CPFM-Derived Quantities

Due to the wide range of fields and wavelengths measured, a large number of geophysical quantities are potential candidates for retrieval. These are listed below along with the fields used in their retrieval:

1.

Photodissociation rates (limb, nadir, and horizontal flux)

2.

Column O₃ above the aircraft (horizontal flux)

3.

Apparent surface albedo (nadir and horizontal flux)

4.

Aerosol vertical profiles and size information (limb radiance and polarization)

5.

Vertical column densities of O₃, NO₂, and BrO above and below the ER-2 (nadir and horizontal flux)

6.

Vertical profile (three or four heights) of O₃ between the surface and the ER-2 (limb and horizontal flux)

7.

Polarization of surface-reflected radiance (nadir radiance, polarization and horizontal flux)

Photodissociation rates, or J-values (see section 2.3.2), are currently the primary data product. Prior to the inclusion of the CPFM on the ER-2, radiative transfer models were the only means available to calculate J-values along the ER-2 flight track. Typically, there can be large uncertainties associated with some input model parameters such as surface albedo and ozone column density. Through direct measurement of the radiation field, J-values can be calculated which better represent the local conditions. This is very advantageous, for example, for chemical modeling along the flight track. Similarly, the calculated J-values can be used in the validation of existing radiative transfer models. McElroy (1995) has shown that by using a combination of the measured nadir radiance, limb radiance, and horizontal flux, it is possible to obtain a proxy for the mean radiance at aircraft height. The total mean radiance, F_tot, at a given wavelength is the sum over contributions from the different fields,

F_tot = F_l + F_n + F_d (5.4)

where F_l, F_n, and F_d, are the mean radiance components from the limb, nadir, and direct solar components, respectively. Each of these can be expressed in terms of measured fields. To obtain their contribution to the total mean radiance, the limb and nadir radiances are multiplied by the solid angle over which they are representative. The lower hemisphere is divided up equally between the two, such that $\Delta\Omega_n=\Delta\Omega_l=\pi$. As long as the sun is high in the sky, the direct solar component can be obtained from the horizontal flux by dividing it by $\cos{\theta_o}$ after the cosine correction factor has been applied. Thus, the total mean radiance can be expressed as,

$$F_{tot} = \Delta\Omega_l \, I_l + \Delta\Omega_n \, I_n + E_d \sec{\theta_o}$$ (5.5)

where I_l and I_n are the measured limb and nadir radiances, respectively, and E_d is the measured horizontal flux. The value used for I_l is the largest in the scan.

Currently, only J-values for the following reactions are calculated,

$$\rm NO_2 + h\nu \rightarrow \rm NO + O$$ (5.6)

$$\rm O_3 + h\nu \rightarrow \rm O_2 + O(^1 D)$$ (5.7)

but in principle J-values for any species which photolyzes in the 300-770 nm spectral region can be determined. Potential candidates include NO₃, HNO₃, H₂O₂, N₂O₅, HOCl, HOBr, ClONO₂, and HO₂NO₂ to list a few. J-values along the ER-2 flight track are shown in Figure 3.6 for one flight from the ASHOE/MAESA campaign and one from the STRAT campaign.

  

Figure 3.6: J-values along the ER-2 flight track for photolysis of (a) NO₂ and (b) ${\rm O}_3 \rightarrow {\rm O(^1D)}$ for flights made on March 18, 1994 and November 5, 1995. Time refers to elapsed time after take-off.

Another data product currently available is the column amount of ozone above the aircraft. A column density or abundance describes the number of molecules between two altitudes above a unit area. Typical units are molecules$\cdot$cm^-2 except for ozone which is given in terms of Dobson Units (DU). The conversion factor is 1 DU $=2.69\times10^{16}$ molecules$\cdot$cm^-2. Column ozone is calculated using the Brewer method applied to CPFM spectral data (McElroy et al., 1998). The Brewer spectrophotometer, and its predecessor, the Dobson spectrophotometer (Dobson, 1957), are the standard instruments for measuring column ozone. They are typically ground-based and measure the solar irradiance between 290-325 nm. There are in excess of 100 stations worldwide, some with ozone time-series dating back more than 30 years. These instruments have made a significant contribution to our current understanding of the ozone distribution and chemistry.

At typical ER-2 altitudes the horizontal flux has a negligible scattered light component. As a result, the Beer-Lambert law for exponential attenuation can be applied to the direct solar beam incident on the horizontal diffuser,

$$E_d(\lambda) = \pi F_o(\lambda) \cos{\theta_o} \exp \left[ -\sec\theta_o \sum_l^{N_l} \tau_l(\lambda) \right]$$ (5.8)

where $\tau_l$ are the optical depths of the absorbers and scatterers. To solve for N_l unknowns, including ozone and excluding Rayleigh which can be calculated directly, N_l+1 wavelengths are required. This is necessary as it is advantageous to use relative irradiances as opposed to absolute to reduce the uncertainties. Other unknowns might include aerosols and SO₂.

 

A sample of column ozone measurements along the ER-2 flight track are given in Figure 3.7. Comparisons with TOMS (Total Ozone Mapping Spectrometer) data, using a climatological profile from SAGE (Stratospheric Aerosol and Gas Experiment) and ozonesonde data to account for ozone below the aircraft, are in good agreement with CPFM column ozone on most flights.

CPFM measurements have also been applied in the calculation of effective surface albedo,

$$\Lambda_{\rm eff} = \frac{\pi I_n}{E_d}.$$ (5.9)

This simple ratio results in the effective albedo of an imaginary surface immediately below the aircraft. This is done for integrated bands centred at 308, 350, 450, and 600 nm. Towards longer wavelengths this approaches the actual surface albedo as long as clouds are not present. At shorter wavelengths, the effective albedo will be artificially enhanced over the true albedo due to a significant contribution from molecular and aerosol scattering below the aircraft.

As one aspect of the research leading up to this dissertation, in part to test the radiative transfer code described in Chapter 4, an attempt was made to calculate the actual surface albedo by accounting for the effects of scattering and absorption below the aircraft. The specific goal was to estimate the wavelength-dependent ocean albedo during clear-skies while also accounting for the non-Lambertian nature of the ocean surface. Using the measured nadir and horizontal flux fields, along with some model calculated quantities, albedo can be estimated directly. This research resulted in an article published in the Journal of Geophysical Research, a copy of which is given in Appendix A.

Items four through six, listed above (see page 49) as potential retrievable quantities, are the main focus of this dissertation. Retrieval of aerosol information will make use of the both total radiance and polarization. The latter is particularly useful as light scattered by aerosols possess unique polarization features. Retrieval of trace-gas, vertical profiles will be done using spectroscopic methods by taking advantage of the well-defined spectral structure of each absorber. Item seven has not been addressed in this work but would be a worthwhile undertaking in the future as little is known about the (de)polarizing properties of different surfaces. For modeling purposes, it is usually assumed that all surfaces are completely depolarizing.