Locally Optimized Precipitation Detection over Land

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

2. 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” doesn’t mean that it is free of environmental contamination!

3. A New View Thresholding and/or RetrievalAlgorithm Precipitationsignal(s) All channels+ancillary 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.

4. Example: Utilization of dual-polarization TB over ocean S=0 no scattering P=0 opaque cloud 300 Warm-cloudrain P=0.6 LWP = min Cold-cloud rain TB,H P=1 cloud free Snow,no rain Cloud-freeocean 150 150 300 TB,V S=10 K

7. 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.

8. 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!

9. 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.

10. 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.

11. 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!

12. Constrained Optimization - Simple Example

13. 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.

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

16. Examples of actual precipitation detection using constrained optimal estimation!!

17. Examples of actual precipitation detection using constrained optimal estimation!! ?

18. 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!

19. 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. :(

20. 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).