WCT History

WINDOW CORRECTION TABLES for MTP/ER2 SOLVE

Introduction

I've re-analyzed four SOLVE ER-2 flights for the purpose of determining a window correction table, WCT, for use for the SOLVE mission. All TB calculations used a tTGT lead of 7 cycles, a tMXR lag of 0 cycles, altitude lead of 0.5 cycles, the gain values you recommended (with no gain dependence upon tMXR), and the "navigation" altitudes modified to approximate MMS altitudes through the use of a pressure correction of -2.584 mb. The Window Correction Table using a weighted average of 4 SOLVE flights (0109, 0111, 0114, 0318), including all RAOB comparisons, is given below:

      60 -0.06 -0.57
      44 -0.37 -0.45
      30 -0.43 -0.78
      18 0.47 0.04
       9 0.81 0.50
       0 -0.12 0.15
      -9 -0.56 -0.81
     -21 0.22 0.27
     -37 -0.19 -0.23
     -58 -0.43 -0.56

Note: The previous WCT, dated 0718 (using higher gains) is given below for comparison:

      60 -0.45 -0.79
      44 -0.60 -0.58
      30 -0.55 -0.79
      18 0.37 -0.01
       9 0.69 0.43
       0 -0.14 0.11
      -9 -0.42 -0.66
     -21 0.41 0.43
     -37 0.02 0.01
     -58 -0.20 -0.29

I've deleted the two RAOB comparisons from ER000109 that were "outliers."

Figure 1. Window Correction Profiles for Ch# 1; flight averages (excluding the two "0109" outliers).

Figure 2. Channel 2 flight average WCT (excluding the two "0109 outliers").

Both channels appear tob e well-behaved, and I recommend using the above WCT for SOLVE.

The SE uncertainties for this data are calculated using standard statistical theory, and are presented in SE_WCT.PCX. Unsurprisingly, the highest SEs are for Ch1 at high elevation angles, where transparency effects magnify small discrepancies between RAOB T(z) interpolations and true T(z) for the epoch and location. Nevertheless, at the worst the WCT appears to be established with an accuracy of better than 0.25 K, and for most WCT entries the SE is under 0.1 K. This is much smaller than the retrieval coefficient TB error table assumptions, which in the past I have estimated to be 1.5 K for Ch 1 at high elevations and 0.7 K at most other elevations, as shown in the table below, taken from an IOM to Steve Keihm concerning POLARIS RCs.

EL# ELEV'N Ch#1_SE Ch#2_SE

1 +60.0 1.5 K   1.0 K
2 +44.4 1.1 K   0.9 K
3 +30.0 0.8 K   0.8 K
4 +17.5 0.7 K   0.7 K
5 + 8.6 0.7 K   0.7 K
6    0.0 (OAT-based; ~0.6 K)
7 - 8.6 0.7 K   0.7 K
8 -20.5 0.7 K   0.7 K
9 -36.9 0.8 K   0.8 K
10 -58.2 0.9 K   0.9 K

The present analysis produces the following set of SE values (which I derived using standard statistical procedures for the existence of 4 measured estimates of a fixed and unknown value):

      60 0.26 0.13
      44 0.24 0.10
      30 0.21 0.08
      18 0.12 0.07
       9 0.06 0.09
       0 0.03 0.05
      -9 0.09 0.11
     -21 0.04 0.14
     -37 0.03 0.09
     -58 0.11 0.08

which is graphed in the next figure.

Figure 9. Plots of SE for the average WCT in the previous two figures (thick black lines).

I recommend orthogonally adding about 0.25 K to the above table before adopting it as a "SE a priori uncertainty WCT table" needed for calculating RCs. This is because you want the SE table to include some stochastic radiometer noise since it will be used with individual data cycles. I've done this to produce the following "SE a priori uncertainty WCT table":

      60 0.36 0.28
      44 0.35 0.27
      30 0.32 0.26
      18 0.28 0.26
       9 0.26 0.27
       0 0.25 0.25
      -9 0.26 0.27
     -21 0.25 0.29
     -37 0.25 0.27
     -58 0.27 0.26

This WCT SE uncertainty table neglects the fact that MTP/ER2 gains may vary from flight to flight, and during a flight, causing the horizon view TB to disagree with true OAT by small amounts. Similarly, it ignores the possibility that we have assigned wrong values for radome window absorption and reflection for the horizon view. It is my position that these additional uncertainties, which are difficult to quantify, will not affect the SHAPE of the retrieved T(z) profile - to first order. If the shape is correct, it is unimportant that the T(z) profile may have a small temperature offset. Recall that MTP's task is to get the shape of T(z) correct; getting the in situ temperatures correct is MMS's job. Therefore it should be "safe" to use the SE a priori uncertainty WCT table, given above.

Conclusion

I recommend using the following window correction table for ER-2 SOLVE flights:

in association with the following SE a priori uncertainty WCT table:

=========================================== UPDATE (December 15, 2000) ========================================

I have re-analyzed the same four flights used above in determinnig the SOLVE/ER2 Windo Correction Table, using new assumptions. For the updated WCT (below) I have adopted the following:

    G1,2 = 19.58 & 17.45 [K/count] for all flights
    GainSlopes = 0.00 & 0.00,
    OAT = Tnav - 1.4 K (I don't think this matters for WCT),
    tTGT Lead = 25 cycles,
    P = Pnav - 3.51 [mb].

The following figures show the individual RAOB/MTP TB-comparisons, expressed as "required WCT correction" versus elevation angle.

Figure 10. WCT for Channel #1 based on 4 SOLVE flights and assumptions given in the text.

Figure 11. WCT for Channel #2 based on 4 SOLVE flights and assumptions given in the text.

I recommend using the following WCT for MTP/ER2 for SOLVE:

     60 -0.38 -0.97
     44 -0.54 -0.68
     30 -0.47 -0.85
     18 0.42 -0.02
      9 0.70   0.43
      0 -0.16   0.12
     -9 -0.38 -0.67
    -21 0.46   0.47
    -37 0.06   0.03
    -58 -0.18 -0.30

It is based on 25 RAOB/MTP comparisons, for the flights ER000109, 000111, 000114 and 000318.

The uncertainty on these numbers is approximately 0.25 K at the elevation extremes, and less near the horizon.

Notice that both channels have approximately the same shape.

The above analysis was completed December 15, 2000.

_____________________________ THE END _______________________________________

Return to Main Page of SOLVE Analyses

This site opened: July 18, 2000. Last Update: January 29, 2001