Locally Optimized Precipitation Detection over Land

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Locally Optimized Precipitation Detection over
Land
Grant Petty Atmospheric and Oceanic
Sciences University of Wisconsin - Madison
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The Old View
RetrievalAlgorithm
Raining Pixels
All Pixels
Screening Operator
Non-Raining Pixels

• Operator(s) classify pixels
• rain vs. no rain
• snow vs. rain, etc.
• Detection is front-end to retrieval algorithms
• But Just because pixel is raining doesnt mean
  that it is free of environmental contamination!

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A New View
Thresholding and/or RetrievalAlgorithm
Precipitationsignal(s)
All channelsancillary data
Decoupling Operator(s)
Environmentalnoise

• Classification/screening of pixels, when needed,
  reduces to thresholding of the extracted signal.
• Cleanly separated signals can then be
  post-processed into actual retrievals
  environmental contamination is greatly reduced.

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Example Utilization of dual-polarization TB over
ocean
S0 no scattering
P0 opaque cloud
300
Warm-cloudrain
P0.6 LWP min
Cold-cloud rain
TB,H
P1 cloud free
Snow,no rain
Cloud-freeocean
150
300
150
TB,V
S10 K
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Applicability to Land Retrievals

• Need analogous multichannel operators/techniques
  to decouple (not merely flag) precipitation
  signatures from background variability (spatial
  and temporal).
• Problem surfaces range from desert sand to
  snow-covered ground.
• Some methods have been demonstrated in prototype
  form but never developed further.

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Examples of strategies over land using microwave
imagers

• Databases, models, and/or retrievals to reduce
  uncertainty in surface emissivity
• Multichannel (e.g., eigenvector) methods to
  separate precip signatures from surface
  variability (e.g, Conner and Petty 1998 Bauer
  2002)
• Use of polarization to reduce sensitivity to
  water fraction (e.g., Spencer et al. 1989)
• Optimal estimation methods - not widely used yet!

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Linear estimation methods

• Traditional Minimum Variance - find linear
  operator that minimizes mean-squared error in
  retrieved quantity.
• Requires Noise covariance and linearized
  forward model or statistical regression using
  real or modeled data.
• Problem This method balances noise
  amplification against scaling errors -- always
  underestimates magnitude of desired signal,
  especially when signal-to-noise ratio is poor.

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Linear estimation methods (cont.)

• Eigenvector methods - find linear operator that
  captures signature of precipitation. Then
  subtract the components that are parallel to the
  the first one or two noise covariance
  eigenvectors to eliminate their contribution.
• Requires Eigenvectors of noise covariance and
  linearized forward model.
• Problem Reduces geophysical noise but does not
  necessarily minimize it.

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Linear estimation methods (cont.)

• Constrained optimization - find linear operator
  that retains properly scaled response to
  precipitation signature while minimizing
  mean-squared error.
• Requires Noise covariance and linearized
  forward model.
• Problem Hardly anyone in our business has heard
  of it!

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Constrained Optimization - Simple Example
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Preliminary Experiments with Constrained
Optimization

• Generate N-dimensional histograms of multichannel
  TBs for each 1x1 degree geographical grid box and
  each calendar month.
• Sort bins in order of decreasing density.
• Identify first M bins that account for 80 of all
  pixels, thus excluding rare events such as
  precipitation. M is location-dependent.
• Compute channel means and NxN covariances from
  pixels falling in the above bins for each month
  combine for entire calendar year 2002
• Use physical model to obtain multichannel
  signature vectors (linear) as function of mean
  background TB
• Use constrained optimization to find unbiased
  linear operator and estimate associated
  geophysical noise.

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Comparison of background noise susceptibility for
TMI - global fixed vs. locally optimized linear
operators
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Examples of actual precipitation detection using
constrained optimal estimation!!
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Examples of actual precipitation detection using
constrained optimal estimation!!

• ?

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Examples of actual precipitation detection using
constrained optimal estimation!!

• ?
• Last weekend, a nearby lightning strike took out
  our 7-terabyte RAID along with all of our TMI and
  AMSR-E swath data and other critical files!

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Examples of actual precipitation detection using
constrained optimal estimation!!

• ?
• Last weekend, a nearby lightning strike took out
  our 7-terabyte RAID along with all of our TMI and
  AMSR-E swath data and other critical files!
• Consequently, even I have not yet seen COE
  applied to swath data yet. (

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Conclusions

• The availability of local background channel
  covariances can be exploited to find linear
  operators that maximum the signal-to-noise ratio
  of a desired signature (e.g., precip).
• Helps solve
• Coastline problem
• Desert problem
• Snow problem?
• Method will be initially tested using TMI in
  order to take advantage of PR as validation.
• Adaptation to AMSR-E is in progress and will
  serve as a more challenging test (high latitude,
  cold season land).