High Resolution Wind Field Estimation Using SAR

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High Resolution Wind Field Estimation Using SAR
David R. Lyzenga Veridian Systems Division July
2002 Progress Report
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Background

• Ocean surface wind speed and direction are
  measured by spaceborne scatterometers using
  multiple fan beams (ERS, NSCAT) and scanning
  pencil beams (QuickScat)
• These measurements have a relatively coarse
  spatial resolution (typically 25km) and are
  therefore unable to resolve small scale
  variations such as those due to convection cells,
  wind fronts, and topographic effects in coastal
  regions
• Synthetic aperture radars (ERS, Radarsat) are
  able to achieve much higher spatial resolutions
  by means of Doppler filtering techniques
• However, spaceborne SAR systems typically operate
  at a single look direction, so they are subject
  to wind speed and directional ambiguities

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SAR Wind Measurements

• Previous work has focused on two methods for
  resolving this ambiguity
• Use of spatial features (e.g. streaks) aligned in
  the wind direction (Wackerman, et al, 1996
  Fetterer et al, 1998 Horstmann et al, 2000)
• Use of wind direction information from other
  sources, such as scatterometers or numerical
  model predictions (Monaldo et al, 2001)
• Both methods have limitations, and of course
  break down on very small spatial scales
• Other problems that can appear on small spatial
  scales include possible non-equilibrium
  conditions and competing phenomena such as
  current gradients and surfactants (slicks)

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Forward Modeling of Wind Speed Effects

• Surface roughness changes due to wind speed
  variations can be modeled by means of the wave
  action equation
• where B(k, ?) is the dimensionless curvature
  spectrum or saturation ratio and Fs(B) is the
  net source function, which accounts for wave
  growth and dissipation effects
• We have implemented a time-stepping solution of
  this equation, using various formulations for the
  net source function
• The predicted spectrum is then used in a
  standard two-scale model to calculate the radar
  cross section at each point

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Equilibrium Spectrum and RCS

• At equilibrium, this model should predict an RCS
  that is consistent with measurements
• We assume an equilibrium spectrum of the form
• B(k,?) Bpm(k,?) F(k,?)
• where Bpm(k,?) is the Pierson-Moskowitz spectrum
  and F(k,?) is a correction function for high
  wavenumbers
• The correction function is represented by the
  ratio of two second order polynomials in k, the
  coefficients of which are selected (using a
  Nelder-Mead minimization procedure) to produce a
  best fit to the CMOD4 model function at
  VV-polarization
• The same spectrum can also be used to calculate
  the radar cross section at HH-polarization (for
  Radarsat)

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Equilibrium Spectrum and RCS for U5 m/s
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Equilibrium Spectrum and RCS for U10 m/s
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Equilibrium Spectrum and RCS for U15 m/s
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Example Results Downdraft Cells

• Assume a cylindrically symmetric downward flow of
  air (as in a thunderstorm core) impinging on the
  sea surface and spreading outward
• Continuity equation implies that near the
  stagnation point the radial velocity varies
  linearly with distance, and for large r the
  radial velocity falls off as r -2
• The radial velocity (in the absence of advection)
  is therefore assumed to have the form
• If this feature is advected by a larger-scale
  flow field, the advection velocity is simply
  added to the velocities from this equation

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Downdrafts Observed in ERS Images D. Atlas,
Origin of storm footprints on the sea seen by
synthetic aperture radar, Science 266, 1364-1366,
1994.

• Confirmed correspondence of ERS image features
  with rain cells by comparison with simultaneous
  surface weather radar images
• Hypothesized that image features are mainly due
  to near-surface air flow, with some effects due
  to wave damping by rain

Hypothesized airflow pattern
ERS-1 SAR image taken at 1536 UTC on 18 July 1992
off Cape Hatteras
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Downdraft (Rain) Cells in Radarsat
Data 05/10/1998 154311.92 GMT
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SSM/I Sequence for 05/09/1998 - 05/10/1998 from
http//www.ssmi.com/
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Surface Winds at NOAA Buoy 46001 (56.30 N 148.17
W) 250 km West of Radarsat Image
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Enlargement of Radarsat Image showing apparent
rain / downdraft cells
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Inverse Problem (Wind Speed Estimation)

• Our basic approach for the inverse problem is to
  vary the input parameters in the forward model
  until it agrees, as nearly as possible, with
  observations (i.e. SAR images)
• For this purpose, we may view the predicted rcs
  field as a function (or
  functional) of the input wind field
• The problem is then to define a procedure for
  making adjustments to the wind field in order to
  reduce the error metric
• where is the observed rcs field
  (SAR image)
• Anticipating that there may be multiple solutions
  to this problem, we also need to formulate an
  appropriate set of constraints in order to make
  the solution unique

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Inverse Problem (continued)

• There are fairly standard procedures for the
  error minimization problem basically these
  involve computing the gradient of the error
  metric with respect to each element of the input
  parameter vector, and then making the change in
  the parameter vector proportional to this
  gradient, i.e. ?pi -? ?E/? pi
• The more difficult problem may be to formulate an
  appropriate set of constraints in order to make
  the solution unique
• For small-scale features such as downdrafts,
  solution may be constrained by minimizing the
  vorticity of the surface wind field
• Another possibility is to force the average wind
  speed and direction to be equal (or as nearly
  equal as possible) to a prescribed value, e.g.
  that obtained from scatterometer data or a
  numerical circulation model

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A Preliminary Exercise

• A preliminary exercise was carried out to test
  the feasibility of estimating downdraft winds by
  minimizing the vorticity of the surface wind
  field
• A wind field was generated using the previously
  described model for a downdraft cell with a
  maximum surface velocity perturbation of 6 m/s
  embedded in a mean wind field of 8 m/s
• The radar cross section was computed using a
  simplified model function of the form
• with ? 1.25 and b2 0.5
• A procedure was implemented for estimating the
  wind field with minimum vorticity consistent with
  this RCS field
• An initial estimate of the wind field was
  obtained by assuming the wind direction to be
  zero everywhere

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Vorticity and Divergence vs Iteration Number
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Results of Preliminary Inversion Exercise
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Future Work

• Incorporate new equilibrium spectrum into wave
  action equation
• Investigate departures from equilibrium in
  small-scale features
• Compare predictions with Radarsat and ERS
  observations
• Implement constrained optimization using full
  forward model
• Apply to Radarsat data from the NOAA/NESDIS
  Alaska SAR Demonstration program