3.2.1 Approach

For the first method, an artificial light source is used as target that is located at a far distance (around 1 to 2 km) from the instrument's telescope and typically close to the visible horizon. Since this method uses an artificial light source, the elevation scan across this target has to be done during nighttime.

During the CINDI-2 campaign, a xenon lamp was used as light source, and it was placed at around 1280 m distance from the measurement site in the main viewing direction of the MAX-DOAS instruments at an azimuth angle of 287^∘ (upper panel of Fig. 3). The lamp was put in the focal point of a large-aperture lens with a diameter of 17 cm, which was achieved by minimising the size of the light beam (this was already done prior to the campaign). Then the lamp was manually directed towards the campaign site. Here, it should be noted that the exact pointing is not critical as long as the instruments are located within the light cone. It was assumed that the diameter of the lens is homogeneously bright. Also, this assumption is not a critical point, because the angle under which the full lens is seen from the campaign site is smaller than 0.01^∘.

Using the connected water channels located next to both the measurement site and the lamp site, we could determine and mark the vertical position of the lamp at the measurement site (lamp mark in the lower panel of Fig. 3). Therefore, the light of a laser level was projected onto a folding rule which was placed in the nearby channels. In that way, first the height difference between lamp and the channel's water surface could be determined. Since all channels were connected to each other (except one step which was determined in the same way), the lamp position could be marked on the containers as indicated in the lower panel of Fig. 3. Thus, the height difference Δh between the optical units of the instruments and the lamp mark could be determined. This Δh was then used to infer the expected elevation angles β of the lamp relative to the horizontal lines of the optical units of the individual MAX-DOAS systems. The layout of the measurement conditions and the measurement geometry are summarised in Fig. 3.

Figure 4(a) Xenon lamp spectrum recorded on 13 September 2016 by the MPIC instrument. The three distinct emission lines at 365.16, 404.90 and 435.96 nm, which are used for the analysis, are clearly visible. (b) Intensity curve at 435.96 nm (blue solid line) recorded on 13 September by the MPIC instrument. The obtained centre of mass is indicated by the dashed blue line. Further, the centre obtained by a Gaussian fit and the corresponding fit are displayed in red.

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Such xenon lamp measurements were done on several days (8, 10, 13 and 19 September) throughout the campaign, although not all instruments participated on all nights. In the next section, the analysis of the lamp measurements is explained in more detail using data from the MPIC instrument.

Figure 5Sketch of the fibre bundle placed in the focal point of the telescope of the MPIC instrument. The grey parts indicate the gladding (additional 20 µm) of the fibres. The white circles represent the light-conducting part of the single glass fibres with a diameter of 200 µm, while the yellow spot indicates the idealised image (neglecting aberration and other effects) of the xenon lamp inside the telescope, which has a diameter of 7 µm. Note that the size of the yellow dot is not shown at the correct scale relative to the fibre diameter and is larger than in reality.

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3.2.2 Results for the MPIC instrument

Data from the far-lamp measurements are available for four nights for the MPIC instrument. On all of these nights, a fixed elevation calibration (same 0^∘ motor position) was used and the scan resolution was 0.02^∘ (except on 8 September, when the scan resolution was 0.1^∘ as indicated in the last column of Table 2). For the MPIC instrument, the pre-calibration of the elevations was done using a water level during the setup of the instrument. Then finer adjustments were performed using the results of the far-lamp scans from 7 (in this night the lamp measurements were tested by our group with a scan resolution of 0.1^∘ but the scanning was done manually), 8 and 10 September. All elevations of the MPIC instrument in this paper are given relative to the elevation calibration, which was obtained by these finer adjustments and which was finally used for the regular measurements.

In the following, the analysis is done for three wavelengths, which are distributed over the detector range of the instrument and correspond to strong emission lines of the xenon lamp. An example spectrum of the xenon lamp which was measured on 13 September is shown in Fig. 4a. The three distinct emission lines at 365.16, 404.90 and 435.96 nm that were used for the analysis are clearly visible.

As first step of the analysis, the measured intensities are normalised with respect to their total integration time and linearly interpolated between the two detector pixels closest to each of the three selected wavelengths. These intensities are then plotted against the elevation angle for the different scans. As an example, the intensity curve at 435.96 nm obtained for 13 September is shown in Fig. 4b. The curve obviously shows a minimum where a maximum would be expected if we assume a Gaussian-shaped curve. However, we can understand this feature when we take into consideration that in the focal point of the telescope, a quartz glass fibre bundle is mounted as illustrated in Fig. 5. First, we calculate the size of the image of the xenon lamp inside the instrument's telescope (yellow spot in Fig. 5). Given the geometry of the measurement setup, namely the diameter of the xenon lamp and the dimensions of the telescope, this leads to an image size of around 7 µm at the entrance of the fibre bundle. Taking into account that the glass fibre bundle consists of four individual fibres with a light-conducting diameter of 200 µm each, the obtained image size is only 3.5 % of a single fibre diameter. In that way, it is possible that the image of the lamp hits the space between the individual fibres when performing an elevation scan (dashed line in Fig. 5 indicates the idealised scan axis) and therefore an intensity minimum is found when exactly pointing at the light source. These calculations were done assuming idealised conditions (fibre exactly located in the focus, no aberration of the lens, etc.) and the resulting image of the xenon lamp would lead to a much more pronounced and wider minimum than the one in Fig. 4b. However, in reality the lens has an aberration and the fibre bundle might be located not exactly in the focus of the lens; further, the scan axis might not pass through the centre of the fibre bundle. These effects lead to a less symmetric intensity distribution which does not reach zero intensity at its centre (Fig. 4b).

Table 2Overview of the lamp elevations obtained for all days and different wavelengths for the MPIC instrument. Additionally, the scan resolution is indicated in the last column.

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In order to determine the elevation angle $\widehat{\mathit{\alpha }}$ under which the xenon lamp could be seen, the centre of the intensity curve (dashed blue line in Fig. 4b) is calculated using the centre of mass formula:

where s_i denotes the intensity measured at the elevation angle α_i. Using this equation yields a lamp elevation of 0.02^∘ for the intensity curve shown in Fig. 4b. Here, it should be noted that Fig. 4b shows the intensity curve of an elevation scan that was performed by approaching the elevation angles from below. For scans where the angles were approached from above, the centres are found consistently at lower elevations by around 0.4^∘. Because of that, we assured that all elevation angles were approached from below for the other calibration exercises since this was the scanning direction prescribed by the regular measurement protocol. It should be mentioned that depending on the kind of stepper or motor, not all instruments suffered from such backlash issues. Some, actively corrected for this by using inclinometers (e.g. LMU and IUP-HD) or active sun trackers (e.g. BIRA). Besides that, most of the instruments which experienced backlash issues solved them by simply scanning always from the same direction (in elevation and azimuth direction). The effect of backlash (maximum difference between both scanning directions) ranges from fractions of a degree to roughly 1^∘. While this effect is very important for the elevations of the instruments, the effect has a much smaller influence on the measurements in the azimuth direction.

Figure 6Sketch of the measurement setup for the near-lamp measurements and the alignment of telescope and lamp.

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Figure 7Measured intensities for the three individual scans (coloured dots) and the fitted Gaussian (red solid line) obtained from the near-lamp measurements by the IUP-HD instrument in the UV spectral range.

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Equation (1) is used to calculate the centres of the intensity curves for all three wavelengths and all 4 d. The corresponding lamp positions are summarised in Table 2. Taking into account that the minimum motor step size is 0.01^∘, the different values are consistent with each other within the span from −0.01 to 0.02^∘ (excluding 8 September, when the scan resolution was only 0.1^∘). Here, it should be noted that the centre of a Gaussian fit (see red fit curve in Fig. 4b) yields consistent lamp elevations compared to the centre of mass approach which was applied here. Therefore, also for the MPIC instrument, a Gaussian fit is used in Sect. 4.1, where the lamp scans of all instruments are analysed in a consistent way.

Figure 8Panels (a) and (c) show the normalised intensity curves for the horizon scans performed by the MPIC instrument throughout the campaign at 340 and 440 nm, respectively. The coloured solid lines indicate the respective Gaussian integral fits. Panels (b) and (d) show the normalised derivatives of the respective intensity curves. The median centres of the horizon scans are represented by the dashed red lines.

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As already mentioned above, the position of the artificial light source relative to the instrument has to be known very accurately in order to calibrate the elevation angles of the MAX-DOAS system. Based on the setup summarised in Fig. 3, an expected lamp elevation of around $-\mathrm{0.04}{}^{\circ }$ is obtained, when using an estimated height difference, Δh, of 1 m between the xenon lamp and the telescope unit. The total error in the determination of the lamp mark (error of ±0.2 m) and the height difference Δh (error of ±0.3 m) is estimated to be around ±0.5 m, which translates to an uncertainty of $\pm \mathrm{0.02}{}^{\circ }$ in the expected lamp position. Further, the Earth's curvature at a distance of 1280 m corresponds already to $-\mathrm{0.011}{}^{\circ }$ and is therefore not negligible. Adding this offset to the obtained lamp elevation, the MPIC MAX-DOAS system should find the lamp at around $-\mathrm{0.05}{}^{\circ }$ elevation. If we compare this value to the values given in Table 2, we can conclude that the instrument sees the lamp close to the expected position. The small deviations between the table values and the expected elevation can be explained by a combination of several small uncertainties, namely the minimum motor step size of 0.01^∘, the used scan resolution of 0.02^∘ and the uncertainties of the calculation of the lamp position $\widehat{\mathit{\alpha }}$ using Eq. (1). Further, also the determination of the expected lamp elevation has an uncertainty as outlined above.

Figure 9Sketch of the measurement setup used by MPIC for the white-stripe scans and the alignment of the telescope and white stripe using a water level.

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The relatively small span of lamp positions obtained on different days and at multiple wavelengths indicates that this method is very stable and reproducible. Furthermore, this approach allows for the calibration of several instruments with the same setup at the same time, since all instruments can point at the same target. However, depending on the slight horizontal distances of the different measurement locations, small differences in the azimuth angle (up to 1.8^∘ for the CINDI-2 campaign) under which the lamp can be seen have to be taken into account. A drawback of this method is that the position of the artificial light source relative to the instrument has to be determined accurately, which might be challenging or even impossible at some locations. Also, finding a suitable location for the lamp can be difficult, e.g. in cities.

3.3.1 Approach

This method also uses an artificial light source (mercury-vapour lamp) during nighttime, but here it is located rather close to the instrument's telescope (a few metres). In order to determine the expected lamp position, namely $\mathit{\beta }=\mathrm{0}{}^{\circ }$, the light source has to be aligned to the (centre of the) telescope unit of the instrument. This alignment is typically done using a laser level which illuminates both the instrument and the position of the lamp. The telescope and the lamp are then centred around the position of the laser beam. The levelling accuracy of the laser level which was used during CINDI-2 was tested in the laboratory and amounts to approximately 0.1^∘. Further, the laser beam has a thickness of about 2 mm, which translates to another 0.04^∘ uncertainty in the relative vertical positions between instrument and lamp. Both the setup and the alignment procedure are sketched in Fig. 6. Using this procedure, the light source should be found at 0^∘ elevation and possible deviations from that position can be used to correct the elevation calibration.

Such near-lamp measurements were not performed for the MPIC instrument during the CINDI-2 campaign. However, the elevation angles of the IUP-HD instrument were calibrated using this method. Therefore, in the following, data from the IUP-HD instrument are used to illustrate this method and its analysis in more detail.

3.3.2 Results for the IUP-HD instrument

Three such near-lamp scans were done by the IUP-HD group in one night in the preparation phase of the CINDI-2 campaign. Mean intensities are calculated separately for the UV and VIS spectrometers of the IUP-HD instrument. The first two scans were performed in an elevation range from −2 to 2^∘, while the last was done in a range from −1 to 0.45^∘. Since the elevation pointing is continuously regulated by comparison of the orientation of the telescope measured by the built-in tilt sensor with the nominal angle, no backlash effects are expected. In order to analyse these measurements, the (normalised) mean intensities are plotted against the elevation angle α reported by the measuring system. Next, a Gaussian function of the form

is fitted to the intensities and the centre $\widehat{\mathit{\alpha }}$ of this function represents the lamp elevation. Further, S(α) represents the fitted intensity at a given elevation, A represents an intensity offset and B describes the maximum of the fitted curve. The width of the fitted curve is controlled by the parameter σ. For improving the statistics, all three scans are plotted in one plot (using different colours for the individual scans), and the Gaussian fit is applied to the whole data set of one spectrometer (Fig. 7).

The retrieved lamp elevation is also shown in this figure. Following this procedure, lamp elevations $\widehat{\mathit{\alpha }}$ of −0.14 and $-\mathrm{0.11}{}^{\circ }$ were found in the UV and visible spectral range, respectively. These lamp elevations can now be used to adjust the initial elevation calibration of the instrument.

3.4.1 Approach

A common method for the calibration of the elevation angles of MAX-DOAS systems is the so-called horizon scan. Here, the elevation β of the visible horizon, which is defined as the transition of the tree tops to the open sky, is used as reference. Since this method does not require an active light source, it can be performed during daytime and the variation in the measured intensity at the horizon is used to determine its position. A Gaussian integral is fitted to the measured intensities and the fit parameters give the horizon position. In practice, sometimes the numerical derivative of the intensity curve is calculated since below the horizon the intensity does not approach zero but the rapid change of the measured intensity allows for the identification of the horizon position $\widehat{\mathit{\alpha }}$. Prerequisites of this method (despite the knowledge of the expected elevation of the visible horizon) are high visibility, the absence of rapidly varying and/or low-lying clouds, and a clear and rapid change in intensity at the visible horizon, which might not be fulfilled during episodes of fog, when the horizon might be blurred. If these conditions are not fulfilled, no clear conclusions can be drawn from horizon scans. Furthermore, the visible horizon should not be too far away (less than a few kilometres) to minimise the influence of atmospheric scattering.

During the CINDI-2 campaign, horizon scans were included in the measurement protocol in order to study the consistency and stability of the elevation calibration of the different measurement systems. Thus, all MAX-DOAS instruments (both 1-D and 2-D) performed horizon scans between 11:40 and 11:45 UTC at a specified total integration time of 5 s while pointing in the main viewing direction (287^∘ azimuth angle). The scans were done using predefined elevation angles between $-\mathrm{5}{}^{\circ }$ and 5^∘, whereby the scan resolution was 0.2^∘ in the interval between −2^∘ and 2^∘ and 1^∘ outside this range.

3.4.2 Results for the MPIC instrument

For the MPIC instrument, horizon scan data are available starting from 17 September until 2 October. Before 17 September some horizon scans were performed as well, but they are of limited quality due to an error in the measurement script of the MPIC system. Further, some days are not used either due to bad weather conditions with fog and many low clouds or due to known pointing problems. Overall, useful horizon scan data are available on 10 d for the MPIC instrument.

First, the measured intensity is normalised with respect to the total integration time. As a second step, the intensity curves are also normalised to their corresponding maximum, allowing a direct comparison of the intensity curves recorded on different days with various sky conditions. The normalised intensity curves obtained at 340 nm for the different days are shown in Fig. 8a (coloured dots). Here, the increase in the measured intensity around the horizon is clearly visible in an elevation range from around 0 to 1^∘. Next, a Gaussian integral of the form

is fitted to the data since this approach is more stable than calculating a numerical derivative. Here, S represents the fitted intensity; α the elevation angle; and the parameters A, B, C, and D determine the exact form of the fitted curve. The parameter $\widehat{\mathit{\alpha }}$ indicates the centre of the fitted function and therefore represents the derived horizon elevation. The resulting daily fit functions are also displayed in Fig. 8a by lines in the corresponding colours.

Additionally, the analytical derivative of Eq. (3) can be calculated. The resulting curves, which are displayed in Fig. 8b, contain information on the instrument's field of view (FOV) since the full width at half maximum (FWHM), which is a typical measure for the FOV, can be derived:

By following this procedure, a value of 0.30^∘ is found as the median centre (vertical red line in Fig. 8) for the fitted functions representing the median horizon elevation for the MPIC instrument at 340 nm. However, there is quite some scatter in the daily horizon scans, which might be caused by varying sky conditions on the different days and is one of the drawbacks of this method. The same procedure is also applied to the intensities recorded at 440 nm in order to study possible wavelength dependencies, the resulting intensity curves and derivatives are shown in Fig. 8c and d. Here, a median horizon elevation of 0.37^∘ is obtained, which is slightly higher than the value for 340 nm. These two wavelengths were chosen for the analysis, because they were reported by all instruments that participated in the semi-blind intercomparison during the campaign, and thus they are well suited for a comparison of the horizon scan results for different instruments, which is explained in Sect. 4.2.

3.5.1 Approach

The white-stripe method can also be applied under daylight conditions and a white or at least bright stripe in front of a black or dark background is used as reference target. In order to calibrate the elevation angles, the (centre of the) white stripe has to be aligned with the (centre of the) telescope, archiving an expected stripe position of $\mathit{\beta }=\text{0}{}^{\circ }$. This can be done by using a water or laser level.

The setup applied by MPIC during the CINDI-2 campaign used an adjustable white stripe in front of a dark plate and a large water level, which consisted of two bottles of water which were connected via a 10 m long tube filled with water and positioned next to the stripe and the telescope. On the telescope side, the water level has to be adjusted to the middle of the telescope; thus, on the plate stripe side the water level indicates the altitude of the telescope. Here, the stripe has to be adjusted to the water level position, which guarantees the alignment of stripe and telescope axis. A sketch of the described setup can be found in Fig. 9. The horizontal distance between the telescope and the white stripe was 342 cm, and the vertical extension of the stripe was around 2.5 cm, which corresponds to a FOV of around 0.4^∘. This apparent FOV is quite large and shows that the setup was not optimised, but the rather short distance between telescope and stripe was determined by the local conditions (a water channel in front of the instrument container limited the maximum distance which could be achieved). Therefore, this calibration method using the here-described setup was applied only once during the campaign and only for the MPIC instrument. However, other groups (e.g. BIRA) applied the same method using their own setups. The scan resolution was 0.05^∘, which was a compromise between speed (needed because of the unstable setup) and accuracy. In the following, the analysis is done for two wavelengths, namely 340 and 440 nm, in order to be consistent with the approach described in Sect. 3.4.

Figure 10Background-corrected intensity curve at 440 nm and corresponding Gaussian fit for the white-stripe scan on 20 September performed by the MPIC instrument. The retrieved apparent stripe positions for the two methods are indicated by the dashed lines.

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3.5.2 Results for the MPIC instrument

Again, the recorded intensities are first normalised with respect to their total integration time. Next, a background correction is applied to the intensity curves, which is needed since the dark background of the white stripe does not absorb all incident light. For that, a second-order polynomial is fitted to the background intensities and subtracted from the measured intensities. The resulting intensity curve at 440 nm and the fitted Gaussian function (compare Eq. 2) are depicted in Fig. 10. Now, the centre $\widehat{\mathit{\alpha }}$ of the Gaussian fit indicates the stripe position. In that way, a value of $-\mathrm{0.01}{}^{\circ }$ is found (dashed red line). Since the intensity curve again shows no smooth behaviour (see Sect. 3.2), additionally the centre of mass approach following Eq. (1) is applied, yielding a stripe position of $-\mathrm{0.02}{}^{\circ }$ (dashed blue line) consistent with the Gaussian approach. Conducting the same procedure for the intensities measured at 340 nm yields values of 0.02 and 0.00^∘ for the Gaussian and centre of mass approaches, respectively.

In summary, a range of −0.02 to 0.02^∘ for the retrieved stripe positions is obtained, which corresponds to only four motor steps. Similarly to the far-lamp measurements (Sect. 3.2), this range can be explained by the minimum motor step size of 0.01^∘, the used scan resolution of 0.05^∘ and the uncertainties of the retrieval of the stripe position $\widehat{\mathit{\alpha }}$. Further, an error of ±5 mm in the alignment between telescope and stripe was estimated, which translates to an uncertainty of $\pm \mathrm{0.08}{}^{\circ }$. Finally, also the angular height (0.4^∘) of the white stripe was quite large.

4.1.1 Full 2-D scans

The first group consists of 2-D instruments which performed full 2-D scans of the xenon lamp in vertical (elevation angle) and horizontal (azimuth angle) direction on at least one night. For these instruments, the measured intensities are first normalised with respect to integration time and interpolated to specific wavelengths in order to compare the results of the different methods and instruments. Column (a) of Fig. 11 shows representative examples of the obtained 2-D intensity distributions for the BIRA, IUP-HD, UToronto and LMU (for this instrument only the mean intensities of the spectra are available) instruments, respectively. Additionally, black dotted lines indicating the azimuth angle under which the maximum intensity was recorded can be found in these figures. The axes of these sub-figures were chosen in a way that they all show the same relative elevation (1^∘) and azimuth span (1.2^∘). While the BIRA instrument shows a very smooth and smeared-out distribution of the measured intensities; the intensity distributions are more sharp for the UToronto (still quite smooth), IUP-HD and LMU instruments. This finding can be explained by the fibre configurations inside the telescope units of the four instruments since they have an influence on the actual shape of the measured intensity distributions. While the LMU and IUP-HD instruments used a ring of fibres inside their telescope units (for the UV channel), the UToronto and the BIRA UV instruments used a spot configuration, consisting of 37 and 51 fibres, respectively. When scanning across the xenon lamp, it might occur that the FOV is not always fully illuminated at the “edges” of the xenon lamp light beam. The ring configuration might be more sensitive (similarly to the fibre effect found for the MPIC instrument in Sect. 3.2) to this effect and introduce more edges to the measured 2-D intensity distributions, leading to a sharper shape. Further, differences in the motor pointing precisions have an effect on the apparent FOVs.

Figure 11(a) shows examples of the 2-D intensity distributions for the BIRA UV (at 365 nm, measured on 10 September), IUP-HD UV (at 365 nm, measured on 13 September), UToronto (at 436 nm, measured on 10 September) and LMU (mean intensity, measured on 10 September) instruments. (b) and (c) show the corresponding transects along the dashed black lines in (a) and the azimuthal sum of the intensities at the different elevations, respectively. Additionally, the respective Gaussian fits and their centres are indicated.

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Two approaches were applied to retrieve the elevation under which the lamp is found for this first group of instruments. For the first approach, the intensities along a transect (black dotted lines in column a) are extracted and a Gaussian function (Eq. 2) is fitted to these intensities. The centres $\widehat{\mathit{\alpha }}$ of these fits represent the lamp elevations; the intensity curves and Gaussian fits for the four examples can be found in column (b) of Fig. 11. For the second approach, all intensities which were recorded at one specific elevation angle are integrated over the different azimuth angles. These values are then used for the analysis, and again the centre of a Gaussian fit indicates the vertical position of the light source. Column (c) of Fig. 11 depicts the resulting curves and fits for the four instruments. The results of the two methods are very consistent for a single instrument. Nevertheless, there is quite some spread between the different instruments, which will be investigated in more detail at the end of this section.

4.1.2 Cross-scans

The second group contains 2-D instruments which performed cross-scans, meaning that first an azimuth scan was performed followed by an elevation scan at the azimuth direction under which the maximum intensity was found. This was done by three instruments using individual scanning schemes. Examples of the obtained intensity curves and corresponding Gaussian fits are depicted in Fig. 12. The different panels of this figure show the curves; fits; and resulting centres for the AUTH (a), BOKU (b), and IUP-B (c) instruments, respectively. The results for the lamp position are rather consistent for the different scans for an individual instrument since the obtained centres are nearly the same. This is also valid when looking at the results for different wavelengths for one instrument (not shown here). However, it can be seen that there is some spread between the different instruments.

Figure 12(a) Intensity curves at 365 nm recorded on 10 September by the AUTH instrument. (b) Intensity curves at 546 nm recorded on 13 September by the BOKU instrument. (c) Intensity curve at 546 nm recorded on 13 September by the IUP-B visible instrument.

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4.1.3 1-D scans

The last group consists of 1-D instruments which performed simple elevation scans of the xenon lamp as described in Sect. 3.2. For these instruments, the normalised intensity is plotted against the elevation angle, and the centre of a Gaussian fit gives the lamp elevation. Examples for the CMA_UV, CMA_VIS, BSU and AIOFM instruments are shown in Fig. 13, with the resulting lamp elevations (centres) also displayed. Since the BSU instrument has a 2-D CCD on which the second dimension represents the elevation angle, this instrument did not really scan across the lamp, but each image on the CCD represents a full lamp scan. The AIOFM instrument is a 2-D instrument, but it was operated in 1-D mode for the far-lamp measurements.

4.1.4 Analysis of the far-lamp scans

For each participating instrument, the intensity curves are extracted for all valid lamp measurements by applying the respective procedure explained above for different wavelengths (365, 405, 436 and 546 nm) corresponding to the individual spectral ranges of the instruments. Further, a Gaussian function (Eq. 2) is fitted to the data. The fit parameters are initialised by A₀=0, B₀=maximum of the measured intensity curve, ${\widehat{\mathit{\alpha }}}_{\mathrm{0}}=\text{centre of mass}$ (calculated using Eq. 1) and ${\mathit{\sigma }}_{\mathrm{0}}=\mathrm{0.5}{}^{\circ }$.

Figure 13(a) Intensity curve at 436 nm recorded on 19 September by the CMA_UV instrument. (b) Intensity curve at 546 nm recorded on 19 September by the CMA_VIS instrument. (c) Intensity curve at 365 nm recorded on 10 September by the BSU instrument. (d) Intensity curve at 365 nm recorded on 8 September by the AIOFM instrument.

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The resulting lamp elevations are summarised in Fig. 14, where the mean of all retrieved lamp elevations (at different wavelengths, scans and/or days) for each instrument is shown as dots. Further, for each instrument, three different measures for the uncertainties of the retrieved lamp elevations are displayed. The left error bar of each instrument indicates the mean of all fit errors of the fits explained above and measures the quality of the individual fits and the shape of the measured curves. The standard error of the mean of all retrieved lamp elevations is represented by the middle error bar. It is a measure of the consistency and stability of the results of the different lamp scans performed by one instrument. This quantity also depends on the actual number of available intensity curves at different wavelengths and days, which is given in brackets behind the institute acronyms on the x axis in Fig. 14. Lastly, the right error bar indicates the daily spread, which is only available for instruments which performed more than one scan on 1 d and for all 2-D instruments, since two methods were applied to extract the 1-D intensity curves. The daily spread of 1 d is defined as the standard deviation of the results of the different scans on that day. If in addition several days are available, the mean of the daily standard deviations is calculated and displayed.

As shown in Fig. 14, a rather high spread of around 0.9^∘ is found for the retrieved lamp elevations. Nevertheless, the values are centred around the expected values of $-\mathrm{0.19}{}^{\circ }$ (dashed blue line) and $-\mathrm{0.05}{}^{\circ }$ (dashed green line) for the instruments located on the upper (mostly 2-D instruments) and lower (mostly 1-D instruments) row of containers installed at Cabauw, respectively. These expected values were calculated as described in Sect. 3.2, where a Δh of 1 m was estimated for the instruments located on the lower row of containers (Fig. 3). The instruments on the second row of containers are placed around 3 m higher than the instruments on the lower row, and therefore the same calculations yield an expected lamp position of $-\mathrm{0.19}{}^{\circ }$. Further, most of the error bars for the individual instruments are quite small, indicating the good stability and repeatability of the far-lamp measurements. The large error bar for the mean fit error for the LMU instrument can be explained by a rather uneven intensity distribution, which leads to bad fit results in some cases.

The deviations between the different instruments are on the one hand caused by slightly different vertical positions (even if they are located on the same container level) of the instruments, since some of the instruments were mounted on tripods or similar devices, while other instruments were placed closer to the container roof. On the other hand, the deviations are also caused by the fact that all groups reported their elevation angles corresponding to their own elevation calibrations. Therefore, the spread of about 0.9^∘ of the retrieved lamp elevations (for one container level) is a measure of variability between the elevation calibrations of the different instruments.

More details will be discussed in Sect. 4.3, where the derived lamp elevations are compared to the corresponding horizon elevations obtained from the daily horizon scans, which are inter-compared in the next section.

Figure 14Overview of the retrieved lamp elevations for the 2-D and 1-D instruments including different measures of their uncertainty, mean of fit errors (left), error of the mean (middle) and daily spread (right). The number of available lamp scans for each instrument is displayed in brackets after the individual institute acronyms. The expected lamp elevations are indicated by the corresponding dashed lines.

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