For the past 5 years the MTP/ER2, aboard the ER-2 aircraft, has produced profiles of air temperature that extend over a 5 km altitude region, approximately centered on flight altitude. On theoretical grounds the MTP/DC8 should yield temperature profiles that extend over an altitude region that is 2 or 3 times greater than for the MTP/ER2. This report evaluates, for the first time, the new techniques incorporated in the MTP/DC8 for enhancing microwave profiling performance. Preliminary scientific results will be dealt with elsewhere.
The MTP/DC8 was constructed for the Airborne Atmospheric Stratospheric Expedition II, for the study of stratospheric ozone depletion. The MTP/DC8 flew 19 times, between January 8 and March 20, 1992. The performance results reported here are based on comparisons of MTP/DC8 temperature profiles and radiosondes, RAOBs. The analysis to be described is based on the 17 occasions that the DC-8 flew close to RAOB sites during the flights of 1992 February 12, 14 and 17 (hereafter referred to as 920212, 920214, and 920217).
The balance of this appendix describes the MTP/DC8's post-flight calibration,
and presents an evaluation of retrieved temperature profile performance,
or accuracy versus altitude. A sample data product is presented,
showing the instrument's tropopause altitude monitoring capability.
The horn antenna and reflector scanning system, and the calibration target, are located on the outside surface of a "window" plate. A protective fairing extends 8 inches from the airframe, and contains a microwave "transparent" window mounted on the front surface to permit an unobstructed view from nadir to zenith. The forward view is offset 15 degrees in azimuth away from flight direction to reduce the reception of microwave emission from the airframe.
Most of the electronics are mounted on the inside surface of the window plate. A rack-mounted chassis contains power supplies, miscellaneous electronics, and a system controller computer that commands the viewing sequence, frequency multiplexing, and noise diode control. Raw data is sent to a real-time analysis computer, which displays retrieved profiles of air temperature on a monitor and plots isentrope altitudes on a printer. The entire sequence of 10 sky measurements at 3 frequencies, plus calibration target and noise diode measurement, and the data analysis and display, are completed every 14 seconds.
The "final calibration" consists of comparing measured antenna temperatures, TA, during flight past RAOB sites with direct calculations of what should have been observed, based on RAOBs launched before and after the DC-8's flight near the RAOB launch site.
The procedure of comparing a measured TA with a predicted brightness temperature, TB, allows for the correction of the many small effects that cause measured TA to be slightly different from the idealized TB. These effects include such things as window losses (absorption and reflection), antenna pattern sidelobe reception of emission from the area surrounding the window, errors in measuring the temperature of the ambient calibration target, frequency passband shape errors, and errors in system gain.
Another advantage of using this type of "final calibration" procedure is that it minimizes the impact of errors in the oxygen absorption model used to derive retrieval coefficients. Retrieval coefficients are determined from an elaborate simulation, involving a "least squares" analysis of simulated observables (TBs). Any errors in adopted absorption coefficient for the atmosphere will lead to biases in retrieved air temperature profiles. But if the same oxygen absorption model used for deriving retrieval coefficients is also used for the calculation of predicted TB in the "final calibration," then small errors in the oxygen absorption model will have negligible degrading effect on retrieved temperatures.
Many RAOB comparisons are required in order to average out the several
errors that can be present when using RAOBs to calibrate an aircraft instrument.
These include: 1) RAOB errors, 2) horizontal temperature gradients (since
we never fly directly over RAOB sites), 3) non-linear temporal changes
(since interpolations across 12-hour intervals are required), and 4) oscillations
of air temperature with time produced by inertio-gravity waves (which will
produce occasional departures of 1 or 2 K from time-average profiles).
System gain for each channel (i.e., frequency) was adjusted so that
measured TA for the horizon view was consistent with a set of 17 radiosonde-derived
outside air temperatures, OAT. It was found that each channel's gain
had the same value throughout each flight, and was the same for each of
the 3 flights, to within 2%.
To summarize, the steps in performing a "final calibration" of MTP/DC8
are: 1) prior to any flights, use a large set of RAOBs to determine retrieval
coefficients for converting TB observables to T(z), 2) after the flights,
use RAOBs (from sites that the aircraft passes) to predict TB, 3) compare
measured TA at the horizon with RAOB-based OAT and refine gains for each
channel (and adopt a set of gain values for all flights, or derive a procedure
for determining gain), 4) compare measured TA (using the final gain set)
with RAOB-predicted TB to create a set of TB - TA differences, called dTA
(dTA = TB - TA), for each channel at each of the 10 elevation angles, 5)
use the dTA data to derive an average "TA to TB correction table," and
6) re-analyze all raw data using the dTA table and RAOB-validated gains
to calculate a corrected observable set of TBs (TB = TA + dTA) for each
observing cycle, and use these TBs as input to the retrieval process to
derive T(z).
Stephen J. Keihm computed retrieval coefficients prior to the first flight. This involved the use of 1045 RAOBs from Northern Canada during October through March, 1978 to 1982. Each RAOB in this archive was used to calculate TBs corresponding to the 10 elevation angles, 3 channels, and 7 representative flight altitudes (6.1, 8.2, 9.5, 10.7, 11.3, 11.9, and 12.6 km). For these calculations the radio frequency response pattern was specified by a double-sideband IF (intermediate frequency) passband response at 7 IF frequencies.
Each observing cycle provides a set of 30 measurements (TB at each of 3 frequencies at 10 elevation angles). A temperature profile retrieval consists of computing separate retrievals for temperatures above and below flight level, after which the two profiles are combined. For retrieving temperatures for altitudes above flight level the following observables are used: TB for each channel at elevation angles +80, +55, +42, +25, +12, and -12 degrees. OAT is also used as an observable, and is derived by combining the horizon view TB's for all channels. For retrieving temperatures for an altitude below flight level the following observables are used: TB for each frequency at elevation angles -80, -42, -25, -12, +12 degrees, plus OAT.
For each of the pre-specified 7 aircraft flight levels, retrieval coefficients were determined for air temperature at 33 altitudes that are offset from flight altitude by specified amounts of pressure altitude units. When the aircraft is flying at an altitude that is between altitudes for which retrieval coefficients have been calculated, the retrieval of T(z) is performed as if the aircraft were at each altitude, then an interpolated T(z) profile is calculated corresponding to the actual altitude.
In deriving retrieval coefficients it was necessary to adopt uncertainties for the TB observables. These were estimated (prior to any flight) to be 0.7 K for all observables except the 55.51 GHz measurements at elevations +80 and +55 degrees, which were assigned uncertainties of 1.5 and 1.0 K, respectively. This is intended to account for the greater sensitivity of these TBs to frequency and system gain errors. A better estimate of TB uncertainties is possible only after comparing observations with RAOB-based predictions. Thus, calibrating a microwave radiometer can be a several-stage process.
For the flight date 920212 there are 3 RAOB sites that meet the criteria, for 920214 there are 4 sites, and for 920217 there are 9 sites. System gains for MTP/DC8's channels 1, 2 and 3 have been computed for each of the 17 occasions that RAOB-based OAT could be compared with TB at the horizon. The gains for each flight date were the same, and are 9.5, 12.8, and 13.2 [counts/K].
Measured TA, TAobsd, and RAOB-predicted TB, TBpred, are compared for each RAOB site. The pattern of differences for all intercomparisons has been used to produce an average pattern of dTA (dTA = TBpred minus TAobsd) versus elevation angle for each channel.
Typical dTA values are less than 1 K, but for the low frequency channel at the +55 degree viewing direction there is a persistent 4 K difference. The dTA correction table seems to be a persistent feature, in that the same gross pattern was present during all the January and February flights that have been analyzed. I believe that it is principally produced by differences in the microwave "transparent" window's absorption and reflection versus location during the elevation angle scan. Also, the window aperture is "illuminated" by a horn antenna pattern that rotates during the scan (since the horn pattern is redirected by a 45-degree parabolic reflector), and the varying amounts of sidelobe illumination of the sides of the window aperture could produce a repeatable pattern of TA differences that vary with scan location. Since I believe that the dTA adjustment table is mainly caused by window effects, I refer to it as the "window correction table."
After adopting the "window correction table," the MTP/DC8 observed TBs were calculated, using TBobsd = TAobsd + dTA. The scatter of "TBpred minus TBobsd" for many intercomparisons can be used to estimate measurement error for the various elevation and channel settings. In this way it was found that the pre-flight estimates were slightly pessimistic; for example, the 0.7 K for most observables could have been 0.6 K, and the low frequency channel's high elevation angle observables, assumed to have uncertainty errors of 1.0 and 1.5 K, are shown by the scatter analysis to be 1.0 and 1.9 K.
A detailed comparison of MTP retrieved T(z) and RAOB measured T(z) was undertaken. Plots of differences versus altitude showed that performance at the high altitudes were slightly worse during low altitude flight (9.1 and 9.5 km), compared with the bulk of the data at flight levels 10.7, 11.3 and 11.9 km. The 3 low altitude intercomparisons were not included in the following analysis, so as to better characterize the high altitude performance for the bulk of the data.
Plots of "retrieved T(z) minus RAOB T(z)" were prepared for the 12 passes having flight altitude > 10 km. A slight pattern of "too warm" was present at 15 to 18 km (about 1.6 K), as well as a pattern of "too cool" at 9 to 12 km (about 0.7 K). This pattern is statistically significant, and is probably due to the observations occurring near the end of the 6-month simulation period used in deriving retrieval coefficients (February/March versus October through March). Since the retrieved T(z) is inherently biased toward the archive average profile, it is to be expected that altitude biases will be present for retrievals not uniformly representing the simulation period. Instead of re-determining retrieval coefficients using only RAOBs from February and March, which is labor expensive, I decided to perform a polynomial fit to the differences data and include it as an additional "seasonal" correction to be applied to the February/March retrievals.
Figure 3 shows the final MTP/DC8 retrieved T(z) for flight near the first RAOB site. The MTP/DC8 retrieved profile is for a 2-minute average of 8 data cycles. The thick trace is the MTP retrieved T(z) with NMC information incorporated. The dotted line is the RAOB T(z), interpolated in time between the preceding and following soundings. The filled triangles are from the NMC temperature field (the NMC data for 920212 are "forecast", not "analyzed"; the NMC data for 920214 and 920217 are "analyzed").
Plots of RMS differences between "MTP/DC8 retrieved T(z)" and "RAOB T(z)." The "observed" RMS trace closely matches the pre-experiment "predicted" RMS trace for all altitudes below about 19 km.
The analysis to this point assumes that RAOBs are free of errors. However, by interpolating RAOB profiles in time, and adopting RAOB sites that were as far away as 300 km from the aircraft's flight path, a component of error has been introduced into the intercomparison analysis by these assumptions. If that error can be assessed, or even assumed, it should be orthogonally subtracted from the observed RMS performance.
Plots were made of the RMS scatter for the 3 comparisons: 1) "MTP versus RAOB," 2) "NMC versus RAOB," and 3) "NMC versus MTP." Note that the RMS of each comparison of the 3-way comparisons can be viewed as a situation of "3 equations with 3 unknowns." This set of equations can used to "solve for" each unknown: the RMS uncertainty of MTP, RAOB, and NMC (at each altitude). For example, if the RMS scatter between MTP and RAOB is denoted by Smr, the RMS scatter between NMC and RAOB is denoted by Snr, and the RMS scatter between MTP and NMC is denoted by Smn, then the RMS of MTP, by itself, Sm, can be calculated:
Sm = %(0.5*(Smn2 + Smr2 - Snr2))
Similar equations specify Sr and Sn, the inherent RMS scatter of RAOB and NMC T(z). These equations can be "solved for" at each altitude.
The result of solving the 3 equations, at each altitude, produced an estimate of inherent RMS of each T(z) type.
This exercise suggests that the MTP/DC8 T(z) inherent standard errors (S.E.) are lower than pre-experiment predictions; indeed, they appear to be as low as 0.5 K in the 9 to 12 km altitude region. This is possible since the estimated observable uncertainties were found to be better than pre-flight estimates, and it is these observables that determine the 9 to 12 km part of the MTP/DC8 retrieved T(z).
It is not possible for the RAOB RMS to be less than 0.5 K, as is called for at some altitude regions (Schwartz and Doswell, 1991). I also doubt that the RAOB RMS can be significantly different at slightly different altitudes. Therefore I adopt a single value for RAOB RMS for all altitudes, and adjust the MTP/DC8 RMS profile accordingly, by orthogonal subtraction. This approach yields an MTP retrieval accuracy of < 1K from 9 to 16 km, <2 K from 6.4 to 18 km, and <3 K from 4 km to 19.5 km.
To achieve a more robust estimate of MTP retrieval accuracy, a simulation analysis was performed using the best estimate for observable uncertainties (based on 12 RAOB comparisons). The set of 15 RAOB's were used to calculate predicted TB's, to which noise was added stochastically in accordance with the measured observable uncertainties (based on 12 RAOB's). These noisy observables were put through the retrieval process to yield MTP predicted T(z), and when compared with the actual RAOB T(z) produced error T(z) profiles. The resulting RMS performance for MTP retrievals (without NMC information) is a slightly degraded version of the 12-RAOB result, due to the presence of more cold events in the additional RAOB's.
I believe this is the most realistic estimate of MTP performance for
Arctic winter conditions, and this final result is shown in Figure 4.
The dashed line with filled trianges, labelled "MTP ALONE," shows the MTP
performance to be approximatley 1 K from 10 to 14 km, < 2 K from 7.7
to 17 km, and < 3 K from 6 km to 18.7 km.
Figure 4 also shows the NMC/RAOB RMS profile, based on the same 15
RAOB's, shown as a dashed line, labelled "NMC NEAR RAOB." I will
argue that this trace is a best estimate of inherent NMC RMS accuracy.
Whereas it could be argued that RAOBs have errors, and these show up in
the NMC/RAOB comparison RMS profile, it is also true that the NMC temperature
field, being based mostly on the RAOBs, shares some of the RAOB errors
and is therefore an under-estimate of the inherent NMC RMS profile. (Satellite-derived
temperatures are also incorporated in the NMC data assimilation, especially
at higher altitudes, but near RAOB sites the bulk of the influence to the
NMC temperature field solution must come from RAOBs.) In adopting
the NMC/RAOB RMS trace as the best estimate for the NMC inherent accuracy
trace, I am assuming that the two compensating errors have approximately
the same magnitude.
Note that the NMC/RAOB RMS profile should apply to regions close to RAOB sites, and for locations distant from RAOB sites the NMC errors should increase (since there are few RAOBs to serve as input to the NMC temperature field, and the satellite temperatures are inherently less accurate than RAOBs). There is no direct way of evaluating the NMC inherent RMS uncertainty at remote locations, for if RAOBs were available at these locations they would be incorporated into the NMC analysis and they would, by definition, no longer be remote locations. Consequently, to provide an estimate of NMC inherent uncertainty that might be expected at remote locations I have arbitrarily orthogonally added 1.5 K to the NMC/RAOB RMS profile. This is shown in Fig. 4 as a dash-star trace, labelled "NMC REMOTE."
One method for estimating an NMC RMS uncertainty profile is to produce a series of MTP/NMC RMS difference profiles corresponding to different distances from the nearest RAOB site. Since the MTP RMS performance should not degrade with distance from the nearest RAOB site, but the NMC performance will, it should be possible to attribute all the increase in NMC/MTP RMS with distance to an increase in NMC RMS error, and thereby determine the dependence of NMC RMS with distance from RAOB sites. This is an activity for future work.
The MTP and NMC sets of T(z) are independent, and thus contain non-redundant information. The proper way to combine them is to use Bayesian estimation theory to derive a "combined" retrieval. An extensive evaluation of this is almost complete, and the tentative conclusion is that a far simpler method is almost equally effective: namely, a weighted average of the MTP and NMC profiles is produced using the MTP alone and NMC alone, using their independnet uncertainties to establish the weightings.
This procedure was used to produce 15 MTP/NMC T(z) profiles, which were compared with RAOB truth to derive a RMS performance trace, shown in Fig. 4 as a solid trace, running through the actual RMS performance results shown by open squares, labelled "MTP/NMC." This is the final performance measure for an MTP operating where NMC data are also available.
The MTP retrieval of T(z), without incorporating NMC information, exhibits an RMS accuracy of about 1.0 K from 10 to 14 km, and < 2.0 K from 7.7 to 17 km. In addition, the MTP retrieved T(z) has a better accuracy than the NMC T(z) from 8.1 to 18.6 km when flying close to RAOB sites.
Using the statistical retrieval method for deriving MTP retrieved T(z), the NMC temperature field is always superior to MTP performance above approximately 19 km. By combining MTP and NMC T(z) information, it is possible to produce a T(z) that exhibits an accuracy of about 1 K from 9 to 15 km, < 2 K from 6.5 to 18.5 km, and < 3 K everywhere else.
This is the first demonstration of an airborne 3-frequency microwave
temperature profiler employing statistical retrieval techniques.
It demonstrates a performance superior to all previous microwave profilers,
and thereby validates the concepts underlying its conceptual design.