Information Content at Different Wavelengths

 

A standard aerosol profile will be used to carry out the sensitivity study. The number density profile is given in Figure 5.1. It is a composite from a number of different sources (McCormick et al., 1996; Kent et al., 1995) and represents typical background stratospheric number densities at mid-latitudes. While more variable, the tropospheric component (0-10 km) is also representative of background conditions (Kent et al., 1995). Note that from 30-100 km, the aerosol profile decreases exponentially with altitude. Russell et al. (1996) showed that under most circumstances, stratospheric aerosol size distributions can be represented using a single mode. Thus, the log-normal size distribution is used with $r_{\rm eff}=0.2~\mu$m (Rosen and Hoffman, 1986) and $v_{\rm eff}=0.17$ (Kent et al., 1995). The sulphate aerosol refractive index is for a composition of 0.25H₂O+0.75H₂SO₄ (Palmer and Williams, 1975).

The geometry used simulates that of the CPFM flying on the ER-2. Limb radiance and linear polarization will be calculated at 20 km for elevation angles (EAs) of $+15^{\circ}$ to $-15^{\circ}$ in 1$^{\circ }$ increments. This range of EAs is about twice that of the CPFM limb scan and it is used to ascertain if there is any additional information which might be retrieved if the current scan configuration were altered. The solar zenith angle is taken as 30$^{\circ }$ and the change in azimuth as 280$^{\circ }$. A surface albedo of 0.3 is used.

It will prove useful to examine the information content at different wavelengths. As the motivation for this analysis is its application towards the retrieval of aerosol properties from CPFM limb radiances, only wavelengths between 300 and 770 nm will be considered. Furthermore, wavelengths at which significant gaseous absorption occurs will be avoided. These include ozone from 300-335 nm and 480-680 nm and NO₂ from 400-460 nm. There are also some O₂ absorption bands centred at 760 nm. As a result, three wavelengths are selected: 340, 475 and 750 nm. Properties of the standard aerosol profile at these wavelengths are given in Table 5.1.

 

Table 5.1: Optical properties of the standard aerosol profile. (Subscript M refers to Mie quantities; n_r is the real component of the refractive index.)

 

Wavelength	$\sigma_M$	$\tau_M$	ke,M(20 km)	nr
(nm)	$(\times 10^{-9}$ cm2)		( $\times 10^{-3}$ km-1)
340	2.37	0.044	1.30	1.462
475	1.61	0.030	0.88	1.432
750	0.70	0.013	0.38	1.427

  

Figure 5.2: Ratio of Mie scattering extinction to total scattering extinction using equation (5.2).

The contribution of Mie to total scattering is obtained through the calculation of,

$$\frac{k_{e,M}(z)}{k_{e,M}(z)+k_{e,R}(z)}$$ (9.3)

where the subscripts M and R denote Mie and Rayleigh, respectively. This ratio is shown as a function of wavelength and altitude in Figure 5.2 using the standard aerosol model. From 300 to 800 nm the Mie cross-section decreases by a factor of four but the Rayleigh cross-section, due to the $\lambda^{-4}$ dependence, decreases by a factor of 50. Hence, at all heights the relative contribution of Mie scattering steadily increases with wavelength. The height in which this ratio is a maximum is 20 km. From this simple analysis, longer wavelengths would appear to contain more aerosol information.

A more diagnostic quantity is the physical location of unit optical depth from the instrument along the line of sight. Any light arriving at the instrument from beyond this point will have been attenuated by at least a factor of e¹. Hence, the majority of the signal will originate from photons scattered into the line of sight inside of this distance. For an instrument at 20 km, the height range over which the slant optical depth reaches unity, $\tau_s=1$, and hence the height range which contains aerosol information, was determined. These ranges are given in Table 5.2 for wavelengths of 340, 475, and 750 nm at selected EAs. At 750 nm, light from all layers reaches the instrument between ${\rm EA}=-5^{\circ}$ to ${\rm EA}=0$, well within the range used in a CPFM scan, and so aerosol throughout the atmosphere is sensed. At 475 nm a range of $-11^{\circ}$ to $+1^{\circ}$ is required while at 340 nm the heights below 11 km cannot be sensed. Also at 340 nm, $\tau_s=1$ is reached well within the aerosol layer for ${\rm EA}\leq2^{\circ}$. In one sense, the increase in Rayleigh scattering at shorter wavelengths is useful as it eliminates the signature from aerosols that are spatially far removed from the instrument. On the other hand, the trade off is that only 10-20% of the signal is due to Mie scattering. Ideally, information at these different wavelengths would be combined. For example, a coarse profile through much of the stratosphere could be obtained first at 750 nm, where the aerosol signal is the largest. Using this as a constraint, higher vertical resolution may be achieved using shorter wavelengths where the aerosol signal is smaller, but more localized.

It is expected that only limited vertical information, at least when using a single wavelength, can be obtained above the aircraft for a number of reasons. All uplooking angles have the largest pathlength through the layers immediately above the aircraft which means that their information content is similar. In addition, above 20-25 km (20 km in the case of the model profile), the aerosol number density falls off rapidly with altitude.

 

Table 5.2: Altitude ranges which contain slant optical depth less than unity for model observations made at 20 km.

 

Elevation Angle	Altitude range (in km) for:
(deg.)	340 nm	475 nm	750 nm
15	20.0-TOA	20.0-TOA	20.0-TOA
3	20.0-TOA	20.0-TOA	20.0-TOA
2	20.0-31.6	20.0-TOA	20.0-TOA
1	20.0-24.5	20.0-TOA	20.0-TOA
0	20.0-21.3	20.0-TOA	20.0-TOA
-1	19.0-20.0a	19.0-21.9b	19.0-TOAb
-2	17.4-20.0	16.1-20.0a	16.1-TOAb
-3	16.0-20.0	12.7-20.0	11.2-20.0a
-4	14.9-20.0	10.2-20.0	4.1-20.0a
-5	13.8-20.0	8.3-20.0	0.0-20.0
-6	12.9-20.0	6.6-20.0	0.0-20.0
-8	11.4-20.0	4.0-20.0	0.0-20.0
-10	10.2-20.0	1.9-20.0	0.0-20.0
-12	9.1-20.0	0.1-20.0	0.0-20.0
-15	7.7-20.0	0.0-20.0	0.0-20.0

TOA = Top of atmosphere
^a $\tau_s=1$ extends past tangent point
^b $\tau_s=1$ extends past tangent point and into layers above 20 km

Limb radiance and polarization are shown in Figure 5.3 at 340, 475 and 750 nm as a function of scattering order. At all wavelengths, the radiance is seen to increase and the polarization decrease with the number of scattering orders used. The reason for the latter is the depolarizing effects of multiple-scattering. All radiances are also observed to increase with decreasing EA as the thicker part of the atmosphere is sensed. At all wavelengths the radiance increases nearly exponentially until $\tau_s=1$ is reached, after which a `knee' or change in concavity in the radiance curve is evident. Below this, the radiance may increase or decrease slightly depending on how the phase function changes, although this will be washed out by multiple-scattering. Any further increases in slant optical depth serve only to decrease the average distance between the instrument and where the light was scattered into the line of sight. Below ${\rm EA}=-4.5^{\circ}$ the radiance is roughly constant at all wavelengths, although the reason for this is different at each: at 475 and 750 nm, the direct surface component is such that it matches the additional scattered component just above ${\rm EA}=4.5^{\circ}$ and will not be the case in general. At 340 nm, there is no significant direct surface component and the radiance is constant for $\tau_s>1$.

The shape of the polarization curves can be understood by considering the fractions of Mie and Rayleigh scattering contributing to the signal. The polarization is observed to increase with decreasing wavelength as Rayleigh scattering becomes more important. This is also the reason for increasing polarization with decreasing wavelength. The main polarization feature present at 750 nm is a sharp increase near EA $=-2^{\circ}$. This arises at approximately this angle since the heights bracketing $\tau_s=1$ ( $\sim 16-20$ km) contain the portion of the aerosol profile which is approximately constant. However, polarizing Rayleigh scattering continues to increase exponentially with decreasing height which leads to a rapid increase in polarization. This can also be observed by examining Figure 5.2 which shows the fraction of Rayleigh scattering increases with decreasing height. The sudden decrease below EA $=-4^{\circ}$ in Figure 5.3c is due to the addition of the direct surface component. Recall from section 2.7.2 that it was assumed that surface-reflected light is completely depolarized. At 340 nm, neither of these features is present due to the proximity of $\tau_s=1$ to the observation point, while at 475 nm, both features are present although much less pronounced.

 

From Figure 5.3 it can be seen that the number of scattering orders required for convergence is 2-3 at 750 nm, 3-4 at 475 nm, and 8-9 at 340 nm. The fact that only two orders are required at 750 nm indicates that many of the single-scattering features should be present, at least in a qualitative sense, in the multiple-scattered field and can possibly be exploited in extracting aerosol information. In addition, most of the increase between one and two orders of scattering at 750 nm is the result of single-scattered, surface-reflected light. In the formulation of the solution of the radiative transfer equation, only the direct surface component is considered single-scattered. The single-scattering angle, $\Theta_{\rm ss}$, expressed in terms of the elevation angle is,

$$\cos \Theta_{\rm ss} = \mu_o \sin(\rm {EA}) + (1-\mu_o^2)^{1/2} \cos(\rm {EA}) \cos(\phi-\phi_o),$$ (9.4)

and for the geometry used, $\Theta_{\rm ss}$ ranges from 72$^{\circ }$ for EA $=15^{\circ}$ to 98$^{\circ }$ for EA $=-15^{\circ}$.