MMS and NAV "Outside Air Temperature" Corrections for POLARIS and SOLVE

Bruce L. Gary


JPL's Microwave Temperature Profiler, MTP, is calibrated using radiodondes, RAOBs.  The procedure for performing this calibration could be performed in the absence of in situ temperatures, but it is more convenient to make use of them to "transfer" temperature field information from the RAOBs to the MTP.  Consequently, the MTP team has invested time assessing the quality of in situ temperature data.  We have discovered that the MMS temperature data has been too warm by 0.8 K throughout the POLARIS and SOLVE missions.  The navigation system temperatures exhibit errors that depend on altitude and ambient air temperature, and also change from flight-to-flight, and may change from mission-to-mission.  By applying offset corrections suggested in this report, MMS data can achieve an absolute calibration standard error, SE, of less than 0.40 K.  After applying a suggested correction equation to the navigation system temperatures it is possible to achieve a calibration SE of approximately 1.0 K.

MTP relies on radiosondes, RAOBs, for calibrating outside air temperature, OAT.  This web page summarizes corrections that must be applied to data from two airborne in situ air temperature measurement systems in the NASA ER-2 aircraft:  1) the "navigation" air temperature system, or NAV, and 2) the Meteorology Measurement System, MMS.  The corrections are intended to produce NAV and MMS temperatures that agree with RAOBs during the POLARIS and SOLVE missions.

For POLARIS 75 flights were analyzed, and for SOLVE 4 flights were analyzed (ER2000.01.09, ER2000.01.11, ER2000.01.14 and ER2000.03.18, hereafter referred to by the more succint labels 0109, 0111, 0114 and 0318).  RAOBs were obtained for epochs before and after the time of flight passage past RAOB sites.  Two RAOB sites were used for cases in which the flight path was too far from one site but a pair of sites straddled the flight path and were approximately equidistant.  For single-site RAOB comparisons sites were used only if they were closer than 200 km (1.8 degrees) of the flight path, whereas for two-site RAOB comparisons each site had to be within 300 km of the flight path.  Temporal interpolations were also performed.  RAOB comparisons were only performed when RAOBs were available for times that were less than 12 hours before AND 12 hours after the time of flying past the RAOB site.

Since there is a discrepancy between the navigation and MMS pressure altitudes for SOLVE, I have adopted a correction the the navigation system's altitudes of -2.8 mb (consistent with a line leak, or perhaps a pressure transducer calibration error).  This correction placed navigation system pressure altitudes in agreement with MMS altitudes.  No corrections were made to navigation altitudes for the POLARIS data (and I am not aware that they are needed).

Navigation System

There were 41 comparisons of the navigation OAT with RAOBs for POLARIS, and 23 comparisons for SOLVE.   The "corrections" that would yield consistency with RAOBs are plotted in the following graph.

Figure 1.  Navigation OAT corrections to achieve agreement with RAOBs.

For POLARIS the average navigation system temperature correction, called OATnavCOR, is -0.21 +/- 0.22 K (population SD = 1.38 K, N = 41).  For SOLVE this correction was -1.60 +/- 0.35 K (population SD = 1.66 K, N = 23).  The required correction changed significantly between POLARIS and SOLVE (the change was 1.39 +/- 0.41, or 3.4 SDs).  The greater temperature correction for SOLVE might be related to the need for an altitude correction that appeared in the SOLVE data, or it might be related to the fact that SOLVE flights were in colder air than POLARIS flights (see below).


For POLARIS there were 58 comparisons with RAOBs, and for SOLVE there were 17.  The "corrections" that would yield consistency with RAOBs are plotted in the following graph.

Figure 2.  MMS OAT corrections to achieve agreement with RAOBs.

For POLARIS the average MMS temperature correction, called OATmmsCOR, is -0.92 +/- 0.11 K (Population SD = 0.81 K, N = 58).  For SOLVE this correction was -0.55 +/- 0.29 K (population SD = 1.20 K, N = 17).  The difference between POLARIS and SOLVE is insignificant, being 0.47 +/- 0.44 (or 1.1 SDs).  Therefore it is appropriate to average the two sets of data, yielding a POLARIS and SOLVE average temperature correction of OATmmsCOR =  -0.84 +/- 0.11 (population SD = 0.91 K, N = 75).

NAV Calibration Changes

Figures 1 and 2 appear to exhibit the same magnitude of scatter, but they have different temperature scales.  The next figure shows daily averages using the same temperature scale.  It is apparent that OATnavCOR changes much more, from flight-to-flight, than OATmmsCOR.

Figure 3.  Daily averages of OATnavCOR and OATmmsaCOR, showing greater flight-to-flight changes for NAV than MMS.

The flight-to-flight variation for MMS is 0.40 K, whereas for NAV it is 1.41 K - or 3.5 times greater.  Some of the 0.40 K scatter of MMS measurements is surely due to limitations associated with using RAOBs to derive true air temperature at a different location and a different time (spatial and temporal interpolation).  The fact that the individual MMS/RAOB comparisons (Fig. 2) exhibit a larger variation than the flight-averaged MMS/RAOB comparisons (Fig. 3) is most likely due to the averaging of RAOB spatial and temporal interpolation effects.  It is likely that the MMS/RAOB comparisons would exhibit a variation smaller than  0.40 K if the RAOB interpolations were not needed (flying over a RAOB site as the radiosonde was passing by the plane).  The measured 0.40 K SE must be the orthogonal sum of the true MMS calibration variation and RAOB-related spatial and temporal interpolation effects.  Therefore, RAOB-related uncertainties are less than 0.40 K (for flight averages).  If we assume that all of the 0.40 K SE is attributed to ROAB-related spatial and temporal interpolations, we may orthogonally subtract it from the measured navigation SE of 1.41 K to arrive at 1.35 K as a minimum SE produced by the navigation system's measurement of temperature.  In other words, flight averages of OATnavCOR exhibit a scatter of at least 1.35 K, and probably closer to 1.40 K, due to navigation system shortcomings.

Apparently the NAV transducer electronics is not temperature-compensated, which could explain the pattern for OATnavCOR in the next figure.

Figure 4.  Dependence of OATnavCOR on ambient air temperature (RAOB-derived).

The above figure shows that a slight OAT dependence exists for OATnavCOR.  An altitude dependence also exists, and the multiple regression result for a 2-term fit, altitude and OAT, is shown in the next figure.

Figure 5.  Measured OATnavCOR versus values predicted by a fit to pressure altitude and ambient air temperature.

The 2-term fit of OATnavCOR to pressure altitude and RAOB-derived OAT exhibits an r2 = 0.31, and leads to a residual standard deviation = 1.37 K (versus 1.66 K without the altitude and OAT corrections).  The fitted coefficients for altitude and OAT are larger than their SE uncertainties by the factors 4.66 and 4.46, respectively, so the two independent variables have statistically significant correlations with OATnavCOR.  The equation fit for OATnavCOR is:

        OATnavCOR [K] = -0.69+0.259 * ( Zp [km] - 18 [km] ) + 0.126 * ( OATraob [K] - 220 [K] )

where Zp is pressure altitude and OATraob is RAOB-based ambient air temperature.

IF it is appropriate to "model" the NAV temperatures with altitude and ambient air temperature calibration dependencies, THEN we are left with the issue of NAV exhibiting a larger residual scatter (to the fitted OATnavCOR equation) than MMS exhibits with respect to its measured offset; namely, 1.37 K for NAV versus 0.91 K for MMS (for the individual RAOB site comparisons, not the flight averages).  Hence, other factors are present that change the NAV temperature calibration, and they amount to approximately 1.0 K (i.e., the orthogonal difference between 1.37 K and 0.91 K).  In other words, even if NAV temperatures are really dependent upon altitude and air temperature in the way I suggest, using the suggested OATnavCOR equation will produce NAV temperatures that will exhibit calibration uncertainties of approximately 1.0 K.

Preliminary analyses indicate that within a flight the navigation and MMS temperatures track each other well after allowing for an offset and an altitude dependence.  One interpretation of this data is that the navigation temperatures undergo flight-to-flight changes, and this is what produces the large residual scatter in Fig. 5.  I do not know enough about the navigation temperature system to identify the origin of the problem.  Rather, I shall merely state that navigation temperatures exhibit calibration changes of approximately 1.0 K SE, and that if they are to be used with the desire of achieving better accuracy it will be necessary to ascertain a calibration offset for each flight.  This can be done by either 1) comparing navigation temperatures to MMS temperatures, after first correcting the MMS temperatures by -0.84 K, or 2) by comparing navigation temperatures to several RAOBs near the flight path, which is a time-consuming task.

Discussion and Conclusions

My analysis of MMS temperatures from an earlier mission (STRAT) suggests that a similar OATmmsCOR was needed (MMS being too warm by almost 1 K).  Thus, MMS temperatures appear to be stable, but too warm by about 0.84 K for the past 5 years.

The ER-2 navigation system must be adequate for pilot navigation safety since the pressure altitude errors (discussed on another web page) are small below 15 km, where other traffic may be encountered, and since navigation system temperatures are usually within 2 K of the correct values.  However, scientific experimenters must be prepared for mision-to-mission changes in the corrections needed for both pressure altitude and temperature, with corrections on the order of 3 mb and 1 or 2 K.  If the NAV temperatures depend on altitude and temperature, then experimenters must be prepared for changes in the coefficients of dependence.  At the present time the navigation system temperatures should be thought of as failing to meet scientific data quality standards, which is the rationale for flying the MMS.  Since some science flights have missing MMS data, there will be a continuing need to monitor the calibration of the navigation altitude and temperature data products.

I recommend using MMS temperatures when they are available, subject to the following correction, and for times when MMS data is not available relying on the navigation system temperatures, subject to the following correction equation:

    OATmmsCOR = -0.84 K for POLARIS

    OATnavCOR = -0.69 + 0.259 * (Pressure Altitude [km]- 18 [km])
                + 0.126 * (OAT [K] - 220 [K])

In other words, MMS temperatures are too warm by 0.84 K, and they have been warm by this amount for several years, whereas navigation system temperatures are usually too warm but because of a dependence on altitude and ambient temperature they simply vary with conditions.  After using the suggested corrections the experimenter can assume that MMS temperatures will exhibit an accuracy of less than 0.40 K, whereas navigation system temperatures will exhibit an accuracy of approximately 1.0 K.

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This site opened:  July 18, 2000.  Last Update: March 12, 2003