Normalization Tangent Altitude

Both the detector noise and the stray light contamination are relatively small com-ponents of the total signal at lower altitudes near the aerosol layer, i.e. below 30 km tangent altitude. However, the upper altitude normalization of the radiance profiles required for the construction of the measurement vector, Equation 5.2, is critical for the retrieval; it eliminates the need for an absolute calibration and provides some insensitivity to uncertainty in the atmospheric neutral density and the albedo. The aerosol number density retrieval algorithm used with the OS measurements presented in previous chapter adopts a reference tangent altitude near 40 km. This point was chosen as it is well above the aerosol layer and the radiance can be reliably modelled without specific knowledge of the aerosol profile. However, if this convention is ap-plied to the IRI measurements, the stray light and detector noise at 40 km result in a non-physical scenario. This is illustrated with the two profiles shown in Figure 6.2.

The modelled profile is calculated for zero aerosol density at all altitudes. If a nor-malization tangent altitude of 40 km is used, the modelled radiance is too low for tangent altitudes between approximately 20 and 40 km. Because the 1530 nm kernel is strongly positive at all altitudes, each iteration of the inversion then attempts to decrease the aerosol density at these altitudes in order to improve the match between the modelled and measured radiances. However, the aerosol density is already zero at all altitudes. Obviously, the stray light contamination of the IRI measurement leads to an incorrect and non-physical interpretation of the radiance for the aerosol inver-sion. A similar effect occurs if there is significant detector noise in the measurement at the reference altitude. Even for retrievals using the OS measurements, which have a much higher signal to noise, the detector noise is the dominant term in the error analysis as shown in Section 5.5.

It is possible to choose the reference exposure at a much lower tangent altitude, one within the aerosol layer, but this is undesirable because the sensitivity of the measurement vector to the state parameter is zero at the reference point, and is small for nearby altitudes. In this work it has been found that a measurement in the altitude region between 25 and 35 km can be used for normalization of the IRI measurements. The solution is essentially a matter of finding a point that minimizes both the impact of the instrumental effects and of the decreased sensitivity to aerosol near the normalization altitude.

The altitude where the aerosol density becomes negligibly small depends on the geographic location. For example, stratospheric circulation patterns near equatorial latitudes loft aerosol particles to high altitudes creating a significant aerosol loading that sometimes extends up to almost 40 km; descent in the Brewer-Dobson circulation often results in a very clean stratosphere above 20 km at polar latitudes. The degree of stray light contamination also varies from scan to scan as it depends of the reflectivity of the scene below the instrument line of sight as well as the solar geometry. Thus, the normalization tangent altitude must be determined on a scan by scan basis by attempting to choose the highest tangent altitude possible to maximize sensitivity to the aerosol profile, and the lowest tangent altitude possible to minimize effects from stray light and detector noise. This is accomplished by using the model result for the clean atmosphere in combination with the knowledge that the 1530 nm Jacobian is strongly positive at all altitudes.

For any given scan, the IRI 1530 nm radiance profile and the corresponding model result for zero aerosol density are successively normalized to each exposure in the tangent altitude range from 20 to 40 km. The best reference exposure is chosen as the highest tangent altitude that results in a normalized measured profile that is larger than the normalized modelled profile at all tangent altitudes below the reference.

For most cases, this method ensures that the reference exposure is not significantly contaminated by stray light. It is possible that an aerosol enhancement at high

altitudes could be lost in the stray light signal. However, it is a fortunate coincidence of the OSIRIS sampling geometry that at equatorial latitudes, where high altitude aerosol is most probable, the stray light contamination is decreased because the solar zenith angle is always near 90 degrees; this effectively limits the upwelling radiation.

When this method is applied to the scan shown in Figure 6.2, the exposure at 28 km tangent altitude is chosen as the reference. Both the measured and modelled profiles are normalized to this point and it can be seen from the figure that 28 km is indeed a reasonable altitude for the normalization point. The enhancement in the measured radiance at the lowest altitude, which corresponds to aerosol scattering, is clearly apparent in the modelled result. Between 25 and 30 km where the aerosol density is negligibly small (see Figure 5.5) the two radiance profiles match very well.

Above 30 km, the measured signal begins to deviate from the model result due to stray light and detector noise as previously discussed.

6.4.3 Inversion

Using this same scan (06432019) as representative of a typical case, the aerosol den-sity was independently retrieved with the algorithm presented in Chapter 4 using λ_l=750 nm and using λ_l=1530 nm. In both cases, λ_s=470 nm is used as the short wavelength reference in the measurement vector ratio. The reference tangent alti-tude, which is the same for both retrievals, is derived from the IRI measurement at h_r=28 km as explained the previous section. A uniform height profile of particle size distribution with mode radius r_g=0.1 µm and mode width s_g=1.5 is assumed in both cases.

Detailed steps of the inversion are not presented here as the procedure is identical to that shown in Chapter 4. However, a brief summary is presented to demonstrate the applicability of the technique at both OS and IRI wavelengths. Figure 6.4 shows the measurement vector from OSIRIS for λ_l=750 nm and for λ_l=1530 nm. The mea-surement vectors for both retrievals constructed from the SASKTRAN forward model

0 1 2

Figure 6.4: The measurement vector using the IR measurements (λ_l=1530 nm) and using the spectrograph measurements (λ_l=750 nm) for OSIRIS scan 06432019. Mod-elled results after the retrieval, using uniform height profile of size distribution pa-rameters (r_g=0.1 µm, s_g=1.5), converge well in both cases.

radiances, before and after the inversion are included in this figure. The OSIRIS vec-tors for the two cases are significantly different in both shape and magnitude as there is a large difference in the limb scatter signal at the two wavelengths. While the for-ward model vector for the initial guess profile varies greatly from the OSIRIS vector, the inversion produces convergence in both cases demonstrated by the close match between elements of the retrieved result and the OSIRIS measurement.

As expected, due to the uncertainty in the assumed size distribution, each of the two inversions yields a different retrieved number density profile. These two profiles are shown in the left panel of Figure 6.5. While not drastically different, the two profiles vary by up to 50% at some altitudes and are not simply separated by a scale factor. Since the assumed size distribution profile is uniform in altitude, it is the shape of the actual size distribution profile that creates this altitude dependent difference between the two number density profiles.

0 20 40 60

Aerosol Number Density (cm⁻³)

Aerosol Extinction (10⁻³km⁻¹)

λl=750 nm λl=1530 nm

Figure 6.5: The retrieved aerosol density and extinction profiles for the assumed size distribution using λ_l=750 nm and λ_l=1530 nm for OSIRIS scan 06432019.

The determination of the particle size distribution parameters from these two retrievals requires the conversion of the result to the equivalent extinction. The scat-tering cross section that corresponds to the assumed size distribution is approximately an order of magnitude smaller at the IRI wavelength, i.e. 2.01 × 10⁻¹⁰cm² at 750 nm and 2.10 × 10⁻¹¹cm² at 1530 nm (see Figure 4.7). Since the assumed distribution is uniform in altitude, the resulting extinction at each wavelength, shown in the right panel of Figure 6.5, is simply a scaling of the retrieved number density by this cross section. These results may be considered a valid retrieval of the extinction in an absolute sense as long as the scattering phase function for the assumed particle size distribution is not significantly in error. As shown by the simulations in Section 5.4 and Figure 5.7, the error in the retrieved extinction at 750 nm is less than the uncer-tainty in the mode radius. For 1530 nm, the error should be smaller yet as there is little atmospheric multiple scattering.