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Next: Shift and Stretch Up: Differential Optical Absorption Spectroscopy Previous: Ring Effect

DOAS Spectral Fits

Figures 6.6-6.9 show the measured and fitted differential optical depths, the residuals, and the measured and fitted differential optical depths for each species, for four different fitting windows. These measurements were obtained from a flight made on 2 May 1997 at 21:42 UTC. A summary of the fitted ACDs are given in Table 6.2. These DOAS fits were made using the nadir field as the fitted ACDs are smaller than limb ACDs due to the smaller path enhancements. The measured differential optical depth for a given species, $D_l'(\lambda)$, is calculated using,

\begin{displaymath}D_l'(\lambda) = D'(\lambda) - \sum_{l'=1}^{N_l} \Delta c_{l'}...
...sigma_l'(\lambda)
= \Delta c_l \sigma_l'(\lambda) + R(\lambda)
\end{displaymath} (11.11)

which is just the fitted differential optical depth plus the residual. Comparing fitted and measured differential optical depths of a single absorber amounts to comparing $\Delta c_l \sigma_l'(\lambda)$ and $\Delta c_l \sigma_l'(\lambda) + R(\lambda)$, respectively. Also, the entire residual is attributed to that absorber. Many of the measured differential optical depths in the panels of Figures 6.6-6.9 will appear to be nearly identical. This occurs when $\Delta c_l \sigma_l'(\lambda)$ is much smaller than $R(\lambda)$. Some of the ACDs resulting from these spectral fits were found to be below the detection limit. The detection limit is essentially an indicator of the $\Delta c_l \sigma_l'(\lambda)$ to $R(\lambda)$ ratio and is calculated using,

\begin{displaymath}\Delta c_l^{\rm min} =\frac{\hat{R}}{\hat{\sigma}_l'}
\end{displaymath} (11.12)

where $\hat{R}$ and $\hat{\sigma_l'}$ are representative mean residual and differential cross-section values, respectively. Clearly from this definition, larger residuals and small differential cross-sections act to increase the ACD detection limit value. Note also that because of this, large ACDs can still be below the detection limit if they have small differential cross-sections.


 
Table 6.2: Summary of retrieved apparent column densities.
Spectral Apparent Column Density r2
Interval O3 NO2 BrO OClO O4 Ring  
(nm) (DU) ( $\times10^{14}$ cm-2) (arbitrary units)  
320-340 487.7 -128a 0.61a 10.5a 6.41 1.72 0.980
345-360 533.4 221a 4.79 0.95a 1.36 3.23 0.973
405-435 2603a 216a - 2.76a 9.87 0.920 0.810
480-515 807.5 166 - - 0.198a 1.02a 0.949

a Below detection limit


The first spectral region considered is 320-340 nm. In the UV the ozone absorption signal, $\sim 4\%$, is fairly large even in the nadir. This is also an order of magnitude larger than the residual. Note that as long as the differential optical depth is small, it can be considered as the fraction of the total signal resulting from absorption. This can be seen by carrying out a small argument expansion on the logarithm in equation (6.3),

\begin{displaymath}\ln{ \left( \frac{I}{I_{\rm ref}} \right) } \approx 1-\frac{I}{I_{\rm ref}}
= \frac{\Delta I}{I_{\rm ref}}.
\end{displaymath} (11.13)

Comparing the size of the ozone differential optical depths with those of other absorbers shows how ozone dominates this portion of the spectrum. The differential optical depths of NO2, BrO and OClO were all much smaller than the residual and hence below their detection limits. Both O4 and Ring were fit reasonable well. Shifting or enlarging the spectral region used did not impact the quality of the fit although it did effect the amount retrieved due to the rapidly changing cross-section in this part of the spectrum.


  \begin{figure}% latex2html id marker 6100
\centering\leavevmode
\psfig{file=/hom...
...ther absorbers
from the measured total differential optical depth.}
\end{figure}


  
Figure 6.7: As Figure 6.6 but for BrO using 345-360 nm.
\begin{figure}\centering\leavevmode
\psfig{file=/home/cmclinden/thesis/c-doas/pl...
...nden/thesis/c-doas/plot/ps/970502_step98_pt2.ps,height=3.4in,clip=}
\end{figure}


  
Figure 6.8: As Figure 6.6 but for NO2 using 405-435 nm.
\begin{figure}\centering\leavevmode
\psfig{file=/home/cmclinden/thesis/c-doas/pl...
.../thesis/c-doas/plot/ps/970502_step98_405_pt2.ps,height=3.4in,clip=}
\end{figure}


  
Figure 6.9: As Figure 6.6 but for ozone using 480-515 nm.
\begin{figure}\centering\leavevmode
\psfig{file=/home/cmclinden/thesis/c-doas/pl...
.../thesis/c-doas/plot/ps/970502_step98_480_pt2.ps,height=3.4in,clip=}
\end{figure}

The next region examined was for BrO: 345-360 nm with results presented in Figure 6.7. The overall fit was quite good despite the much smaller optical depths, about a factor of five smaller than for ozone. The residual is down to an impressive 0.002 or smaller. The general shape of the BrO spectrum is captured but as it is only a factor of two larger than the residual, it appears quite noisy. Some ozone and NO2 structure can be observed from their fits but each hovers near its detection limit. Ring and O4 are fit quite well which is essential for the proper retrieval of BrO as their signals are roughly two and five times stronger than BrO, respectively. This rather narrow window was selected as it produced the best fits. Increasing or shifting the spectral region used decreased the quality of the fits, perhaps in part due to the Ring spectrum. Small changes in the ability to fit the Ring results in large increases in the residual. However, the fitted BrO ACD remained reasonably stable (within 10-20%) when deviating from the 345-360 nm region. It is worthwhile noting that this region is used almost exclusively by other researchers when retrieving BrO, perhaps for reasons similar to that expounded upon above.

Results from the 405-435 nm spectral region, often used to fit NO2, as shown in Figure 6.8. Of the different regions examined, this produced the worst fit. The magnitude of the residual is about twice that of the NO2 differential optical depth and so it is actually below the detection limit. Ozone was well below the detection limit and the fitted ACD is an unrealistic 2600 DU. In the nadir, the pathlength enhancement factor will be on the order of 2-4 (see Section 6.3) and so the maximum expected ozone ACD is about 1000 DU. The structure of both O4 and Ring were fairly well captured and were the two largest components to the total differential optical depth; NO2 was a factor of two smaller. One reason for the relatively large residual may be the result of either a missing absorber or a problem with the Ring spectrum. The NO2 visible bands possess line widths which are roughly similar to that of Fraunhoffer spectra (and hence Ring also) and represents the region where the Ring effect has the largest impact (Vountas et al., 1997). In addition, the widths of the NO2 absorption lines are only a factor of two larger than the resolution of the CPFM instrument.

The most impressive fits came using the 480-515 nm region as shown in Figure 6.9. The residual is down to 0.001. It was discovered that including H2O, which has a large absorption feature near 500 nm, helped immensely in reducing the residual. Looking in the nadir ensures that the entire tropospheric water vapour column is sensed. The ozone ACD was considerably larger at 808 DU than recovered in the UV. This is because in the UV at 320 nm, the absorption and scattering are increased near 400 nm so that much more of the signal is originating close to the instrument and the entire ozone column below the ER-2 is not sampled. This region was found to be the best for fitting NO2 even though the absolute NO2 cross sections are a factor of three smaller than at 400 nm. Also encouraging is the agreement between the NO2 ACD retrieved here and that using the 405-435 nm window despite the latter's poor fit. A large amount O4 is fit which is consistent with much of the signal originating very low in the atmosphere. Only a small amount of Ring was fit which means the Ring cross-sections used may not be appropriate for this region.

Many of the cross-sections required for the DOAS retrieval are temperature-dependent. Since any given measured spectra will contain absorption signals from many different heights and thus many different temperatures, the retrieval process is complex. To recover the correct ACD, the cross-section used should be an ozone-weighted average of the altitudes sensed. Of those discussed, the species with the most pronounced temperature-dependence is ozone in the Huggins bands. The strong cross-section temperature-dependence combined with the rapid change in cross-section with wavelength allows this region to be used to extract limited profile information in the nadir (Munro et al., 1998).


  \begin{figure}% latex2html id marker 6133
\centering\leavevmode
\psfig{file=/hom...
...ation of retrieval as in Figure~6.6.
See text for further details.}
\end{figure}

The effective temperature below the ER-2 is now estimated using the same nadir spectra as shown in Figures 6.6-6.9. This is done by varying the temperature of the ozone cross-sections iteratively until a minimum residual is obtained. The ozone cross-sections used were measured at three temperatures: 202, 221, and 241 K (Burrows et al., 1997b). cross-sections at other temperatures are determined by linearly interpolating between these. The results are summarized in Table 6.3.


 
Table 6.3: Summary of ozone effective temperature fitting.
Temperature ACD r2
(K) (DU)  
202 461.9 0.9796
221 486.7 0.9802
241 512.6 0.9783
219 481.5 0.9807

Clearly the choice of temperature has a large impact on the retrieved ozone ACD. Between 221 and 202 K and 241 and 221 K there was a 5% difference. Iterations were performed until a minimum residual was reached to within 2 K. For this scan, 219 K was the best fit temperature. A temperature this low suggests that the effective altitude is near the tropopause, approximately 8 km.

The impact of temperature on ozone cross-section is shown in Figure 6.10a. The cross-section fractional difference, relative to those at 219 K, are shown between 320 and 340 nm. Note that the differences are the largest at longer wavelengths, up to 25% for 241 K. In Figure 6.10b, the increase in absolute value of the residual at 202, 221, and 241 K, over that at 219 K, are plotted. The form of the difference in residuals mimics that of the cross-sections. Also, the differences are largest at shorter wavelengths which is due to the change in the absolute value of the cross-sections with wavelengths; at 320 nm they are 200 times larger than at 340 nm and so the shorter wavelength end controls the fitted ozone amount to a large extent. At 241 K, the residuals are about 3% larger than at 219 K while the error in the fitted ozone is 6%. Thus, small increases in residuals can lead to larger changes in the ACDs.


next up previous
Next: Shift and Stretch Up: Differential Optical Absorption Spectroscopy Previous: Ring Effect
Chris McLinden
1999-07-22