OATnav GAIN EXAMPLE

This web page illustrates the derivation of gains using OATnav, using CAMEX4 flight ER2001.09.23.

Figure 1.  Flight track for ER010923, with kilosecond ticks.

Figure 2.  Roll, pitch and altitude.

The MTP horn antenna receives photns from 3 sources:

    1) The atmosphere, having a brightness temperature of TB as seen from outside the MTP radome window,
    2) The window's emission, consisting of 0.4% emission "losses" from radome window material having a physical temperature tWIN,
    3) The MTP radiometer, consisting of 0.6% reflections by the window of MTP components having a physical temperature approxiamted by tMXR.

The measured antenna temperature, Ta, while viewing the horizon is:

    Ta (horizon) = TB * (1 - L - R) + L * tWIN + R * tMXR

        where L = 0.004, R = 0.006

The measured antenna temperature, Ta, while viewing the base target is:

    Ta (base target) = tTGT

        which assues that the base target is 100% emissive and all the antenna pattern is intercepted by the target.

For any view the measured counts is

    C = Co + g * (brightness temperature of the scene in question)

Replacing (1 - L - R) by 0.99, we have for the horizon and base target views:

    C (sky horizon) = Co + g * ( 0.99 * TB + L * tWIN + R * tMXR )

    C (base target) = Co + g * (tTGT)

Solviong for gain, g:

    g = (Cb - Cs) / (tTGT - 0.99 * TB - L * tWIN - R * tMXR)

We may replace OATnav for TB since we are assuming it is safe to use OATnav as an approximation to the line-of-sight average of air temperature when viewing hte sky horizon.  Hence:

    g = (Cb - Cs) / (tTGT - 0.99 * OATnav - L * tWIN - R * tMXR)

It ahs been determined that for CAMEX4 we must correct OATnav by -1.5 K.  After doing this, and solving for channel 1 and 2 gains, I get the following:

Figure 3Gains derived using the above equation for MTP's channel 1 (red) and channel 2 (green), versus time. Also shown is the difference between the base target and OATnav (blue).

Figure 4Gains derived using the above equation for MTP's channel 1 (red) and channel 2 (green).

 Note: I use the terms "tIFA" and "tMXR" interchangeably.  My eyeball fit to the above gain versus mixer temperature is:

    G1 = 18.7 * (1 - 0.0208 (tIFA - 43.2)
    G2 = 16.4 * (1 - 0.0661 (tIFA - 43.2)

After obtaining these OATnav-based gain equations, I re-processed the raw data file using these equation gains and produced TBs. After deleting noisy MTP data, and performing a 10-cycle running-average, I get the following for OATnav (corrected by -1.5 K) and gain equation based MTP horizon brightness temperatures:

Figure 5First half of the flight, showing agreement of MTP (green) horizon TBs and OATnav (red).

Figure 6Second half of flight, showing agreement of MTP (green) horizon TBs and OATnav (red).

This analysis did not employ lead or lag corrections.  This probably accounts for the offset at the beginning of the flight, during which MTP TBs are about 1.0 K too warm.  However, late in the flight, at about 84 ks, there's a 1 ks period of 1.0 K disagreement that gradually comes and goes. I can't account for that.

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This site opened:  December 14, 2001.  Last Update: December 14, 2001