Uncertainty budgets of major ozone absorption cross sections used in UV remote sensing applications

Detailed uncertainty budgets of three major ultraviolet (UV) ozone absorption cross-section datasets that are used in remote sensing application are provided and discussed. The datasets are Bass–Paur (BP), Brion–Daumont– Malicet (BDM), and the more recent Serdyuchenko– Gorshelev (SG). For most remote sensing application the temperature dependence of the Huggins ozone band is described by a quadratic polynomial in temperature (Bass– Paur parameterization) by applying a regression to the crosssection data measured at selected atmospherically relevant temperatures. For traceability of atmospheric ozone measurements, uncertainties from the laboratory measurements as well as from the temperature parameterization of the ozone cross-section data are needed as input for detailed uncertainty calculation of atmospheric ozone measurements. In this paper the uncertainty budgets of the three major ozone cross-section datasets are summarized from the original literature. The quadratic temperature dependence of the crosssection datasets is investigated. Combined uncertainty budgets is provided for all datasets based upon Monte Carlo simulation that includes uncertainties from the laboratory measurements as well as uncertainties from the temperature parameterization. Between 300 and 330 nm both BDM and SG have an overall uncertainty of 1.5 %, while BP has a somewhat larger uncertainty of 2.1 %. At temperatures below about 215 K, uncertainties in the BDM data increase more strongly than the others due to the lack of very low temperature laboratory measurements (lowest temperature of BDM available is 218 K).


Introduction
The three ozone absorption cross-sections in common use for many remote sensing applications are the Bass Paur (BP) data (Bass and Paur 1985;Paur and Bass, 1985), the Daumont-Brion-Malicet (BDM) data (Daumont et al., 1992;Brion et al., 1993;Malicet et al., 1995) and the very recent Serdyuchenko-Gorshelev (SG) data (Gorshelev et al., 2014;Serdyuchenko et al., 2011;2014). While the data from BDM and SG are absolute cross-section measurements, the BP data were scaled to the 25 so-called Hearn value at the Hg line wavelength (253.65 nm). The standard retrievals applied to the ground Brewer and Dobson spectrophotometer data use the BP data (e.g. Redondas et al., 2014), while the satellite community uses any of the three data sets or other data (WMO-GAW, 2015;ACSO, 2010;Orphal et al., Absorption cross-sections of ozone -Status report 2015, manuscript in preparation). Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-34, 2016 Manuscript under review for journal Atmos. Meas. Tech. For the review of uncertainties, original publications reporting on results of the experimental work were considered first. 30 Since BP data was absolutely scaled using Hearn data (Hearn, 1961), the latter is also included in this review. There is a lack of consistency in the presentation of measurement uncertainty budgets across different papers. Neither of the publications uses the guidelines and recommended definitions as outlined in JCGM-100 (2008). An attempt to analyze and harmonize the reported uncertainties is made in the following sections. In some cases not all measured quantities were reported and in most cases detailed description of the data processing procedures is missing. It is very likely that the published measurement 35 uncertainties are incomplete and the overall uncertainties thus underestimated.
In this paper we start with a brief summary on measurement principles in the laboratory (Section 2), followed by a review of the uncertainties of the UV ozone cross-section data (Section 3). In Section 4 the temperature dependence in the three major ozone cross-section datasets are discussed followed by Section 5, which summarises the Monte-Carlo simulation to obtain the overall uncertainty budgets of the major datasets. Section 6 provides a summary and conclusion. 40

Measurement technique
Ozone absorption cross-sections are produced by performing spectroscopic measurements and subsequent analysis to convert the recorded spectra into absorption cross-sections in units of cm 2 /molecule. The absorption spectroscopy is based on the Beer-Lambert law, which describes the attenuation of the light intensity transmitted through the absorbing medium.
For gaseous species the Beer-Lambert law can be written as: 45 . (1) Here is the light intensity in the absence of absorbing molecules (background), is the absorbing gas number density, which is generally a function of temperature , pressure , and the position along the beam path, is the total absorption path length and [cm 2 /molecule] is the wavelength-dependent (and normally also temperature-dependent) absorption crosssection.
In a laboratory environment it is possible to control the experimental conditions with sufficient precision, so that the 50 number density [cm -3 ] is assumed to be homogeneously distributed along the absorption path of a known length [cm].
where A is the unitless absorbance. The unitless optical density (OD) is then expressed as .
( 3) Absolute cross-sections can be derived from the optical density if species concentration, temperature and absorption path 55 length are known. Since ozone is a reactive and highly explosive gas, many measurements were done using a flow of oxygen/ozone mixture, where the partial pressure of ozone is unknown and values from other published absolute ozone cross-section measurements are used to find a scaling factor that converts the measured optical density into absorption crosssection (e.g. Chehade et al., 2013a, b) Alternatively, measurements performed at selected wavelengths with a special attention to control of the experimental 60 parameters are used to calibrate the relative cross-sections (optical densities). The latter was done for the BP data Paur 1985, Paur andBass, 1985) as all their relative spectra were scaled to the ozone absorption cross-section value at 253.65 nm (mercury line) as reported by Hearn (1961). Thus the uncertainties in the reference data propagate into the calibrated spectra.
Depending on the kind of spectrometer used for broadband (Fourier transform, grating) or single wavelength 65 measurements, registered spectra are inevitably subject to multiple sources of uncertainties -stochastic intensity variations caused by detector noise, light source intensity fluctuations etc. (JCGM-100, 2008). Spectral random error can be characterized by the signal-to-noise ratio (SNR), and one of the ways to improve the quality of the measurements is acquisition of multiple spectra obtained under repeatable conditions (JCGM-100, 2008). Uncertainty of the resulting average value is represented by the standard deviation of the mean. 70 Spectrometers are characterized by the spectral resolution and wavelength calibration to some reference values, which influences the wavelength uncertainty of the produced data. For example, dispersion-based instruments can be wavelengthcalibrated using isolated atomic emission lines of Hg or Cd lamps, and Fourier-transform spectrometers are auto-calibrated with the built-in stabilized He-Ne laser.
Instrumental uncertainties of other measured quantities -temperature T, ozone (partial) pressure p, absorption path length 75 L are also contributing to the total absorption cross-section uncertainty. For broadband laboratory measurements covering a large wavelength range, like the Hartley-Huggins band of ozone, cross-section values change by up to seven orders of magnitude, so that optical density spectra are recorded using different combination of cell lengths and partial pressures (e.g. Gorshelev et al. 2014, Serdyuchenko et al. 2014. The various spectra are then concatenated to cover the entire spectral range, which leads to additional uncertainties. 80

3
Review of reported uncertainties 3.1 Uncertainty budget of Hearn Dating back to 1961, Hearn reported on ozone absorption cross-sections at six selected wavelengths, of which the value at λ = 253.65 nm is of particular interest, since it has been measured in many studies and is considered a standard reference (see Viallon et al. (2015) and references therein).The following information of the laboratory measurements by Hearn (1961) 85 Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-34, 2016 Manuscript under review for journal Atmos. Meas. Tech.  Table 1 provides the original notation of uncertainty budget from Hearn (1961). The uncertainties are divided into type A and type B uncertainties (JCGM-100, 2008). Type A uncertainty means that it is derived from a statistical analysis and an observed frequency distribution. Type B uncertainties are not derived from a statistical analysis and it assumes a probability 95 distribution that is based upon past experiences or is derived from external specifications. The breakdown of evaluation type of the uncertainties is color coded in Table 1. Little to no detail is provided on the accuracy of the instruments used during measurements. Given the reported ± 2.4x10 -19 cm 2 interval around the 114.

3.2
Uncertainty budget of BP The team of Bass and Paur Paur 1985, Paur andBass, 1985) provided cross-section data for a broad spectral range 110 and at several temperatures. The following information is available from the BP data:  Table 2 summarises the uncertainties of BP data, with a type A/B breakdown color-coded in different gray shadings. The relative standard measurement uncertainty of the BP ozone absorption cross-section is stated to be around ±1%. It seems to be an underestimation, since BP relative spectra were scaled to the Hearn value at 253.65 nm, which is reported with a 1.4% relative standard measurement uncertainty (see Section 3.1). 120 Uncertainty budget of BDM Ozone absorption cross-sections provided by Brion et al. (1993), Daumont et al. (1992) and Malicet et al. (1995)   Light source reference spectra: recorded before and after the ozone spectra  Absolute scaling: measurements of total pressure Table 3 provides the original notation of the uncertainty budget of BDM data with Type A / Type B breakdown colorcoded in gray shadings. The information on the relative standard measurement uncertainty of the BDM ozone absorption 140 cross-section is wavelength-dependent (see last row of Table 3).

Uncertainty budget of SG
Ozone absorption cross-sections reported by Serdyuchenko et al. (2014) were obtained for 11 temperatures in a wide spectral range using two spectrometers (Fourier-transform and Echelle-grating spectrometers). Tables 4 and 5 summarize the information on the experimental details and uncertainties for the SG cross-section data. 150 In the 213-350 nm wavelength region the relative standard measurement uncertainty of the SG ozone absorption crosssection is wavelength-dependent and ranges between 1 -3 %. The dominating uncertainty source is the statistical repeatability of the spectral registration, influenced by stability of the light source and detector noise. These two factors have a greater impact when the intensities of the spectra contributing to the OD calculation either differ greatly (strong absorption, close to saturation) or are very close to each other. This effect is demonstrated in Figure 1, showing the concatenated OD 155 spectrum and relative uncertainties of the corresponding constituent spectral cuts. The latter were calculated according to law of propagation of uncertainty using standard deviation (variances) and mean values of I and I 0 spectra which determine the optical density OD (see Eq. 3). Table 6 summarises the uncertainties for all cross-sections datasets discussed here.

Temperature dependence and uncertainties
In general the ozone cross-sections were determined at selected atmospherically relevant temperatures. BP and BDM data encompass six and five temperatures, respectively, while SG is available at eleven temperatures. The original data can 185 be obtained from http://satellite.mpic.de/spectral_atlas/cross_sections/Ozone/O3.spc. Table 7 summarises the available temperatures for all three datasets. BP (Paur & Bass, 1985) 203, 218, (228), 243, 273, 298 245 -343 BDM (Malicet et al., 1995) 218, 228, 243, (273), 295 195 -345 SG (Serdyuchenko et al., 2014(Serdyuchenko et al., ) 193, 203, 213, 223, 233, 243, 253, 263, 273, 283, 293 213 -1100 The temperature dependence of the ozone absorption cross-sections is commonly described by the so-called Bass-Paur parameterisation (Paur and Bass, 1985), which is a quadratic polynomial: . (4) The temperature coefficients are determined in a multivariate linear regression using the cross-section data measured at various temperatures . They were calculated in the wavelength range 290-360 nm (BP: up to about 338 nm), which is the spectral range with the highest temperature sensitivity (Huggins ozone band). The temperature t in Eq. 4 is 195 given in degree Celsius (t=T-273.15 K). The uncertainty of the calculated cross-section at a given temperature is then given by . (5) The 228 K temperature data of BP has been excluded from the polynomial fit as there is a gap between 295 and 304 nm. Liu et al. (2007) noted a systematic bias in the 273 K BDM data and reported better ozone retrieval fit results if this temperature is excluded. This temperature data also does not provide data below 300 nm. As noted by Orphal and Chance (2003) and 200 Weber et al. (2013), there is a systematic wavelength shift between BP and BDM. Shifting the BP data by +0.029 nm leads to better agreement (to within 0.5%) between BDM and BP . The SG data wavelength scale agrees to within uncertainties with BDM (Gorshelev et al., 2014). Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-34, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 14 April 2016 c Author(s) 2016. CC-BY 3.0 License. Figures 2 to 4 show the temperature coefficients including the 1-sigma uncertainties (see Eq. 5) for the BP, BDM, and SG data, respectively. As the SG data are somewhat noisy near 300 nm, in the July 2013 version of the SG data a fast 205 Fourier transform filter was applied in the spectral range 213-317 nm. Figure 5 shows the uncertainty from the polynomial fit as a function of wavelength for T=193 K and 227 K. BP data uncertainties are getting fairly large above 330 nm reaching nearly 25% for some wavelengths at 220 K and more than 60% at 193 K. The uncertainty of the BDM data ranges between 0 and 2% up to 330 nm, while SG data show a fairly constant uncertainty of about 1% on average at T=227 K. The uncertainties are doubled at the lower temperature. The very low 210 uncertainty for BP and BDM at some wavelength is mainly due to the very low number of available temperatures (4-5) that leads in some cases to overfitting of the data with a quadratic polynomial.
The spectral resolution of the three datasets varies from 0.01 nm (BDM) to 0.05 nm (BP). The instrumental slit function can be easily applied to each of the temperature coefficients in order to match the spectral resolution of the cross-section data in form of Eq. 4 to any type of instruments. 215

Overall uncertainty: Monte -Carlo simulation
The uncertainty given in Eq. 5 reflects only the uncertainty from the temperature parameterisation using a polynomial (if we assume that a quadratic dependence in temperature is true). In order to estimate the overall uncertainty including uncertainties from measurements (random and systematic), wavelength registration, and the temperature parameterisation, an extensive Monte-Carlo simulation (JCGM-101, 2008) was carried out. 225 c a b d Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-34, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 14 April 2016 c Author(s) 2016. CC-BY 3.0 License. Table 8 summarises the uncertainties simulated. The numbers are mainly based upon the uncertainty as reported in Table   6. It was assumed that the probability density function (PDF) is Gaussian for all uncertainties.

230
Uncertainty type (290 nm -370 nm) Value (1-sigma) Measurement at each T (random) 1% Measurement at each T (systematic) 1.3%* Wavelength registration at each T (random) 0.005 nm Wavelength registration at each T (systematic) 0 nm** Temperature T (random) 0.5 K Temperature T (systematic) 1 K Polynomial in T combined resampling residuals and wild boot strap (normal distributed)  2% for BP ozone cross-sections  it is assumed that wavelength shifts can be corrected in ozone retrievals (e.g. Coldewey-Egbers et al., 2015) The values used here are the minimum uncertainties (see Table 6), however, it should be noted that the (random) 235 measurement uncertainties varies with wavelengths, but this is neglected here. Random uncertainties are simulated by randomizing for each temperature data in a given simulation, while systematic errors means an uncertainty drawn from the random generator being applied to all the temperature data simultaneously.
In order to estimate the effect of the measurement errors on uncertainties from the T-polynomial a combination of the resampling residual and wild boot strap method was applied (Wu, 1986). The residual from the polynomial fit is given by 240 , where is the fitted polynomial (see Eq. 4). In the Monte Carlo simulation the residual is distributed randomly to different temperatures as follows (7) and the polynomial fit repeated. is a normal distributed random number. The normally distributed random number generator used in the MC simulation is based upon the Box-Muller transform (Box and Muller 1958). The total sample size selected was 10 4 , which provided a reasonable compromise between computation time and precision of the simulation. For 245 each wavelength between 290 and 370 nm (BP: ~339 nm) in steps of 0.01 nm the Monte-Carlo simulation was carried out. the BP data (2%) leads to larger overall uncertainties in the BP data. At 319.4 nm there appears to be some issue, since the 203 K BP measurements are much lower than SG leading to rather large polynomial fit errors as observed earlier. Figure 8 shows the uncertainties as a function of wavelengths for selected temperatures. At 227 K the overall uncertainties are about 1.5% for both BDM and SG, while BP uncertainties are about 2.1% (1-sigma). Above 330 nm the uncertainties increase for all datasets. At very low temperatures, e.g. 193 K, the BDM uncertainties increase to about 4% (1-255 sigma), while SG remains at 2% (1-sigma). BP uncertainties are about 2.5% (1-sigma) and are also lower than BDM. Similar to 227 K, the uncertainties increase at the longest wavelengths. At temperatures above 215 K, the uncertainties of BDM and SG are very similar, at lower temperatures the BDM uncertainties significantly increases due to the lack of very low temperature measurements.

Summary and conclusion 260
Realistic and comparable uncertainty budgets were derived from three major ozone absorption cross-section datasets that are used in various remote sensing applications. First a review of the published literature on the uncertainty of the BP, BDM, and SG datasets was given. The uncertainties of these three datasets are summarized in Table 6 and are now directly comparable between the various datasets. For remote sensing application, in particular in the Huggins ozone band, the temperature dependence of the ozone cross-sections have to be accounted for and this is typically done using a quadratic 265 polynomial as a function of temperature. Using the updated uncertainty estimates from Table 6 and a residual boot strap method for estimating the uncertainties from the temperature polynomial, a Monte Carlo simulation was carried out.
However, one should note that due to lack of information from the peer-review literature on the exact wavelength dependence of the uncertainties (see Table 6) this was neglected in our simulations.
In the Huggins band the overall uncertainty of the temperature dependent ozone cross-section is about 1.5% (1-sigma) for 270 BDM and SG and 2.1% (1-sigma) for BP up to about 330 nm. At temperatures below about 215 K the uncertainty in the BDM data increase more strongly than for the others, as the lowest measured temperature for BDM is 218 K and the extrapolation of the polynomial leads to larger uncertainties. Above 330 nm the uncertainties increase significantly for all datasets. Ozone retrievals exploiting the UV spectral range usually focus on wavelengths below 335 nm.
The temperature coefficients for the three major cross-section data with uncertainty estimates from the polynomial fit 275 alone as well as from the MC simulations are available at http://www.iup.uni-bremen.de/~weber/ATMOZ. Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-34, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 14 April 2016 c Author(s) 2016. CC-BY 3.0 License.