OAT CALIBRATION TUTORIAL

Bruce L. Gary

Introduction

This web page describes how I "calibrate" in situ air temperature measurements using RAOB data.

I use the terminology "Outside Air Temperature," or OAT, following the convention of commercial pilots.  The correction that should be applied to measured OAT in order to achieve agreement with RAOB profiles is called OATxxxCOR, where "xxx" refers to a specific OAT-measuring instrument.  OATmmsCOR, for example, refers to a correction meant for use with the MMS instrument (Ames Research Center's Meteorology Measurement System).

I claim that it is possible to compare OAT with RAOBs in a way that achieves a SE uncertainty of 1.0 K for a typical comparison.  By averaging many RAOB/OAT comparisons it is then possible to achieve a mission-average OATxxxCOR SE uncertainty that is typically ~0.30 K.  One purpose for this web page is to describe the procedure I use so that others may achieve similar results.

For most of my years of calibrating the Microwave Temperature Profiler I've adopted RAOBs as my primary calibration standard. Since in situ systems, such as MMS, typically differ from RAOBs by significant amounts (ranging from 0.8 to 0.1 K, depending on the mission), I have undertaken calibrations of the in situ OAT-measuring system before calibrating the MTP.  This is convenient since the in situ OATs can be used to establish MTP instrument gains throughout a flight, provided the in situ system has been corrected.  Thus, in situ systems like MMS are used by MTP as a secondary calibration standard, transferring the occasional primary temperature standard of ROABs to the always-present secondary temperature standard.

The procedure for obtaining an OATxxxCOR calibration begins with an inspection of a flight track to determine which RAOB sites are located closer than ~150 km.  A list of times and RAOB site designations is produced, and the RAOBs are downloaded from the following web site:  http://weather.uwyo.edu/upperair/sounding.html  These RAOB profiles are converted to my standard format, which facilitates their use for both OAT calibartion and WCT determination (WCT stands for Window Correction Table, a calibration needed only by an MTP).  The RAOB files are imported to a spreadsheet where plots of T(z) can be viewed (and printed out) for conducting interpolations in altitude, time and space (if necessary).  Spatial interpolation is used when the flight path is straddled by two RAOB sites at approximately equal distances.  For each OAT/RAOB comparison event a RAOB interpolation fraction is calculated for temporal interpolation between the "before" and "after" RAOBs.  An average aircraft-based OAT is calculated by averaging  ~3 minutes worth of OAT measurements.  This constitutes one RAOB/OAT comparison, which typically exhibits a standard error uncertainty of 1.0 K.  Therefore, many such RAOB/OAT coparisons are needed in order to achieve an average OAT correction that has an associated SE uncertainty of approximately 0.30 K, which is a desired goal.

This procedure is described in more detail in the following sections.

Determining RAOB Comparison Events

To illustrate my procedure I'll use one RAOB site encounter and provide abundant detail.  The Crystal-Face WB-57 flight of 2002.07.31 will be used.  This flight has both MMS and NOAA PTW OAT measurements.  I will use MMS data for this illustration.

The following graph shows the ground track for this flight.

Figure 1. Ground track for flight WB020731 (WB-57 flight of 2002 July 31).  The flight originates in Key West, FL and lands at Ellington Field near Houston, TX.  Marks at 2000 second intervals are shown. RAOB sites are indicated by green open squares; some RAOB sites have3-letter site designations.  At 53 ks the ground track passes over the Tallahassee (TLH) RAOB site.

Using a ground track map allows for ready identification of RAOB sites closer than about 150 km.  In the stratosphere air temperature has a horizontal auto-correlation function such that temperatures at the same altitude but 150 km apart differ by <0.7 K, typically.  There's a trade-off in setting the proximity requirement; if it's much less than 150 km then there won't be many RAOB/OAT comparisons to use, but if it's much more than 150 km the RAOB/OAT comparisons will suffer from large differences between the actual temperature at the aircraft and the distant RAOB.  My adoption of 150 km is based on trial-and-error during many missions.

There are a couple of exeptions to the 150 km proximity rule: 1) the presence of mountain waves causes vertical motions of air parcels, and therefore temperature oscillations, which can ruin a RAOB/OAT comparison if the waves are present at either the RAOB or aircraft location, and 2) flight in the troposphere is a quite different environment with considerations unique to that setting.  Tropospheric RAOB/OAT comparisons are generally more difficult because small errors in altitude produce large errors of temperature.  Aircraft pressure altitude readings can be low by several hundred meters if there's a pressure leak in the line between the outside air intake and the pressure transducer.  This can cause errors of several degrees in the troposphere (but usually much smaller errors in the stratosphere). This source of error does not affect the 150 km criterion, but it does represent a "cause for pause" before attempting a tropospheric RAOB/OAT comparison. If pressure altitude is known to be accurate, then tropospheric RAOB/OAT comparisons can be attempted provided strong convection is not present at either the aircraft or RAOB locations.  Since horizontal gradients are smaller in the troposphere than in the stratosphere (when convection is absent) a larger value than 150 km should be useable.  I don't have sufficient experience with tropospheric RAOB/OAT comparisons to suggest a distance criterion for the troposphere.

The data used to create a ground track plot can be used to create a list of times when the aircraft flew closer than 150 km to RAOB sites. Times are selected which do not include rolls since some OAT systems cannot correct properly for the perturbing effects of a roll.  Approximate altitudes should also be noted.  The flight in this example had 4 RAOB encounters, listed below:

    #    utsec    Site      Zp [km]

    1    51142    TBW        13.7
    2    53019    TLH        13.7
    3    54793    FFC        16.2
    4    63183    SHV/LCH    13.7

Encounter #4 is a 2-RAOB encounter, passing between sites SHV and LCH.  Spatial interpolation is required for 2-RAOB comparisons.  The example for detailed explanation of this web page is encounter #2, at 53019 seconds.

At this stage it is not known whether all RAOB/OAT candidate comparisons can be used.  For example, RAOB data may not exist for the "before" and "after" epochs for a site, or a RAOB might not have data above the aircraft's altitude.  A candidate RAOB/OAT comparison must be rejected if either of these conditions exist.

Getting RAOBs

RAOB data can be obtained from many web sites.  My favorite is http://weather.uwyo.edu/upperair/sounding.html .  At this site you first select a region of the world, then a start epoch (date and hour) and an end epoch.  Then you click on the RAOB site symbol on the map.  This spawns a new web browser and web page displaying the desired RAOB information as text.  Save this web page as a text file (to avoid html marks), using a filename that includes the site's 3-letter name.  Repeat this process for all desired RAOB sites.

When specifying a start and end epoch, keep in mind that most sites launch at 0 and 12Z, whereas some launch at 6 and 18Z.  Also, sometimes a site will miss a RAOB (due to balloon burst at low altitude, for example).  In our example, with a utsec = 53019 (which is between the 12Z and 0Z epochs, i.e., between 43200 and 86400 utsec), we want to interpolate between the following two launch epochs:  start = 2002.07.31 at 12Z, end = 2002.08.01, 00Z. This should capture 2 RAOB profiles.

Note whether or not the RAOBs that are needed include data that extends above flight level, Zp [km] in the above table.  If a RAOB doesn't extend above the aircraft'sZp, then that RAOB/OAT comparison event should not be used (unless you're "desperate," and willing to go to the trouble to determine whether or not temperature trends are small, in which case a preceding or following RAOB may be used).

The following is the relevant portion of RAOB site TLH for the "before" epoch, 2002.07.31, 12Z:

72214 TLH Tallahassee Muni Observations at 12Z 31 Jul 2002
-----------------------------------------------------------------------------
   PRES   HGHT   TEMP   DWPT   RELH   MIXR   DRCT   SKNT   THTA   THTE   THTV
    hPa     m      C      C      %    g/kg    deg   knot     K      K      K
-----------------------------------------------------------------------------
 1012.0     21   23.0   23.0    100  17.83    340      3  295.1  346.5  298.3
 1000.0    161   23.8   22.8     94  17.83    320      7  296.9  348.7  300.1
  985.0    294   24.4   22.1     87  17.33    288     13  298.8  349.5  301.9
  .
  .
  169.9  13411  -59.7  -72.9     17   0.01     40     11  354.1  354.2  354.1
  166.0  13560  -60.7  -73.7     17   0.01     41     10  354.9  354.9  354.9
  150.0  14190  -60.9  -74.9     14   0.01     45      6  365.0  365.0  365.0
  144.0  14443  -61.7  -75.7     14   0.01     41      7  367.9  367.9  367.9
  126.2  15240  -67.4  -81.4     12   0.00     30     10  371.6  371.7  371.6
  117.0  15699  -70.7  -84.7     11   0.00     30      9  373.7  373.7  373.7
  102.8  16459  -73.7  -86.8     12   0.00     30      8  382.1  382.1  382.1
  100.0  16620  -74.3  -87.3     12   0.00     40      8  383.9  383.9  383.9

and also representative portions of the "after" epoch, 2002.08.01 at 00Z:

72214 TLH Tallahassee Muni Observations at 00Z 01 Aug 2002
-----------------------------------------------------------------------------
   PRES   HGHT   TEMP   DWPT   RELH   MIXR   DRCT   SKNT   THTA   THTE   THTV
    hPa     m      C      C      %    g/kg    deg   knot     K      K      K
-----------------------------------------------------------------------------
 1009.0     21   30.0   23.0     66  17.89    240      4  302.4  355.5  305.6
 1000.0    134   28.2   23.2     74  18.28    245      6  301.4  355.4  304.6
  993.0    197   27.0   22.7     77  17.85    247      7  300.8  353.4  304.0
  .
  .
  162.0  13717  -62.1  -73.1     22   0.01     22     26  355.0  355.1  355.0
  154.2  14021  -62.7  -73.7     21   0.01     30     15  359.0  359.0  359.0
  150.0  14190  -63.1  -74.1     21   0.01     30     13  361.2  361.2  361.2
  145.0  14399  -62.5  -73.5     21   0.01     19     13  365.7  365.8  365.7
  126.2  15240  -69.0  -81.0     16   0.00    335     11  368.7  368.7  368.7
  125.0  15300  -69.5  -81.5     16   0.00    336     11  368.9  368.9  368.9
  113.9  15850  -71.0  -83.0     15   0.00    345     13  376.0  376.1  376.0
  100.0  16620  -73.1  -85.1     15   0.00     15      7  386.2  386.2  386.2

It should be mentioned that radiosonde balloons do not ascend vertically.  Their location when reaching stratospehric altitudes can be several tens of km away from the launch site.  It is inconvenient to correct for this hoizontal motion of the RAOB, and neglecting it represents one component of SE uncertainty in performing RAOB/OAT comparisons.  It is probably smaller than the uncertainty produced by the useof RAOBs whose launch sites are as far as 150 km from the aircraft grond track.

Determining RAOB Temperatures

I will describe two ways for determining a RAOB temperature for comparison with OAT.

First, and perhaps the simplest, is to calculate a pressure value for the event in question.  A more accurate pressure altitude has to be used, and I average 5 MTP cycles (about 75 seconds) of pressure altitude data for this purpose.  Zp [km] can be converted to pressure [mb] using "standard atmosphere" equations.  Then, for the "before" and "after" RAOBs a pressure interpolation is performed.  If two RAOB sites are to be used (as in Event #4, above), this interpolation is repeated for the other RAOB site.  A temporal interpolation is then performed.  For example, 53019 utsec is 23% of the way from the "before" epoch (2002.07.31, 12Z) to the "after" epoch (2002.08.01, 00Z).  Again, for the 2-RAOB comparison, this temporal interpolation is performed twice, then the two results are spatially interpolated.

Following is a plot of RAOB temperature versus pressure for Event #2:

Figure 2RAOB temperature versus pressure for Event #2, above.  The red dotted trace is from the "before" RAOB, and the green contiuous trace is from the "after" RAOB.  The vertical blue line, at 147.3 mb, corresponds to the flight altitude of 13.72 km associated with Event #2.  A temporally interpolated temperature of 211.7 K is determined to be the RAOB temperature for comparison with OAT.

This interpolation procedure assumes that air temperature at a given altitude varies linearly during the 12-our interval between RAOB launches.  Temperatures typically vary by 1 or 2 K during such an interval, and this variation is obviously not linear on most occasions.  This imperfect temporal interpolation is therefore a significant component of the 1.0 K SE uncertainty that will be shown to exist for RAOB/OAT comparisons.

A second method, the one I use most often, is to convert the downloaded RAOB files to my standard format (I do this because I also use these RAOB profiles to determine MTP "window corrections" - that won't be described here).  Computer programs process MTP data files to produce, among other products, Zp averaged for a 5-cycle interval at the specified RAOB/OAT comparison time.  A spreadsheet is used to perform the interpolations in altitude and time (and space when a 2-RAOB comparison is being performed).

Here's a graph showing how my spreadsheet is used to perform the altitude and temporal interpolation.

Figure 3Plot of RAOB temperature versus altitude for "before" (green dotted) and "after" (continuous green).  The horizontal black line is at the WB-57's pressure altitude, 13.72 km.  The blue oval is a 23% temporal interpolation between the "before" and "after" profiles at the aircraft altitude.  (Ignore the red trace, which is an MTP retrieval using inappropriate retrieval coefficients).

Note that both methods yield the same result for RAOB temperature, 211.7 K, at the aircraft's pressure altitude and at the time it close to the TLH RAOB launch site.

Determining OAT Temperatures

It is appropriate to average aircraft sampled OAT before comparing it to a RAOB interpolated temperature.  With no averaging there will be unwanted mesoscale structure, which is especially important at stratospheric altitudes (mesoscale temperature fluctuations grow with altitude in accordance with the reciprocal of square-root of air density).  Given that the RAOB site is typically 100 km away, it is reasonable to require an OAT that is averaged for a comparable distance.  The WB-57 travels this distance in ~550 seconds, so averaging OAT for as much as 500 seconds would be reasonable.  I have chosen to average over 180 seconds (~35 km), as this smoothes out essentially all discernible mesoscale structure.

Here are graphs of OAT from the MMS and PTW instruments.

Figure 4OAT from MMS for flight WB020731.  The black trace is a 180-second smoothed version.

Figure 4OAT from NOAA's PTW instrument for flight WB020731.  The black trace is a 180-second smoothed version.

Readings at 53.0 ks yield OATmms = 211.5 K and OATptw = 211.4 K.

Comparing OAT With RAOB Temperatures

The two OAT readings, above, are the values that are to be compared with the RAOB value of 211.7 K for the second RAOB site encounter (TLH).  The following table summarizes RAOB, MMS and PTW temperatures for the case-study flight:

    #    utsec    Site      Zp [km]  RAOB      MMS      PTW    MMS-RAOB   PTW-RAOB

    1    51142    TBW        13.71   209.3    207.9    208.1     -1.4      -1.2
    2    53019    TLH        13.72   211.7    211.5    211.4     -0.2      -0.3
    3    54793    FFC        16.18   204.5    204.4    204.4     -0.1      -0.1
    4    63183    SHV/LCH    13.72   204.2    205.4    205.3     +1.2      +1.1

With just these 4 comparisons it is not possible to estimate the average correction that must be applied to the OAT measurements to achieve agreement with RAOBs.  The comparisons exhibit about 1 K of scatter, and with only 4 RAOB/OAT cmparisons their average will have a SE of ~0.5 K, which is not a small enough uncertainty for OATxxxCOR to be useful.

Nevertheless, it is possible to crudely estimate the accuracy of the individual RAOB/OAT comparisons based on the scatter about their average.  The standard error, SE, for these two sets of 4 differences is 0.87 K, and this is approximately the same that is derived from a much larger set of comparisons (SE = 1.0 K).  Thus, we can easily estimate that approximately 24 RAOB/OAT comparisons will be needed to achieve an OATxxxCOR that is accurate to ~0.3 K.

The average differences are -0.1 and -0.1 K.  If this is all the data that was available we should use the negative of these differences to correct measured OAT so that we are on the same scale as RAOBs - i.e., apply the correction OATmmsCOR = +0.1 K and OATptwCOR = +0.1 K to the MMS and PTW temperature measurements.  However, this result came from just one flight of a mission consisting of 14 flights suitable for the same analysis.

This concludes the description of my procedure for deriving values for OATxxxCOR.   The next section illustrates how a larger set of OATxxxCOR can be assembled to arrive at statistically significant corrections.

OAT Calibaration Results for a Mission

The following graph is a plot of MMS measured OAT versus RAOB determined temperature for the Crystal-Face mission.  The six best flights for this purpose were analyzed, yielding 27 RAOB/OAT comparisons.

Figure 5.  Measured OAT versus RAOB temperature for WB57/MMS flybys of RAOB sites during the Crystal-Face mission.  The dotted line is a fit to the MMS data, and is offset +0.51 K from RAOB temperatures.  The MMS data is the provisional version submitted shortly after each flight.

The graph above uses provisional MMS data, which appears to be too warm by 0.51 +/- 0.22 K.  Note that by averaging 27 independent RAOB/OAT comparisons the SE on the average is a low 0.22 K!  After this graph was made a set of final MMS files were archived, and these final values averaged 0.3 K colder.  Thus, without help from the graph shown here the MMS final calibration produced temperatures that are in better agreement with RAOBs than the provisional temperatures.  Their final data requires a correction of OATmmsCOR = -0.2 +/- 0.2 K.

It should be noted that the correlation of measured OAT with RAOB temperature appears to have negligible correlation with RAOB temperature for this data set.  The ER-2 navigation system on at least one mission had a significant temperature dependence, as described on another web page.

The following graph shows results of the same analysis applied to PTW OAT data.

Figure 6.  Measured OAT versus RAOB temperature for WB57/PTW flybys of RAOB sites during the Crystal-Face mission.  The dotted line is a fit to the PTW data, and is offset +0.34 K from RAOB temperatures.

These PTW data have not been revised, so the present analysis applies:  OATptwCOR = -0.34 +/- 0.22 K.  Any temperature dependence of OATptwCOR appears to be small.

Population SE Versus Number of RAOB/OAT Comparisons

The above analysis was for Crystal-Face.  The same analysis has been performed for many missions.  The last 10 missions have provided RAOB/OAT comparisons numbering 5 to 58.  As expected, the more RAOB/OAT comparisons there are, the smaller is the SE on the average RAOB/OAT difference.  The following graph shows this dependence.

Figure 7Summary of SE versus number of RAOB/OAT comparisons used for the last 10 stratospheric missions studied.  Each symbol represents a mission that provided a different number of RAOB/OAT comparisons.

The fitted line in this graph has the required 1/(N-1)0.5 dependence.  The only degree of freedom is a vertical offset.  The SE Uncertainty model which accounts for this fitted line incorporates a Population SE of 1.02 K.  In other words, a typical RAOB/OAT comparison can be thought of as having an uncertainty of 1.02 K.

Conclusion

The comparison of in situ OAT measurements with RAOB-inferred temperature interpolated for aircraft altitude, time of flyby and spatial location provides a means for assessing the calibration offset of measured OAT.  The accuracy with which this offset correction can bhe determined is such that a half dozen flights, affording ~15 or 20 RAOB/OAT comparisons (typically), allows the OAT correction to be determined with an accuracy of ~0.2 K.  Given that this result is based on 10 missions with 265 RAOB/OAT comparisons, it can be thought of as a robust result.

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This site opened:  April 17, 2003 Last Update:  April 18, 2003