Calibration of Limb Viewing Angle

In examining the behaviour of both the limb radiances and ozone ACDs, it appears as if the formula for calculating the limb elevation angle given by equation (3.1) may not be sufficiently accurate. This necessitates calibration of the elevation angle using the limb radiances. Starting with equation (3.1) and adding a term for refraction, as discussed in Section 4.7, as well as a constant offset correction term, the absolute elevation angle is^11.1,

$${\rm EA}=4.1^{\circ} - 1.5^{\circ} \cos10^{\circ} \cdot {\rm STEP} - {\rm ROLL} + r({\rm EA}) + \Delta{\rm EA}$$ (11.34)

where r is the refraction term and $\Delta{\rm EA}$ is the correction term to be determined in the calibration process. Initially, the assumption is made that $\Delta{\rm EA}$ is a constant for all scan steps such that limb elevation angles given by equation (3.1) are correct relative to each other, refraction notwithstanding (McElroy, personal communication, 1998).

The elevation angle calibration process makes use of forward model calculations. Essentially, measured radiances are shifted until they are aligned with the model radiances and the shift in EA at which this occurs is $\Delta{\rm EA}$. The limb radiances used in the calibration are taken from 21 September 1997, the Fairbanks to Hawaii transit flight. Three successive scans are used from 2248 UTC (35.8$^{\circ }$N, 155.0$^{\circ }$W) to 2355 UTC (28.2$^{\circ }$N, 155.5$^{\circ }$W) at a 5 nm integrated band centered at 747.5 nm. Three scans are used to reduce the impact of random errors associated with the measurements. These scans were chosen as both the CPFM-derived and TOMS-derived albedo were less than 0.2 throughout the scans which suggests little or no cloud cover. In addition, the SZA angle varied by only 1.4$^{\circ }$ and the ER-2 altitude by 0.4 km over the course of the scans.

 

 

For purposes of calibration, the model elevation angles will be adjusted as opposed to those of the measurements (which will be the normal procedure). The results of the calibration are shown in Figure 6.26. Radiances from the individual scans are consistent with each other indicating that atmospheric conditions have changed very little throughout these scans. The shift required to align the measurements was $\Delta {\rm EA}=+3.8^{\circ}$. Also shown in Figure 6.26 are the model radiances at the unrefracted elevation angles, although it was hard to differentiate as the largest refraction correction was about 0.2$^{\circ }$. In practice, the calibration was done by first interpolating the model radiances (calculated at 1$^{\circ }$ increments) to the elevation angles of the measurements, shifted by a specified amount. The RMS-difference was computed and the amount of the shift was varied in 0.1$^{\circ }$ increments until a minimum was reached. Several values of total aerosol optical depth were used as this will impact both the magnitude and the curvature of the limb radiances. Also varied was the surface albedo. An aerosol optical depth of 0.015 and an albedo of 0.1 were found to give the best agreement.

To assess how sensitive the calibration is to aerosol optical depth, the limb-viewing angle was calibrated for optical depths of 0.01 and 0.02. The results are shown in Figure 6.27. To calibrate to the 0.02 optical depth case, an additional shift of 0.5$^{\circ }$ was required while calibration to the 0.01 optical depth case required a 0.5$^{\circ }$ shift decrease, relative to that for the optimal 0.015 case. However, by observing the dashed lines in Figure 6.27, neither is able to capture the curvature of the measured radiances. This is the reason that the RMS-difference was a minimum for the 0.015 optical depth case.

As the difference in $\Delta{\rm EA}$ is large (0.5$^{\circ }$ between aerosol optical depths of 0.01 and 0.015 and between 0.015 and 0.02; recall refraction corrections were no larger than 0.2$^{\circ }$), the correct aerosol profile must be used to properly calibrate the limb-viewing angle. One important question which needs to be addressed in future work is can two markedly different aerosol profiles and hence different values of $\Delta{\rm EA}$ give comparable minimum least-squares differences? If the only aerosol profile variable in question were the total optical depth, the answer would be no. However, shape of the profile and altitude of the peak, for example, are variables that have not been examined but will also impact the calibration. From Chapter 5, it appears that three or four pieces of profile information are available from the limb radiances. It should be possible to substitute one of these pieces for $\Delta{\rm EA}$. That is, retrieve a, b, c, and $\Delta{\rm EA}$ together (where a, b, and c are fitting coefficients as discussed in Section 5.4).