Differential Optical Absorption Spectroscopy

Differential Optical Absorption Spectroscopy (DOAS) is the process whereby column abundances of trace-species are derived from measurements of electromagnetic radiation in a specified spectral interval. Spectroscopic NO₂ measurements were made as early as 1973 (Brewer et al., 1973). DOAS as is currently applied to the atmospheric sciences was pioneered by Noxon (1975) in the mid-1970s and later by Platt et al. (1979, 1980). With the advent of the photodiode array detector and the charge-coupled device (CCD) array detector, which allows the simultaneous measurement of many wavelengths, the use of DOAS has greatly expanded. The main advantage of this technique over others is that it allows real-time measurements of several different trace-gas species with a single instrument (Platt and Perner, 1983). Discussion of optimal DOAS instrument design characteristics can be found in Plane and Nien (1992). Recently, improvements have been suggested in the form of a combined lidar-DOAS system which uses a broadband source and has the advantage of much improved vertical resolution (e.g.: Strong and Jones, 1995).

To perform DOAS, two spectra are necessary: one, referred to as the reference, in which the light has passed through little (ideally none) of the absorber in question and one in which the light has passed though a large amount of the absorber. The retrieved DOAS quantity is the apparent column density (ACD). When the instrument is pointed towards the sun the measured signal comes from direct sunlight. In this case the physical interpretation of the ACD is relatively straightforward: it represents the difference in the column density of the absorber between that along the line-of-sight and that in the reference. Often, however, the viewing direction is away from the sun and so the the source of the measured signal is scattered light. The ACD no longer has a clear physical interpretation as the path of the light through the atmosphere is complex and the measured sunlight may have been scattered in the atmosphere or reflected by the surface several times. Despite this complication, the ACD still represents the difference in absorber column density in the viewing direction and that in the reference.

The most common DOAS geometry is a ground-based instrument pointed at the zenith sky. The effective path along which the light travels is determined primarily by the solar zenith angle. As the sun rises or sets the pathlength will change by an order of magnitude. The reference spectrum is obtained in the afternoon for solar zenith angles less than 80$^{\circ }$ and the retrieval is performed on spectra obtained at larger solar zenith angles, typically 88-95$^{\circ }$. For the zenith-sky geometry, care must be taken when obtaining ACDs of species which possess a large diurnal variation, such as NO₂.

Another geometry for which DOAS is used is nadir. An example of this is the Global Ozone Measurement Experiment (GOME) on the ERS-2 satellite (Munro et al., 1998). GOME uses an extraterrestrial solar spectrum, obtained with the GOME instrument, as a reference. In the nadir, apparent pathlength enhancements are not as large, which will reduce the signal-to-noise ratio and the vertical resolution is reduced due to the increased width of the weighting functions. The main advantage in using nadir geometry is that better horizontal resolution can be achieved.

The third type of DOAS geometry is the limb scan, an early example of which was the Solar Mesosphere Explorer (SMR) launched in 1981 to measure ozone, NO₂ and water vapour in the upper stratosphere and lower mesosphere (Houghton et al., 1984). The Optical Spectrograph and Infra-Red Imaging System (OSIRIS) instrument on the Odin satellite, scheduled for launch in spring 1999, will also use the limb scanning technique. By scanning the limb of the atmosphere different height regimes are sampled. The reference used by OSIRIS is the 70 or 80 km tangent height radiance where there is little atmosphere. By measuring through the limb, large path enhancements and good vertical resolution is obtained. The trade-off is poor horizontal resolution which makes inversion problematic if there are large gradients along the path. One potential problem for this geometry is the contamination of the reference by surface reflection and multiple scattering in the lower atmosphere. As light from the surface, scattered into OSIRIS's line-of-sight at 80 km, will have passed through the layer of absorbers twice, it will contain an artificially large amount of absorber.

 

The geometries relevant to this study are the nadir and limb scan, those produced by the CPFM. The two geometries are shown schematically in Figure 6.2. The contribution to the pathlength from the direct solar beam will be approximately the same, the measurement made in the limb will clearly have a much larger pathlength than the measurements made in the nadir. The reference spectrum is taken as the horizontal flux, also indicated for the two geometries in Figure 6.2. At 20 km, this is almost entirely composed of the direct solar beam so contamination by surface reflection and multiple scattering is not a problem. The general DOAS procedure is outlined below.

Let the limb, nadir, or zenith-sky radiance be $I(\lambda)$ and the reference spectra be $I_{\rm {ref}}(\lambda)$. Assuming that each can be expressed in terms of the Beer-Lambert law,

$$I(\lambda) \exp{ \left[ - \sum_{l=1}^{N_l} \sigma_l(\lambda) c_l \right] }$$ = (11.1)

$$I_{{\rm ref}}(\lambda) \exp{ \left[ - \sum_{l=1}^{N_l} \sigma_l(\lambda) c_{{\rm ref},l} \right] }$$ = (11.2)

where the sum is over all species absorbing at wavelength $\lambda$, $\sigma_l$ is the absorbing cross-section of species l, c_l is the ACD, and $c_{{\rm ref},l}$ is the ACD in the reference. Taking the logarithm of the ratio,

$$D(\lambda) = \ln{ \left[ \frac{I_{\rm {ref}}(\lambda)}{I_i(\l... ... } = \sum_{l=1}^{N_l} \sigma_l(\lambda) (c_l-c_{{\rm ref},l})$$ (11.3)

where $D(\lambda)$ is identified as the optical depth. The DOAS retrieved quantities are the ACD differences, $c_l-c_{{\rm ref},l}$. The main advantage of using a relative spectrum instead of an absolute spectrum is that the Fraunhoffer structure from the extra-terrestrial solar spectrum is removed. To eliminate the influence of Rayleigh and Mie scattering, $D_i(\lambda)$ is separated into high and low frequency components. In this study, a second-order polynomial is fitted to $D(\lambda)$ and then subtracted from it which gives the differential optical depth, $D'(\lambda)$. A second order polynomial is used to ensure that much of the curvature, due to Rayleigh scattering, Mie scattering, or a low-frequency trend in the absorption cross-sections, in $D(\lambda)$ is removed. The absorption cross-sections are filtered in an analogous manner which produces the differential cross-sections, $\sigma_l'(\lambda)$. The differential optical depth is the high frequency component of the optical depth and it is attributed to molecular absorption. It is equated to the high frequency component of the cross-sections as follow,

$$D'(\lambda) = \sum_{l=1}^{N_l} \sigma'_l(\lambda) (c_l-c_{{\rm ref},l}).$$ (11.4)

The differential cross-sections for ozone in the visible and BrO in the UV are shown in Figure 6.3.

  

Figure 6.3: Differential absorption cross-sections for (a) ozone in the Chappuis bands and (b) BrO.

 

Table 6.1: Species, and their spectral regions, which may be retrieved using differential optical absorption spectroscopy. Also given is the reference for the cross-sections used in this study.

Species	Wavelength	cross-section
	Region (nm)	Reference
O3	315-345	Burrows et al. (1997b)
	450-600	Burrows et al. (1997b)
NO2	390-490	Burrows et al. (1997a)
BrO	340-380	Wahner et al. (1988)
OClO	350-390	Wahner et al. (1987)
H2O	500-600	Sarkissian (1992)
O4	320-550	Greenblatt et al. (1990)

A linear least-squares fit is performed to recover the column density differences, $\Delta c_l=c_l-c_{{\rm ref},l}$. This is done by determining the $\Delta c_l$'s which minimize,

$$\varepsilon(\Delta c_1,\ldots ,\Delta c_{N_l}) = \sum_i^{N_{\... ...bda_i) - \sum_{l=1}^{N_l} \Delta c_l \sigma'_l(\lambda_i) \}^2$$ (11.5)

where $N_{\lambda}$ is the number of wavelengths used in the fit. In general, a spectral interval of at least 15 nm is required at 1 nm resolution or better. The following species are included in the least squares fit: O₃, NO₂, BrO, OClO, H₂O, O₄, and Ring. The Ring effect, discussed in section 6.2.1, arises from inelastic Raman scattering and can be treated, at least in an approximate manner, as an absorbing species. Other species which may be necessary to include in the fit are: ClO, HONO, SO₂, HCHO, or NO₃. The species O₄ is a short lived collision dimer of O₂. Its cross-section is proportional to the O₂ number density and it possesses relatively broad absorption features from 330-1140 nm. As O₂ is well mixed below 120 km, the magnitude of the ACD of O₄ retrieved can be used to infer information about origin of the measured signal. Larger columns imply the signal originated from lower altitudes where the density is greater; smaller columns from higher altitudes. Due to the rapid variation of O₄ cross-section with pressure it is difficult to retrieve an absolute ACD value and usually only relative cross-sections are used. A table of the absorbing species, the spectral regions where they can be fitted, and the reference for the absorption cross-sections are given in Table 6.1. Note that ozone has two regions where it can be retrieved: the Hartley-Huggins bands in the UV and the Chappuis bands in the visible. Due to the larger optical thicknesses in the UV, the two regions may not give the same value of ACD.

One quantity which can be used to assess the quality of the DOAS fit is the fit residual, $R(\lambda)$, defined as the difference between the measured and fitted differential optical depth,

$$R(\lambda) = D'(\lambda) - \sum_{l=1}^{N_l} \Delta c_l \sigma'_l(\lambda).$$ (11.6)

If the magnitude of the residual compared to that of the differential optical depth is very small, this is an indication of good signal-to-noise ratio and the differential cross-sections used form a suitable basis for the least-squares fit. The residual is also useful in diagnosing problems. For example, if the residual resembles the absorption spectrum of a species not included in the fit, it indicates that that this species is present in large enough quantities that it should be included. Similarly, if the residual resembles the absorption spectrum of an absorber which is included in the fit, this may suggest it is at the wrong temperature or a slight wavelength shift relative to the measured spectra. Further, if the residual contains rapidly varying structure near the edges of an absorption band (i.e. reminiscent of the derivative of a delta-function) this may indicate that there is a wavelength shift in the cross-sections or reference spectrum (or both) relative to the DOAS spectrum.

Also useful is the root-mean-square (RMS) of the residual, where the averaging is done over many DOAS fits at each wavelength. The RMS of the residual can be used to evaluate the performance of the DOAS fitting over a portion of a flight, an entire flight, or many flights. This also gives an indication of any systematic problems such as bad pixels in the detector array.

Another measure the quality of the least-squares fit is the coefficient of multiple determination, r², and r is defined as the multiple correlation coefficient. It is closely related to the standard deviation but takes on values between 0 and 1. Values of r² close to unity are indicative of good fits. It is defined as (e.g.: Devore, 1987),

$${\rm r}^2 = 1 - \frac{\sum_i^{N_{\lambda}} \{ D'(\lambda_i) -... ...N_{\lambda}} \sum_l^{N_l} \Delta c_l \sigma'_l(\lambda_i)]^2}.$$ (11.7)

The multiple correlation coefficient describes the fraction of total variation explained by the multiple regression. This quantity is useful in quantifying the quality of a fit using a single number, but cannot be used to diagnose where problems with the fit might exist. In general, least-squares fits which produced a value of r² less than 0.8 were not used as this indicated a poor overall fit.

 

An example of the various stages of the DOAS process, in this case for the retrieval of ozone from the limb using the Chappuis bands, is illustrated in Figure 6.4. Panel (a) shows the two original spectra used in the fit (in arbitrary units). In panel (b), the optical depth and its second-order, polynomial fit are presented while panel (c) shows the difference of the two curves in (b), the differential optical depth, along with the DOAS fit. The value of the multiple correlation coefficient, r²=0.99, indicates a good fit. In this example, the ozone ACD contained 4340 DU. A review of the corrections and general considerations for zenith-sky DOAS retrievals, most of which are also relevant to nadir and limb DOAS, is given by Platt et al. (1997). It includes scattering due to tropospheric and stratospheric clouds, chemical enhancements, and measurements across boundaries of air parcels. A method of estimating the error of the derived concentrations based on the uncertainty of the wavelength-pixel mapping and the influence of random residual structures has been developed by Stutz and Platt (1996).