Locally Optimized Precipitation Detection over Land

Grant PettyAtmospheric 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

RetrievalAlgorithm

A New View

All channels+ancillary data

Decoupling Operator(s)

Precipitationsignal(s)

Environmentalnoise

Thresholding and/or RetrievalAlgorithm

● 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.

300 150 150

300

TB,V

TB,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-cloudrain

Cloud-freeocean

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!!

Examples of actual precipitation detection using constrained optimal

estimation!!

?

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!

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).