The NIR solar absorption spectra to which the calibration is applied are measured with a solar FTIR spectrometer located at the high-altitude observatory on the summit of the Zugspitze, Germany (47.42∘ N, 10.98∘ E; 2964 m a.s.l.). The spectrometer setup is described in detail in Sussmann and Schäfer (1997). An overview of the FTIR spectra acquisition settings is provided in Table 1. Briefly, the measurements are obtained with a Bruker IFS125HR interferometer. The interferometer's field of view actively tracks the position of the center of the solar disc by means of feedback from a quadrant diode. Interferograms were recorded with a maximum optical path difference (OPD) of 45 cm and averaged over four to eight scans.

Spectra are typically measured with a liquid-nitrogen-cooled InSb detector (1850 to 9600 cm-1) in combination with a KBr beam splitter. An alternative setup consisting of an InGaAs detector (4000 to 12 800 cm-1) and a CaF2 beam splitter is available. This setup has the advantage of an improved signal-to-noise ratio, especially above 6000 cm-1, and avoids a spectral interval of low instrumental sensitivity between 5200 and 5800 cm-1 attributed to low transmissivity of the KBr beam splitter. However, for routine operations of the solar FTIR spectrometer, especially for the long-term determination of atmospheric trace gas column amounts and vertical profiles (e.g., Borsdorff and Sussmann, 2009; Sussmann et al., 2009, 2012; Hausmann et al., 2016), the first option is more suitable. Therefore, most spectra to be calibrated were recorded with the InSb/KBr setup, while the InGaAs/CaF2 setup was only used in a number of single-day measurement campaigns. While the calibration scheme presented here is applicable for both configurations, we therefore focus on the InSb/KBr setup throughout the remainder of this paper.

The calibration procedure makes use of a blackbody calibration source installed in the Zugspitze solar FTIR dome. The calibration source (MIKRON M330-EU, Lumasense Technologies) is shown in Fig. 1, while its technical specifications according to the manufacturer are given in Table 2. Blackbody spectra are measured with the solar FTIR using the solar tracker optics and an additional gold-coated 90∘ off-axis mirror. The thermal radiation emitted by the calibration source is directed to the solar tracker by means of the additional off-axis mirror, whose distance to the blackbody cavity interior is set to its focal length of f=478 mm. Blackbody source and off-axis mirror are aligned in order to produce a parallel beam with a diameter of 156 mm that is incident at a 90∘ angle on the solar tracker elevation mirror.

Spectral radiance measurements of the blackbody calibration source described in Sect. 2.2 are used to determine the shape of the calibration curve in spectral intervals between the points suitable for precise Langley calibration. Contrary to the calibration approach described by Gardiner et al. (2012), using a source with a temperature of 3000 K, a lower cavity temperature of 1973.15 K can be used in the Zugspitze experiment due to the combination with Langley measurements. The settings of the FTIR spectra acquisition were similar to the Langley measurements (see Table 2).

As for the Langley measurements, dry atmospheric conditions imply more narrow spectral intervals affected by water vapor line absorption and thereby improve the blackbody calibration accuracy. Therefore, only measurements with an atmospheric water vapor density ρH2O < 1 g m-3 at the Zugspitze summit observatory were considered for calibration. The blackbody thermostat generally compensates for the effect of changing air temperature inside the FTIR dome to keep the temperature inside the blackbody cavity constant and thereby avoid temporal variation of the emitted blackbody radiance. This is demonstrated in the red line in Fig. 6, which corresponds to 2 times the standard deviation of all normalized blackbody calibration curves. The measurements show that within a range of ambient temperatures from 263 to 273 K, the blackbody calibration results show only very little variation. However, fast temporal variations in air temperature cannot be compensated for by the blackbody thermostat instantaneously and lead to short time intervals with temporally unstable blackbody radiance. Such measurements were discarded before further analysis.

Only spectral points outside water vapor lines were considered to avoid bias in the calibration. More specifically, only points less than 10σ (where σ designates the mean measurement noise) below the upper envelope of the measured spectra were selected (black spectrum in Fig. 4). The influence of measurement noise can then be further reduced by applying a median filter (20 cm-1 width) to the spectra (red spectrum in Fig. 4). Finally, the blackbody calibration curve cbb(ν) is calculated from the averaged spectra by dividing the Planck curve at the cavity temperature Tbb by the measured spectrum. Standard lamps constitute an alternative to the high-temperature blackbody that can also be used in the combined calibration scheme. However, the spectral radiance of such calibration sources is typically prone to higher uncertainty than for blackbody sources.

The combined calibration strategy takes advantage of the low-uncertainty Langley calibration at suitable spectral points (see Sect. 3.1). In between the Langley points, the shape of the calibration curve is constrained by the blackbody measurements (see Sect. 3.2). The combined calibration curve c(ν) is given by the relation c(ν)=cbb(ν)⋅clan, linear(ν)/cbb, linear(ν), where cbb designates the blackbody calibration curve derived according to Sect. 3.2. clan, linear and cbb, linear designate linear interpolations constructed as follows: at the Langley calibration points, clan, linear and cbb, linear are set to the Langley and blackbody calibration results, respectively. In between these points, clan, linear and cbb, linear are calculated by linear interpolation. The combined calibration curve calculated according to Eq. (4) from blackbody measurements made on 24 February 2014 and Langley measurements made on 13 December 2013 is shown in Fig. 5.

Several contributions to the calibration uncertainty budget are associated with the Langley measurements. A first contribution results from the uncertainty of the Langley fit. This contribution is calculated as an error-weighted mean over the 2σ uncertainties of the Langley calibration results for all spectral points contributing to each Langley point, i.e., it represents the uncertainty of the Langley extrapolation to air mass 0. In between Langley points, the uncertainty estimate is obtained by linear interpolation between the uncertainty values at the Langley points. The Langley contribution to the calibration uncertainty ranges from 0.35 to 0.72 % throughout the spectral range considered for calibration and is shown in Fig. 6 (blue line). The low uncertainty of the Langley fit is a result of the spectral point selection outlined in Sect. 3.1.3, which restricts the use of Langley results to spectral points with low fit uncertainty, while blackbody measurements are used to constrain the calibration curve in between these points. Note that, in addition to the Langley contribution, further uncertainty is induced by the combination with blackbody measurements between Langley points. This additional contribution leads to an increase in overall uncertainty between Langley points and will be outlined in Sect. 4.3.

Furthermore, the reflectivity of the solar tracker mirrors feature spatial inhomogeneity due to dirt and aging effects. Due to nonideal alignment of optical elements of the solar tracker, the area covered by the instrument's FOV of the tracker mirrors changes over time, i.e., depending on the azimuth and elevation of the instrument's line of sight. This leads to spurious radiance variations in the Langley calibration and increases the calibration uncertainty. To obtain an estimate of this error, the position of the instrument FOV on the tracker elevation mirror for the azimuth and elevation values encountered during the Langley calibration has to be measured. This was achieved using an outgoing laser beam aligned with the instrument's optical axis, whose position on the tracker mirrors for a given azimuth and elevation is then monitored. In the spectral regions with least atmospheric absorption, the diurnal variation of the measured solar radiance is about 5 %. This variation is due to a combination of several contributions: a first contribution is due to the change in atmospheric optical depth (OD) with air mass as visible in the Langley plot in Fig. 2. In addition, other atmospheric effects such as temporally variable clouds contribute to the observed signal. A final contribution is due to the mirror-related effect mentioned above. A conservative estimate of the FOV-related error is obtained assuming that the observed diurnal variation is solely due to mirror inhomogeneity and that mirror reflectivity drops abruptly by this amount (5 %) outside the area initially covered by the FOV. Consequently, the error estimate is obtained by multiplying the 5 % reflectivity change with the fraction by which the area within the field of view has changed throughout the time interval over which measurements contributing to the Langley fit were made. The interval is deduced from the laser measurements. The resulting Langley calibration uncertainty due to mirror inhomogeneity is ∼ 0.2 % (cyan line in Fig. 6). Note that for the Zugspitze solar FTIR, the angle of incidence on the solar tracker mirrors does not vary significantly during measurements or in between blackbody and atmospheric measurements. Therefore, the angular dependence of mirror reflectivity is not included in the calibration uncertainty estimate. However, for different instruments, this contribution may have to be taken into account (see Gardiner et al., 2012).

The accuracy of the Langley results is also limited by errors in the air mass values used for the fit. Firstly, this is due to inaccurate solar zenith angle input. A second and by far dominant effect is due to the fact that the relative air mass for absorbing species with different concentration profiles is not equal for a given solar zenith angle. Depending on the spectral region, the dominant contribution to atmospheric OD for most Langley points is either due to water vapor or aerosols. For our analysis, water vapor relative air masses were used. The difference in the calibration results when performing the analysis with relative air columns instead of water vapor columns is up to 0.5 % and was taken as an estimate of the air-mass-related calibration uncertainty (see orange line in Fig. 6).

An additional uncertainty contribution of up to 0.25 % results from the uncertainty of the mispointing correction outlined in Sect. 3.1.3 (purple line in Fig. 6). This contribution includes two effects related to the mispointing uncertainty: the effects of air mass uncertainty in the Langley fit and the uncertainty in the solar limb darkening correction outlined in Sect. 3.1.3.

A further uncertainty contribution is associated with the ESS used in the Langley calibration. While no uncertainty estimate was provided by the authors for the spectrum of Kurucz (2005), the 2σ uncertainty of the Thuillier et al. (2003) spectrum is reported to be in the range of 1.2 % at 4000 cm-1 to 1.8 % at 8000 cm-1. Menang et al. (2013) state an uncertainty (1σ) of 3.3–6.0 % for their ESS derived via the Langley method.

However, recent studies on the NIR ESS have yielded results which are partly inconsistent within the respective uncertainties and feature differences of up to 5–10 % (see, e.g., Menang et al., 2013; Bolsée et al., 2014; Thuillier et al., 2014, 2015; Weber et al., 2015). The ongoing discussion about the magnitude of the ESS in the NIR implies that the ESS uncertainty estimates reported by recent studies may underestimate the real uncertainty. Therefore, the absolute radiometric uncertainty of the calibration scheme presented in this study remains tentative and more definite constraints require improved knowledge of the NIR ESS.

However, the ESS uncertainty only has a very minor influence on the main aim of this study, namely the use of calibrated solar FTIR spectra in a closure experiment for quantification of the NIR water vapor continuum. This important feature results from the fact that the same ESS is used for calibration and synthetic spectra calculation in the closure experiment and is demonstrated in the companion paper Part 3. Therefore, in the context of closure experiments, the relevant uncertainty budget does not include the ESS contribution and is shown in Fig. 6.

A further contribution to the calibration uncertainty results from the blackbody measurements. The blackbody calibration curve uncertainty was calculated as 2 times the standard deviation of all normalized blackbody calibration curves recorded under suitably dry atmospheric conditions (near-surface atmospheric water vapor density ρH2O< 1 g m-3). These measurements include spectra at Tbb= 1923.15 to 1973.15 K cavity temperature. The relative error in the combined calibration curve resulting from the uncertainty of the blackbody measurements does not exceed 1.5 % and is shown in Fig. 6 (red lines).

The combined calibration according to Eq. (4) is based on the assumption that the blackbody calibration curve between suitable Langley points can be approximately described by multiplying the Langley calibration curve with a linear function, i.e., that the following relation is fulfilled: cbb(ν)/cbb, linear(ν)≈clan(ν)/clan, linear(ν). Equation (5) is not exactly fulfilled if the reflectivity of the additional off-axis mirror used for blackbody measurements does not vary linearly between Langley points. As a consequence, an additional contribution to the calibration uncertainty results from the use of the combined approach presented in Sect. 3.3. In order to obtain an estimate of this shape error contribution, the following procedure was applied: i.

The calibration error induced by omitting the Langley result at each single Langley spectral point νi and using only the neighboring points νi-1 and νi+1 is calculated. A preliminary shape error curve is then constructed from the error values at all νi by linear interpolation.

Thermal emission from instrument parts at room temperature contributes a fraction of less than 10-5 to the measured solar radiance within the considered spectral interval. Contrary to the situation for instruments operating in the far-infrared spectral range, this contribution is therefore of negligible importance for the calibration error budget. Within the Zugspitze radiative closure experiment, the same ESS is used for Langley calibration and radiative transfer calculations. Therefore, the accuracy of the water vapor continuum optical depth derived in closure experiments from the calibrated spectra is not heavily affected by errors in the extra-atmospheric solar spectrum. The overall uncertainty relevant for water vapor continuum detection, i.e., not including the extra-atmospheric solar spectrum contribution, is shown in Fig. 6 (black lines). It is typically below 1 % within the calibration range, except for regions with sparse Langley point density or low beam splitter transmissivity where maxima of up to 1.7 % uncertainty exist. The error budget including the uncertainty of the solar spectrum of Thuillier et al. (2003) is about 1.5–2 % throughout the 4000 to 7800 cm-1 wavenumber range. However, as outlined in Sect. 4.2, the ESS uncertainty is a topic of ongoing debate and therefore the overall uncertainty budget should be treated as tentative and needs confirmation or adjustments by future ESS studies.

A first method to validate the calibration results and the associated error estimate is to investigate the self-consistency of different calibration cases, i.e., the reproducibility of the calibration. The self-consistency of blackbody measurements is presented in Sect. 4.2. This result is then used as an estimate of the blackbody-related contribution to the total calibration uncertainty. As outlined in Sect. 4.2, this uncertainty contribution does not exceed 1.5 % throughout the spectral interval considered for calibration. The reproducibility of the Langley results is estimated by comparing the Langley measurements made on 12 December 2013 with the ones made on 13 December 2013. As shown in the Fig. 7a, the calibration curves determined from those two Langley measurements typically differ by less than 1 % outside absorption bands. In regions with sparse coverage of Langley points, i.e., within water vapor absorption bands, differences are typically around 1.5 %. Throughout 91.1 % of the calibration spectral range (2500 to 7800 cm-1), the calibration curves are consistent within the calibration uncertainty estimate of Sect. 4 (grey shaded area in Fig. 7a). This extensive consistency consolidates the validity of the error budget presented in Sect. 4.

Note that modifications to the solar FTIR instrument such as realignment of optical elements requires repetition of the calibration procedure and the calibration results are only valid during periods with no significant change of instrument characteristics. Such changes can be detected, e.g., by monitoring the modulation efficiency of the FTIR or the instrumental line shape, which is achieved via routine HCl cell measurements (Hase et al., 2013). During the time interval covered by the measurements included in this study, no significant changes in instrument characteristics were detected.

Apart from modifications to the instrument which were discussed above, the accuracy of the radiometric calibration can decrease over time due to ice formation on the liquid nitrogen cooled InSb detector in the case of leaks in the detector's vacuum enclosure (see Gardiner et al., 2012). As outlined in the companion paper Part 3, the additional absorption by ice formation is most pronounced in the 3000 to 3400 cm-1 range and was estimated using lamp spectra routinely recorded with the solar FTIR. The maximum influence of ice formation on the measured radiance was 1.6 % at 3200 cm-1 and was included in the uncertainty budget of the closure experiment.

A further consistency check of the calibration error estimate provided in Sect. 4 can be obtained by a closure of calibrated spectra with synthetic solar absorption spectra obtained by radiative transfer model calculations, which enables us to detect any large deviations of the real calibration accuracy from the uncertainty estimate given in Sect. 4. More specifically, a set of calibrated spectra is compared to synthetic spectra obtained with the LBLRTM_v12.2 radiative transfer model (Clough et al., 2005). The atmospheric state used as input to the line-by-line radiative transfer model (LBLRTM) calculations was determined as outlined in Part 1. In summary, we use water vapor column data retrieved from the solar FTIR spectra. Water vapor profiles were set according to four-times-daily National Center for Environmental Prediction (NCEP) resimulation data, while for temperature profiles we used a combination of NCEP reanalysis results and a fitted near-surface profile obtained from FIR thermal emission spectra. CO2, CH4, and N2O column values were measured with the nearby Garmisch solar FTIR. Aerosol optical depth was constrained with sun photometer measurements.

For the closure analysis, we used spectra measured under clear-sky conditions during the December 2013 to February 2014 period, during which no realignment or other modifications to the spectrometer were performed. All spectra with an air mass greater than 9.0, i.e., a solar zenith angle greater than ∼ 84∘, were discarded due to increasing inaccuracies in the ray tracing calculation and significant air mass variation during the spectral averaging period at high zenith angles. Additionally, the validation data set only includes spectra for which the radiance uncertainty due to FOV variations on the tracker mirrors (see Sect. 4.1) is negligible (< 0.1 %). These selection thresholds lead to a validation data set of 52 spectra. For calibration, the 13 December 2013 Langley and 24 February 2014 blackbody results were used.

The corresponding synthetic spectra were then computed for all calibrated spectra in the validation data set. Figure 7b shows the mean measured (black) and synthetic (red) radiance for this set of spectra. It illustrates the very good general level of agreement between calibrated and synthetic spectra. The mean spectral residuals, i.e., the difference between synthetic and measured radiance is shown in red in Fig. 7c, while the standard deviation of the residuals is shown in grey. Quantitatively accurate closure is only possible outside solar lines due to the high ESS uncertainty within the lines. We therefore exclude these regions from the comparison based on the selection criterion provided in Sect. 3.1.3. Within atmospheric lines, the uncertainty of the closure is dominated by atmospheric state and line parameter uncertainties and therefore does not provide substantial insights into the calibration accuracy. We therefore discarded these spectral points by excluding all spectral points below 99 % of the upper envelope to the mean radiance in 20 cm-1 wide bins. As outlined in Sect. 3.2, the blackbody measurements demonstrate that the calibration curve varies only slowly with wavenumber and contains no narrow line-like features. Therefore, it is sufficient to validate the calibration results in suitable windows between spectral lines as outlined above. The residuals shown in Fig. 7 and their further quantitative analysis given hereafter refer to these suitable validation windows.

The accuracy of the calibration uncertainty provided in Sect. 4 can be assessed by comparing the mean spectral residuals to their estimated uncertainty (blue lines in Fig. 7c). In addition to the calibration uncertainty according to Sect. 4, the residual uncertainty given in Fig. 7 contains several further contributions. These contributions describe the atmospheric-state uncertainty and further contributions related to the solar FTIR spectral radiance measurements. A detailed assessment of this closure uncertainty budget is given in Part 1, Sect. 6. In addition to the contributions listed in Part 1, the uncertainty contribution associated with the water continuum absorption has to be taken into account. Since no uncertainty is provided for the MT_CKD 2.5.2 model (Mlawer et al., 2012) used in the synthetic spectra calculation, the continuum error estimate was set to the difference between the upper and lower end of continuum results provided by recent studies, namely the studies by Ptashnik et al. (2012, 2013) and the MT_CKD 2.5.2 model. A more detailed description of these data sets is given in Part 3.

As visible in Fig. 7c, the mean residuals show very good consistency with the estimated uncertainty. More specifically, a fraction of 97.7 % of the residual values lies within the 2σ residual uncertainty estimate. The mean residuals correspond to 1.2 % of the measured radiance at each spectral point on average for the suitable comparison windows. This extensive agreement of the mean residuals with the uncertainty estimate further substantiates the calibration uncertainty budget presented in Sect. 4. However, the closure analysis relies on an accurate representation and a comprehensive uncertainty budget of the atmospheric optical depth obtained via the LBLRTM calculations. This uncertainty budget is presented in detail in Sect. 6 of the companion paper Part 1. A comparison of the model results to the atmospheric OD derived directly from the Langley measurements shows very good agreement within the uncertainties as outlined in Sect. 4 of the companion paper Part 3. Note that since for both Langley calibration and model calculations the same extra-atmospheric solar spectrum is used, the closure analysis does not provide information on the accuracy of the ESS used. In addition to the calibration uncertainty, further sources of radiance uncertainty contribute in the closure setup, e.g., IWV uncertainty or uncertainties related to the water vapor continuum. Therefore, the closure analysis does not enable a full validation of the calibration uncertainty budget. Instead, the analysis provides an indication that the calibration uncertainty budget excluding the ESS contribution presented in Sect. 4 contains no major underestimation of the real uncertainty.