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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