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SWOT Hydrology Workshop
Ka-band Radar Scattering Ka-band Radar Scattering From Water and Layover From Water and Layover
IssuesIssues
Delwyn Moller
Ernesto Rodriguez
Contributions from Daniel Esteban-Fernandez & Michael Durand
SWOT Hydrology Workshop
Overview and ContextOverview and Context• Instrument simulation for SWOT shows that hydrology requirements
are achievable for nominal operation• Focus on SWOT performance and capabilities in potentially limiting
scenarios:— Establish realistic performance and their dependencies (e.g.
environmental, regional etc).— In limiting scenarios identify possible mitigations, either
operational or algorithmic.— Help specific science interests develop realistic plans for data
interpretation.
• Discuss here the evaluation of two phenomena that can impact the SWOT data product for terrestrial hydrology science:1. Temporal decorrelation of the water surface2. Layover due to topography of the surrounding region
SWOT Hydrology Workshop
Temporal Decorrelation ImpactTemporal Decorrelation Impact• For a synthetic aperture system the scene must remain correlated over the
aperture synthesis time in order to achieve full resolution.
Note: this does not effect the height error - just the spatial along-track resolution
• Since there is little by way of Ka-band correlation measurements over surface water we collected some initial data from which we were able to derive this quantity
v
€
L = vτ c
ra∝1
L
L1
L2
ra1
ra2
SWOT Hydrology Workshop
Temporal Coherence ResultsTemporal Coherence Results• Correlation times ranging from 3ms to 44ms were found with the
higher wind measurements producing the shorter correlations. • For a 950km orbit the effect of decorrelation time on the achievable
alongtrack resolution is shown to the right.
- At the shortest anticipated decorrelation times a resolution of ~45m results.
- This may limit our ability to estimate the width (not the height).
SWOT Hydrology Workshop
A simple test “river” was generated” • 80m wide• No topography (flush with land)• Running at a 55 degree angle to the
radar• 10m (4.4 look) posting along-track, 1
look in range• Realistic thermal and speckle noise• Classification based on power
threshold alone
A Simple Test CaseA Simple Test Case
Classification for Perfect Coherence Classification (c = 7ms) Widening due to Finite (7ms Correlation Time
Algorithm “robustness” issues can occur due to the narrowness of the river (in # of pixels)
SWOT Hydrology Workshop
Ability to Estimate Width: ResultsAbility to Estimate Width: Results
• Little averaging is required to converge on a mean width estimate
• This is relatively independent of water decorrelation time
€
σwe (∂l) = std
1
∂lw(l)dl
l
l+∂l
∫ ⎛
⎝ ⎜
⎞
⎠ ⎟
Note: We are ultimately limited by finite pixel sizes in estimating width even as the decorrelation -> infinity.
Approaches to correcting for bias shall be investigated next
Width Estimation Variability for an 80m River
Width Estimation Bias due to Decorrelation
Wid
th E
stim
atio
n B
ias(
m)
€
σwe
μw
SWOT Hydrology Workshop
• Reaches of a few hundred meters are sufficient to average for the estimate of mean width to converge
• Bias is not a function of river width so for very large rivers the percent bias is less
• The next step is to work on an algorithm and sensitivity analysis for correcting the bias
- Radar point-target response can be characterized
- In the mission we may be able to process to different aperture lengths to estimate the correlation time from the azimuth widths
• Temporal decorrelation needs to be better understood and characterized => important to get more experimental data/statistics
Temporal Decorrelation Impact SummaryTemporal Decorrelation Impact Summary
SWOT Hydrology Workshop
Effects of Topographic Layover: RevisitedEffects of Topographic Layover: Revisited
Layover due to topography occurs when a topographic feature occurs at the same range as the water and thus the energy from both the water and the land occur at the same time and cannot be distinguished
SWOT Hydrology Workshop
47
45
46
-124 -123 -122
Sample Region for Layover Study: Pacific NorthwestSample Region for Layover Study: Pacific Northwest
Data Sources
DEM: NED 10m posting
Water mask: SRTM water bodies database
• For simplicity we have assumed the spacecraft velocity is constant in longitude.
• For each water pixel, every land pixel who’s range is within the radar range resolution is located
• When layover occurs, the proportional increase of the height error is calculated as follows:
€
lr =1+PLiPw
⎛
⎝ ⎜
⎞
⎠ ⎟
i
∑2
And 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.
3. The relative σ0 between the land and water. Note a 10dB water/land σ0 ratio is assumed at nadir which is then corrected for the local angle of incidence
SWOT Hydrology Workshop
Layover Simulation ResultsLayover Simulation Results
Note: layover regions are spatially localized and predictable
SWOT Hydrology Workshop
Layover Statistics Layover Statistics
Height error “scaling” factorHeight error “scaling” factor
• The impact of topographic layover is geographically isolated (and could be predictably removed )
• The magnitude of the additive error is typically very small (>99% of pixels have lr<1.1)
SWOT Hydrology Workshop
SummarySummary
• Temporal decorrelation of water-bodies can be rapid and consequently limit along-track resolution and our ability to accurately determine the spatial boundaries of the water. However greater statistical knowledge is needed to bound expectations and we will investigate algorithmic approaches to produce a methodology for correction.
• Layover due to topography is usually small and geographically isolated so is not expected to have any significant performance impact.
SWOT Hydrology Workshop
Backups
SWOT Hydrology Workshop
Width Finding Algorithm
X axis
Y a
xis
x0 x1
y1
y0
(xc,yc)
w
dx= x1-x0
d y=
y1-
y 0
€
xc,yc( ) = x0 + dx /2,y0 + dy /2( )
tanθ =dydx
w = dx sinθ = dy cosθ
w =dx sinθ( )
2+ dy cosθ( )
2
2
Width finding algorithm: For each i:1. Starting from yi, scan along x until you
find start and end x for intersection. Calculate dx and xc.
2. Starting (xc,yi), find y0 and y1 by scanning up and down. Compute dy and yc.
3. Compute the tangent of the angle, dy/dx. Note that the sign is positive if (y1-yc)/(xc-x0)>0, negative otherwise.
4. Compute the width using the square root formula
5. Save center, width, angle6. Given the direction of the slope, move
to the next neighboring point that is classified water, and repeat. Mark used points as you go.
7. Once a river is completed, restart process with unused water pixels.
8. Smooth center and width along the reach