Simulations Using Synthetic Spectra

To ascertain what errors may arise from the assumptions made in the retrieval process, independent of noise and uncertainties in the measurements, synthetic radiances were generated using the radiative transfer model. From these, ACDs were then computed which were, in turn, used in the retrieval algorithm. These retrieved column abundances can then be compared against the model input absorber profiles used to generate the synthetic radiances.

 

Table 6.6: Percent difference between model input and retrieved column abundances for idealized synthetic spectra.

	Optimal	Percent Difference in Retrieved Quantity
Absorber	Recovery	Column	Column	0-12 km	12-16 km	16-20 km
	Wavelength	Above	Below	Layer	Layer	Layer
	(nm)
O3 (vis)	500	<1	1	15	6	4
NO2	440	<1	1	9	5	4
BrO	352	2	2	29a	11	4
O3 (uv)	328	4	3	35a	12	4

^a The column amount in this layer was taken as the difference between the total column below the aircraft and that recovered between 8-16 km and 16-20 km.

Tests were performed for O₃ (320-345 nm and 480-515 nm), NO₂ (420-460 nm) and BrO (345-360 nm) with the results summarized in Table 6.7. Model calculations were made using $\theta_o=60^{\circ}$, $\phi-\phi_o=280^{\circ}$, a surface albedo of 0.6, and background stratospheric sulphate aerosols. The column above the aircraft was recovered almost exactly in the visible (NO₂ and O₃) and with errors of 2-4% in the UV (O₃ and BrO). The small errors in the UV are likely due to the presence of a non-zero diffuse component in the downwelling irradiance at 20 km. While small, these photons will have traversed a much longer path than those in the direct component. The use of $\sec{\theta_o}$ is valid up to about 75$^{\circ }$, above which the path enhancement is no longer a simple geometric factor. As recovery of the column above the aircraft is absorption-DOAS (unlike the nadir and limb which are scattering-DOAS), the larger optical depths at shorter wavelengths do not pose any problems (above and beyond the small scattered component). The columns below the aircraft were recovered to within 1% in the visible and within 2-3% in the UV.

Larger errors are expected in the columns retrieved in the three layers between 0 and 20 km for reasons mentioned previously: the number density of each absorber varies through a given layer but the air mass factor is calculated assuming a constant profile. This was indeed the case. The 16-20 km layer was retrieved reasonable well with a 4% error. Errors up to 12% were found for the 8-16 km layer. In the visible, errors of up 15% were found for the 0-12 km layer, likely due to the decreased sensitivity and the small column amounts. They were much larger in the UV ($<50\%$) and it was found that a better column amount was obtained by taking the difference between the total column below the aircraft and subtracting from it the recovered 8-16 km and 16-20 km columns. It is interesting to note that NO₂ has the smallest errors. This may be due to the fact that the model NO₂ profile possessed a smaller vertical gradient than the O₃ profile.

There is also some question as to which wavelength to use for the calculation of the air mass factors as the DOAS ACDs are obtained using a range of wavelengths. The optimal recovery wavelength was found to be at the center of the fitting window, or slightly shortward of it. They are also listed in Table 6.7.

The results indicate that the retrieval method should be able to accurately recover the columns above and below the aircraft, and provide a reasonable value for the abundance immediately below the aircraft. A reasonable estimate of tropospheric columns may be obtained in the visible but in the UV, errors in of about 30% resulted. It should be mentioned that these results are idealized in the sense that no noise was added to the synthetic spectra and, as such, represent a `best case' scenario. The number of iterations required for convergence was 12-15.