CHAPTER 9
Stratified and Other Variants of the Statistical Retrieval Procedure

In the previous chapter it was assumed that prior to deployment on a mission to a specific region during a specific season a single set of retrieval coefficients, RCs, would be calulated from RAOBs in an existing archive from the same region and season. This is what was done for the first airborne MTP missions that used the statistical retrieval procedure (~1988).

Before the 1980s Ed Westwater, at NOAA's Wave Propogation laboratory, had shown the power of retrieval coefficient "stratification" for ground-based microwave temperature profilers. He used RC sets for each season for a fixed-location profiler. At JPL, while pursuing airborne MTPs, I stumbled upon the same stratification concept by accident. The mission wanted "ferry flight" MTP data, but the ferry flights went from mid-latitudes to the polar vortex region. I recognized that the mid-latitude temperature field was very different from the polar vortex field, so I prepared two RC sets, one from mid-latitude RAOB stations and the other from high-latitude RAOB stations (both for the winter season). As the airplane's latitude changed I forced a graduated transition of reliance from RCs of one set to the other. This is a simple example of RC stratification.

I did the same RC stratification for missions that were flown in different seasons. After several missions a large number of RCs had accumulated. The next step for improving their use was to change the switching algorithm from simply latitude-based to one based on retrieved temperature at two carefully selected altitudes. For example, the temperature difference between 8 and 15 km is good at distinguishing between being equatorward or poleward of the sub-tropical jet. An iterative procedure was used to select whether the mid-latitude RCs or tropical RCs were to be used, and this objective procedure for selecting RCs was better than assuming that the sub-tropical jet was always at 30 degrees latitude. The procedure was a 2-step iteration: first retrieve T(z) using "global RCs" (based on a mixture of tropical and subtropical RAOBs) and decide from the "T8-T15" parameter whether to use the tropical or mid-latitude RCs. This is another variant of the statistical retrieval procedure.

After I retired Dr. MJ Mahoney developed procedures that are better than stratification. He used "observables" for each RC set to evaluate the appropriateness of using the RCs for a specific single-scan MTP observation. For example, if there are 10 RC sets, with their associated TB observables, it is a simple matter to compare an MTP single-scan set of observables with each of the 10 sets of RC observables, and then select for use the RC set with the lowest RMS observables difference. This can be done so quickly that it can be implemented for real-time analysis aboard the aircraft.

Another Mahoney variant is somewhat "incestuous" and can only be done where there are RAOB sites in the region of interest. It also can only be done after RAOBs for that time appear in the public archive. Step 1 is to obtain a RAOB close to the region of interest, then search for RAOBs within a larger region that have a similar T(z) shape (temperature offsets are permitted). Step 2 is to calculate RCs using those RAOBs having the similar shape. Step 3 is to retrieve T(z) using the
MTP observables with the RCs just derived. This sounds like cheating, but it simply makes use of available information, and is therefore compatible with the Bayesian philosophy of using whatever information is available. As a defender of this method might proclaim, "To ignore extra information is wasteful."

I've been promoting a more ambitious retrieval procedure, but so far it hasn't been tried. Starting with an immense set of RAOBs, covering all geographical locations and all seasons, produce a large archive of calculated observables for every RAOB. For each MTP observable set look for the best match (allowing offsets) with the immense archive of calculated observables. There will always be a "best match" so a solution is guaranteed. This procedure also lends itself to a straightforward way to assess uncertainty of the matched T(z) (notice that I use the term "matched T(z)" instead of "retrieved T(z)"). For evaluating the T(z) SE simply repeat the process using observables adjusted by their uncertainty. In this way it is possible to derive both SE components, the stochastic and systematic.

I can see a practical problem with this method - if the MTP's RF passband is ever revised the entire set of RAOB to observables calculation would have to be repeated. Therefore, if the method is to be used there should be a careful measurement of the MTP RF passband (IF passband plus upper and lower sideband imbalance).

In the next chapter I will describe some fundamental ambiguities for all retrieval (and matching) procedures.

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