Error estimation

The total uncertainty of the VMRs inferred with the O₄ scaling method according to Equation 10.15 is comprised of several parts: The errors in the measured SCDs of the different trace gases, the uncertainty arising from the calculation of the ratio α^∗_x/α^∗_O

4, and the error of the atmospheric pressures p and temperatures T . The total error of the VMRs inferred with the O₄ scaling method

10.1. Scaling method with a gas of known profile 173

can be determined according to the following formula:

∆VMRxj =

In the following, the different errors and uncertainties are specified. The dSCD errors ∆dS of the measured trace gases correspond to the DOAS spectral fit error as given by the WinDOAS pro-gramme (Section 8.3). Systematic dSCD errors are not taken into account in this error estimation.

∆dS typically varies between 5 and 20 %, depending on the trace gas. The SCD errors ∆S of the O₄ SCDs determined using a Kurucz spectrum as a FRS are also given by the DOAS spectral fit error and typically vary between 10 and 15 % for the UV and between 5 and 10 % for visible wavelength range. The uncertainty of S_refx of the different trace gases estimated using different 3D cloud scenarios is given by the standard deviation of the mean S_refx (Table 10.1). The resulting error of the SCD Sx of a trace gas x can be calculated according to:

∆S_x =q

∆dS_x²+ ∆S_ref²

x. (10.18)

The temperature and pressure sensors of the Falcon aircraft are calibrated by the DLR flight de-partment. The final error in the static pressure measurement is ∆p ≈ 0.5 hPa, whereas the accuracy of the static temperature yields ∆T ≈ 0.5 K (http://www.dlr.de/fb/en/desktopdefault.aspx/

tabid-3718/). However, it is important to note that when flying within clouds or precipitation events the sensing elements can get wet, possibly leading to inaccurate measurements.

The major uncertainty that propagates into the total error of the inferred VMRs is caused by the uncertainty in the determination of the correction factor α^∗. In the following, sensitivity studies are performed in order to estimate the uncertainty of the ratio α^∗_x/α^∗_O

4. Sensitivity studies are performed for HCHO for sortie 1 on 16.11.2011. Figure 10.10 shows α^∗_HCHO, α^∗_O4, and the ratio α^∗_HCHO/α_O^∗

4 for the base run described in Section 10.1.3 as well as for different RT settings. These different RT settings include changes in the aerosol extinction profile, in the ground albedo, and in the roll angle of the Falcon aircraft. An aerosol profile with an extinction that is twice the extinction of the base run is assumed. Furthermore, a cloud layer is implemented between 0.5 and 1 km with an extinction of 20 km⁻¹. The albedo is changed from 0.05 in the base run to 1 in order to account for bright clouds. Since the assignment of the roll angle of the aircraft to the DOAS spectra can be erroneous, ±1^◦ is added/subtracted from the assigned roll angle. The different RT settings lead to large differences in α^∗_HCHO and α^∗_O

4 as compared to the base run. However, these differences decrease when calculating the ratio α^∗_HCHO/α^∗_O4, i.e. the ratio is less influenced by changes in the RT settings than the single α^∗factors. Overall, the deviations of the ratio α_HCHO^∗ /α^∗_O

4 from the base run in the MBL are smaller than ±(15 − 20) %. Exceptions are the scenario including a cloud layer between 0.5 and 1 km with an extinction of 20 km⁻¹ and the scenario with an albedo of 1. If the flight altitude corresponds to the altitude of the cloud, the deviation of the ratio α^∗_HCHO/α^∗_O

4 from the base run increases to approximately 40 %. When the albedo is set to 1 the deviation reaches values of approximately -40 % in the free troposphere. However, flight sections within clouds or very close to a cloud layer can be identified with the colour index, the brightness, and the O₄dSCDs as described in Section 9.1.

(a) (b)

(c) (d)

Figure 10.10: (a) α^∗_HCHO, (b) α^∗_O4, (c) α^∗_HCHO/α^∗_O4, and (d) the deviation of the ratio α^∗_HCHO/α^∗_O4 from the base run for different RT settings for sortie 1 on 16.11.2011.

Further uncertainties can arise from the choice of the assumed trace gas profiles. Thus, different artificial HCHO profiles are generated to investigate their influence on α^∗_HCHO. These profiles in-clude a linearly decreasing profile, a smoothed box-shaped profile, and two exponentially decreasing profiles with different exponential decay constants (Figure 10.11a). Overall, for the range of the assumed HCHO profiles deviations in α^∗_HCHO of approximately up to ±80 % can be observed rela-tive to the base run. However, a linearly decreasing HCHO profile seems to be rather unrealistic.

In order to receive a more realistic estimation of the typical variability of the HCHO profiles en-countered during the SHIVA campaign, the variability in the HCHO profiles is estimated from the TOMCAT profiles simulated for each sortie of the Falcon aircraft. Figure 10.11b shows an overview of the different TOMCAT HCHO profiles. The maximum and minimum profiles that constitute the total range of the HCHO concentration are extracted and extended up to 30 km (Figure 10.11a).

Overall, the maximum and minimum TOMCAT profiles lead to a deviation of α^∗_HCHOand thus to a deviation of the ratio α^∗_HCHO/α^∗_O

4 from the base run of up to approximately ±40 % (Figure 10.12).

The standard deviation of the average deviation corresponds to approximately 20 % for both the maximum and minimum TOMCAT profiles, respectively.

In the following, the uncertainty of the ratio α^∗_HCHO/α^∗_O

4 is set to a fixed value of 40 % in order to completely cover the different possible uncertainties arising from different RT settings or from the choice of the input profile. This value represents a rough estimation. In extreme cases, this value