Locally Optimized Precipitation Detection over Land Grant Petty Atmospheric and Oceanic Sciences University of Wisconsin - Madison

The Old View ● 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” doesn’t mean that it is free of environmental contamination! All Pixels Screening Operator Raining Pixels Non- Raining Pixels Retrieval Algorithm

A New View All channels +ancillary data Decoupling Operator(s) Precipitation signal(s) Environmental noise Thresholding and/or Retrieval Algorithm ● 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.

T B,V T B,H S=0 no scattering P=0 opaque cloud P=1 cloud free P=0.6 LWP = min S=10 K Example: Utilization of dual-polarization TB over ocean Snow, no rain Cold-cloud rain Warm-cloud rain Cloud-free ocean

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.

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!

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.

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.

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!

Constrained Optimization - Simple Example

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.

Comparison of background noise susceptibility for TMI - global fixed vs. locally optimized linear operators

Examples of actual precipitation detection using constrained optimal estimation!!

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? 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!

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. :(

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).