Aerosol Retrieval Algorithm

Based on the results of the sensitivity study described above, an aerosol retrieval algorithm was developed. As a guide to which quantities may be retrieved, recall that in the visible the absolute uncertainty in the radiance is estimated at 10%. Similarly, the uncertainty in the polarization is estimated at 0.03. Again, quantities are deemed potentially retrievable if the radiance or polarization were observed to vary by at least these amounts over the expected range for this quantity. For example, polarization did not change by 0.03 over the range of refractive indices expected for stratospheric aerosols and so refractive index is not a good candidate for retrieval. Further, attention will be restricted to stratospheric aerosols and so only elevation angles which do not probe into the troposphere are considered. This excludes EAs below $-3.5^{\circ}$.

A summary of the sensitivity results is given in Table 5.5 where the degree to which a given parameter can be retrieved has been estimated. Both radiance and polarization were found to be sensitive to both the amount and the height of the aerosol number density, indicating that the retrieval of a vertical profile of the extinction coefficient is possible. When examining the size parameters, radiance was found to be largely insensitive while polarization was sensitive to the effective radius and effective variance (the latter only for $v_{\rm eff}<0.3$). This suggests polarization can be used to retrieve size information. Refractive index had a very small impact on radiance and moderate impact on polarization. Over the range expected in the stratosphere, 1.39-1.46, less than a 0.02 variation in polarization was found. This suggests that refractive index can not be retrieved to better than 0.07. Finally, neither radiance nor polarization can be used to determine the vertical variation of effective radius. The range in scaling factors used was fairly restrictive ($\pm40\%$) and in many cases the aerosol amounts exceed those of the standard background profile by factors of 2-5, such as after a recent volcanic eruption. Under these conditions, the Mie scattering signal should increase but it is difficult to determine by how much without further model calculations.

 

Table 5.5: Summary of sensitivity study indicating to what extent aerosol parameters may be retrieved by radiance and polarization. An `$\times$' indicates an insensitive quantity.

Aerosol Parameter	Radiance	Polarization
Profile
Thickness	10%	50%
Placement	2 km	4 km
Size Distribution
Effective Radius	$\times$	0.03 $\mu$ma
Effective Variance	$\times$	variable
Other
Refractive Index	$\times$	0.1
Vertical Inhomogeneities	$\times$	$\times$

^a For ideal geometry, 0.05 $\mu$m otherwise.

To simplify the retrieval process, it is broken down into two parts; extinction coefficient profiles and size distribution are determined separately. As radiance was observed to be sensitive to the amount of aerosol but less sensitive to the size parameters for a given optical depth, it is used to first determine the extinction coefficient profile. However, as only 6-8 steps in a scan will be used and with the information contained in each not independent of the others, it will not be possible to obtain a detailed profile. Despite this, the main characteristics can be captured by supplementing the information from the measurements with a priori knowledge. McCormick et al. (1996) has suggested that the stratospheric extinction coefficient profiles are well represented by,

$$\log{k_{e,M}}(\lambda,z) = a(\lambda) + b(\lambda) (z-z_t) + c(\lambda) (z-z_t)^2 + d(\lambda) (z-z_t)^3$$ (9.9)

where a, b, c, and d are fitting coefficients, z is the altitude and z_t is the altitude of the tropopause. The profile coefficients are determined by forcing the model radiances to match the measured radiances. This process is carried out at 750 nm which is the most sensitive to the variation in aerosol extinction.

Once the extinction coefficient profile is known, the polarization data can be used to obtain the effective radius and effective variance. Values of $r_{\rm eff}$ and $v_{\rm eff}$ are determined by varying them, using a log-normal size distribution, until the model polarization matches the measurements. Again a wavelength of 750 nm is used. As the limb radiance was not totally insensitive to the effective radius (maximum difference of 30% between 0.10 and 0.30 $\mu$m), the first step should be performed again using the estimated values of $r_{\rm eff}$ and $v_{\rm eff}$. If there is a substiantial change in the values of $a(\lambda)$- $d(\lambda)$, the second step should also be repeated. It is estimated that two iterations should be sufficient.

Once the size distribution is known, Mie cross-sections can be computed to obtain a number density profile,

$$N(z) = \frac{k_{e,M}(\lambda,z)}{\sigma_M(\lambda)}.$$ (9.10)

Comparisons can be made with two in-situ instruments also flown on the ER-2. The first is the ER-2 Condensation Nucleus Counter (CNC) II which counts particles with radii between 0.004 and 1 $\mu$m (Wilson et al., 1983). The second is the Focused Cavity Aerosol Spectrometer (FCAS) II which also detects particles over this same range (Jonsson et al., 1995). The FCAS II also measures aerosol surface area per unit volume and aerosol volume per unit volume. For comparison with retrieved aerosol densities at ER-2 height, the surface area and volume densities for the log-normal size distribution can be computed,

$$4 \pi \frac{r_{\rm {eff}}^2}{(1+v_{\rm {eff}})^3} N(z)$$ SA(z) = (9.11)

$$\frac{4 \pi}{3} \frac{r_{\rm {eff}}^3}{(1+v_{\rm {eff}})^3} N(z)$$ V(z) = (9.12)

where SA(z) is the log-normal surface area density and V(z) is the log-normal volume density. In addition, comparisons can be made against satellite extinction profiles, such as the 1.02 $\mu$m SAGE II channel. Once the number density profile is known, the extinction profile at any wavelength can be calculated.

This algorithm was applied to limb scans from two flights made as part of the POLARIS campaign. The algorithm and retrieved aerosol properties are described in an article entitled ``Observations of stratospheric aerosols using CPFM polarized limb radiances'' accepted for publication in the Journal of the Atmospheric Sciences in January 1998. A copy of this paper is given in Appendix C.