times. The phase standarddeviation can be expressed as:
2

1
=
2N

1

We assume = exp(-(t/c)2) for the surface, as is often assumed for the ocean. A least-squares fit to the standard-deviation of the phase as a function of lag yields an estimate of the decorrelation time c. Figure 3 shows the
experimental results where the coherence time can vary by over an order of magnitude. The implication of this for an imaging radar is that the effective resolution can be fundamentally limited by the scene coherence such that:

R
ra =
2Tc v sp

The effects of a finite decorrelation are shown in Figure 4, where a simulation indicates a) the reach of a river required to converge on a mean width and b) the bias of that mean as a function of decorrelation time. Note however,
that this should not affect the height accuracy - only the along-track resolution.

Figure 4: Simulation of the effect of
water coherence time for a simple test
case. The upper figure shows the
reach averaging required to converge
on an estimate of the width where:
1
(l) = std
l
e
w

we
w

w(l)dl
l

l +l

The lower plot shows the mean width
bias as a function of correlation time.

Note
we are ultimately limited by finite
pixel sizes in estimating width even as
the decorrelation -> infinity.
The next step is to work on an
algorithm and sensitivity analysis for
correcting the bias

- Radar point-target response can
be characterized
Figure 2: Bridge-based radar experimental
configuration. The antenna is mounted at the
end of a stiff boom on a precision positioner
for scanning in elevation about nadir. An
anemometer is mounted on the structure for
ground-truth, and current measurements were
made from the bridge.

- In the mission we may be able to
process to different aperture
lengths to estimate the correlation
time from the azimuth widths

Figure 3: Temporal coherence estimates derived from
phase statistics of pulse-pair measurements. The
coherence estimates did not change significantly at an
incidence angle of 5o.

Temporal decorrelation needs to be
better understood and characterized
=> important to get more
experimental data/statistics

47

Layover Due to Topography:
Although significant height contamination can occur
in cases of either high topography or extensive
vegetation, it may be possible to identify the
contaminated regions and exclude them from the height
product. For example, Figure 5 indicates height error
due to layover in the high topographic relief of the Pacific
Northwest area, but one can see that this is localized. A
further area of study is to examine classification
schemes utilizing correlation properties to identify these
areas of layover and thereby exclude them.

References:
[1] Alsdorf, D. E., E. Rodrguez, and D. P. Lettenmaier (2007),
Measuring surface water from space, Reviews of Geophysics, 45,
RG2002, doi:10.1029/2006RG000197.
[2] Andreadis, K. M., E. A. Clark, D. P. Lettenmaier, and D. E.
Alsdorf (2007), Prospects for river discharge and depth estimation
through assimilation of swath altimetry into a raster-based
hydrodynamics model, Geophysical Research Letters, 34, L10403,
doi:10.1029/2007GL029721.

Figure 5: Layover due to topography in the
Pacific Northwest region. The regions of layover
are localized and predictable.
2

PLi
lr = 1+
P
i w

46

The relative power ratio accounts for:
1. Projected
area of the land relative to the

water.
2. The dot product between the normal to the
2d facet and the incident wave.

Height error scaling factor

45
-124

-123

-122

3. The relative 0 between the land and water.
Note a 10dB water/land 0 ratio is assumed
at nadir, which is then corrected for the local
angle of incidence.
The magnitude of the additive error is typically
very small (>99% of pixels have lr<1.1) Classification of these regions should avoid significant contamination. Height error scaling factor

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