Sensitivity to Aerosol Vertical Inhomogeneities

Finally, the effects of an inhomogeneous aerosol mass are examined. It has been assumed thus far that a single size distribution is appropriate. In fact, this is likely to be the exception and not the rule. Aerosol size and refractive index are both functions of altitude as both the water vapour mixing ratio and fallout size decrease with height. Based on the results of Yue et al. (1994), four profiles of varying effective radiance are defined. From the results of the previous section, a variable refractive index will likely have negligible effects. Instead of performing Mie calculations for different aerosols at each height, two aerosol types are used: one which is representative of aerosol near the tropopause and one which is representative of aerosol in the middle and upper stratosphere. The four profiles are based on linear combinations of the two types of aerosol which have individual number densities profiles, N₁(z) and N₂(z), such that their total is equal to that of the standard profile,

N₁(z) = f(z) N(z) (9.5)

N₂(z) = [1-f(z)] N(z) (9.6)

where,

$$f(z)= \left\{ \begin{array}{lcrcl} 0 && 30~{\rm km} < & z & \... ...~{\rm km} \\ 1 && & z & < 10~{\rm km} \\ \end{array} \right.$$ (9.7)

and z is in km. Hence the transition is linear between the two types of aerosol between 10 and 30 km. At 20 km, N₁=N₂.

 

Table 5.4: Summary of the four inhomogeneous aerosol scenarios. Subscript 1 refers to upper stratospheric properties and 2 to lower stratospheric and tropopause region properties.

Scenario	$r_{{\rm eff},1}$ ($\mu$m)	$r_{{\rm eff},2}$ ($\mu$)
A	0.10	0.20
B	0.10	0.30
C	0.15	0.25
D	0.20	0.30

 

Results are shown in Figure 5.13 using four variable aerosol types summarized in Table 5.4. The `1' subscript aerosols represent middle and upper stratospheric aerosols while the `2' subscript aerosols are representative of lower stratosphere and tropopause region. Clearly the effect on radiances was small overall, particularly for scenarios C and D. The effects on polarization was more pronounced. Both A and B, which both used 0.10 $\mu$m for the upper stratospheric aerosol, produced polarizations larger by 0.03-0.06. The other two cases, C and D, which used larger upper stratospheric aerosol, deviated from the homogeneous case by no more than 0.02. For most of the scan, ${\rm EA}=0-15^{\circ}$, the homogeneous case resembles scenario D to about 0.01, a value which is quite constant. It appears that using a homogeneous profile with $r_{\rm eff}=0.21~\mu$m would match scenario D exactly. Thus for uplooking angles, the retrieved effective radius will be indicative of that at 25-30 km. Near the horizon, the homogeneous case matches scenario C exactly. Near ${\rm EA}=-3^{\circ}$ all four scenarios converge rapidly which is due to the rapid increase in the relative contribution from Rayleigh scattering. This also suggests that there is very little aerosol information available at EAs below this.

Note that by using this combination of two profiles it is difficult to make a true comparison as this effectively constitutes a bi-modal distribution. However, the general conclusion should still be valid.