FTIR instruments record mid-infrared solar transmission spectra at high spectral resolution. The spectra contain the signatures of molecular rotational–vibrational transitions of numerous trace gases (including ozone) in the terrestrial atmosphere as they absorb solar radiation. The spectra are analyzed to measure the total columns as well as vertical concentration of these trace gases in the atmosphere using the pressure and temperature dependence of the absorption line shapes. For ozone, the FTIR vertical sensitivity is good from the surface to approximately 50 km . The retrieval strategy is based on the inversion method developed by , and the details are described in . An important aspect of the method is the necessity of a priori vertical profiles of both the target gas and interfering species (species that have absorption lines in the same spectral window considered for the analysis of the target gas) as well as the a priori covariance matrices of the target gas (and interfering species). The vertical information is characterized by the averaging kernel A, defined through 1x=xa+Ax^-xa+ϵx, which relates the retrieved state vector x to the true state x^ and the a priori state vector xa, where ϵx contains the measurement and forward model errors. As an example, Fig.  shows the averaging kernel for one measurement relative to the a priori. Additionally, the figure shows the sensitivity of the retrieval, which is the sum of the rows of the averaging kernel and indicates the contribution of the measurement to the retrieval compared to the contribution of the a priori. Zero sensitivity would mean that only the a priori contributes to the retrieved profile and the retrieved profile is independent from the real profile. These a priori profiles are additionally shown in Fig. , which, for FTIR, is the same for every retrieval irrespective of when the spectrum is taken.

The selection of lines from the full solar spectrum (also called microwindows), the a priori information, and the spectroscopic database all influence the retrieved ozone profile, and thus their treatment requires great care and they have been harmonized within the InfraRed Working Group (IRWG; https://www2.acom.ucar.edu/irwg, last access: 18 November 2024) of the international collaboration NDACC . The amount of vertical information that can be obtained is quantified by the degrees of freedom for signal (DOFS), which is the trace of the averaging kernel matrix. The total DOFS depend on this retrieval strategy but of course also on which gas is retrieved and the instrument with which it is observed. For the ozone measurements at Lauder, the total DOFS are typically around 4 to 4.5.

Since the ozone retrieval strategy plays a crucial rule in the information that can be obtained from the spectra, we use new retrieval strategy throughout this work, which is explained in more detail in Appendix . Whenever we use the older FTIR strategy as laid out in , for example to compare to previous studies, this will explicitly be stated using “FTIR V08” to avoid confusion.

For each of the measurements, we need to consider the instrument uncertainties during the intercomparison study (see Table ). These are divided into systematic uncertainties and random uncertainties, which capture the accuracy and the precision of the measurement, respectively. The sources of the FTIR random uncertainties are the measurement noise, errors in the forward model parameters, and the smoothing error due to the low vertical resolution. This smoothing error, however, is considered separate from the other errors as suggested by the NDACC IRWG. For FTIR, the biggest contribution, apart from the smoothing error, to the random uncertainty is typically from the temperature profile . In the case of the systematic uncertainty, the largest contribution actually comes from the spectroscopic database. Specifically, the ozone line strength parameter has the biggest uncertainty in the FTIR retrievals. We set it to 3 % . While the ozone infrared line intensities have been improved to better match the UV cross-sections, with an accuracy of 1 % for the more intense lines, the systematic uncertainties for the weaker lines are still set to 2 %–5 % . The FTIR choice of microwindows includes both intense and weak lines, with different dependence on pressure and temperature, which ensures obtaining the desired vertical information (4–5 DOFS). As explained in more detail in , the assumed uncertainty sources are propagated to an uncertainty in the retrieved profile following the technique of , which is captured by a full error covariance matrix Sx. Additionally, the smoothing error is calculated from the averaging kernel and the a priori covariance matrix Sa through 2Usmooth=A-ISaA-IT, with I the unit matrix and Sa obtained from the Whole Atmosphere Community Climate Model WACCM; as an estimation for the error covariance. With this information we can assess which errors dominate at which altitudes, which we have calculated for 1 year of data at Lauder. We see that the smoothing error always has the largest contribution in the troposphere. Concerning the other random errors, the uncertainty in the temperature profile has the second-biggest contribution, followed by the measurement noise. Above 25 km, the random uncertainty is usually dominated by the temperature profile. As for the contributions to the systematic uncertainty, as mentioned above, the largest contribution comes from the spectroscopic parameters; most notably the line strength parameter (around 3 %), followed by the spectroscopic pressure and temperature broadening parameters, respectively (around 1 %–2 %). The uncertainty in the temperature profile also plays a role in the contribution to the total systematic uncertainty, starting to become more important above 25 km.

The microwave ozone radiometer at Lauder measures the spectrum produced by a thermally excited rotational ozone transition at 110.836 GHz. Similar to the FTIR retrieval method described above, the profile retrieval makes use of the change in pressure broadening as a function of altitude with a vertical extent between approximately 20 and 50 km. The DOFS here, also computed from the trace of the averaging kernel matrix, are higher than those of FTIR at around 7. An example of the MWR averaging kernel is shown in Fig. . The experimental technique was described in , and technical details on the instrument used for this work are given in .

A formal error analysis for the microwave ozone measurements was presented in , and error estimates for Lauder were updated in . The net precision was determined to be 5 %–7 % between 56 and 1.3 hPa, and the accuracy is 7 %–9 %. The vertical resolution of the Lauder measurements is ∼ 6–8 km (FWHM, full-width at half-maximum) near 10 hPa. Vertical profiles are provided up to 68 km; however, retrievals in the mesosphere have somewhat degraded accuracy, precision, and vertical resolution relative to those in the stratosphere.

The Umkehr method of estimating the vertical profile of ozone using the Dobson ozone spectrophotometer has been performed since the early 1930s (; ), and the Umkehr measurements are some of the longest vertical profile records of ozone collected. The Umkehr method is performed using the “C” wavelength pair of the Dobson ozone spectrophotometer taken during zenith sky measurements at 12 nominal solar zenith angles (SZAs) across the range of 60–90°. A prism inside the Dobson breaks down the sunlight spectra and a pair of slits rejects light outside a narrow band of chosen wavelengths. The C wavelength pair consists of a “short” wavelength (centered on 311.5 nm) and a “long” wavelength (centered on 332.4 nm). In this range of wavelengths of UV light, absorption by ozone decreases with wavelength, creating differential observations between strong and non-absorbing solar spectra. The log of the ratio of measured intensities is called the N value. The N value changes between 90 and 60° SZA as the Sun rises or sets and the instrument records the so-called “Umkehr” curve that is sensitive to the vertical ozone distribution above the instrument.

The current NOAA operational Umkehr retrieval algorithm uses the absorption cross-section with its temperature dependence. The profiles are derived using the optimal estimation technique that includes the a priori ozone profile from ozone climatology , measurement error, and a priori uncertainties which define the averaging kernels and vertical resolution of retrieved profiles (see Fig.  for an example of averaging kernels for Umkehr). The measurements allow vertical information to be retrieved from the surface to approximately 50 km. The vertical information that we can get from the averaging kernel matrix for the typical Umkehr measurements gives DOFS of around 3.5.

The Lauder Umkehr record is homogenized by the method described in to create a coherent record for the long-term trend analysis of monthly mean anomalies. The method includes a correction to the Umkehr profiles for the stray light that is outside of the nominal band-pass of the Dobson instrument but is not completely filtered out by slits. The record is homogenized using the MERRA-2 GMI (Modern-Era Retrospective Analysis for Research Applications version 2 Global Modeling Initiative) model as a reference to minimize step changes in the record caused by a change in the optical characteristics of the instrument. Individual N values have a correction factor at each SZA as described in .

A full uncertainty analysis of the Umkehr observations at Lauder is currently not available, but we can estimate the uncertainties from similar measurements at Boulder, CO, USA, using the same technique (see Table  for the random and systematic uncertainties used in this study). This provides us with an analysis of the measurement noise as well as the smoothing error as a function of altitude. This measurement noise is calculated from simulated MERRA-2 GMI profiles with added random noise based on the error matrix of Umkehr observations. Considering that the measurement noise is only part of the random error in the remote observations, this estimated uncertainty is an underestimation of the true random error. The smoothing error is calculated using Eq. () with Sa from the climatology described in .

Umkehr total column ozone (from now dubbed Umkehr TCO) is integrated from the vertical profiles supplied by the Umkehr retrieval algorithm. The retrieved integrated Umkehr TCO is constrained by the algorithm to be within the measurement uncertainty of the observed TCO from the Dobson measurements. Additionally, regular TCO measurements are made with the Dobson ozone spectrophotometer (from now dubbed Dobson TCO) using the log of the ratio of solar irradiances made during either direct-Sun or zenith sky measurements made at regular nominal times (usually one near local solar noon, one in the morning, and one in the afternoon). Dobson TCO is typically derived from the A (305.5 and 325 nm) and D (317.5 and 339.9 nm) or C and D wavelength pairs, with corrections made for Rayleigh scattering and air mass . The use of double pairs is designed to minimize the influence from aerosol scattering and clouds. The precision of the Dobson measurement from direct-Sun observations is around 1 %, with an accuracy estimated to be around 5 % . It can be seen in Fig.  that the sampling of the Umkehr is reduced compared to direct Dobson TCO measurements. Therefore, for the total column comparisons with FTIR, the Dobson TCO will be preferred to the Umkehr integrated columns.

The Lauder stratospheric ozone lidar is a differential absorption lidar (DIAL) that was installed by RIVM (Rijksinstituut voor Volksgezondheid en Milieu) and began measurements in 1994. This lidar system and first results are described in . It relies on two different beams to extract information about the vertical ozone distribution from approximately 10 to 50 km in altitude. It uses an XeCl excimer laser for the primary 308 nm beam and a 2 m Raman cell of hydrogen gas at 1.3 bar to produce a 353 nm beam. The 308 nm light is moderately absorbed by ozone, while the 353 nm light acts as the reference beam. The time of flight from pulse emission through detection gives the vertical distribution information, and the abundance is computed from the ratio of 308 and 353 nm backscattered light signals. Over the instrument's multi-decadal lifetime, a number of intercomparisons have been staged with the NDACC traveling standard ozone lidar e.g.,. Currently, measurements are available up to July 2021, when the excimer laser failed. The lidar measurements are well resolved in altitude, with the resolution standardized within NDACC according to . This resolution ranges from a few hundred meters at 10 km to several kilometers in the upper stratosphere at 50 km. Concerning the lidar uncertainties (see Table ), there is a systematic uncertainty of approximately 3 %, which is mainly associated with uncertainty in the determination of the temperature-dependent absorption cross-section differential. The assumed random uncertainty for lidar, on the other hand, comes from the photon-counting noise.

Ozonesondes are small balloon-borne instruments carried by weather balloons and attached to radiosondes to measure the vertical ozone distribution from the surface to altitudes between 30 and 35 km. The ozonesondes launched in Lauder since 1986 are electrochemical concentration cell (ECC) ozonesondes. In these ozonesondes, a small gas sampling pump forces the ambient air through the cells that are filled with a neutral-buffered potassium iodide sensing solution. The principle of the ozone measurement is then based on the titration of ozone in this solution so that each O₃ molecule causes (ideally) two electrons to flow in the external circuit. This measured electrical current can then be converted to ozone partial pressure by knowing the gas volume flow rate of and the temperature in the pump. At Lauder, ozonesondes from the two different ECC ozonesonde manufacturers (SPC and EnSci; switch made in May 1994) have been launched, and different sensing solution types (SST1.0 and SST0.5; changed in August 1996) have been used as well. As biases exist between the different manufacturer ozonesonde types and between different sensing solution types, the Lauder ozonesonde time series had to be corrected for such biases. Additionally, the location of the pump temperature sensor changed throughout the years, which should also be homogenized. These additional processing steps have been taken into account in the reprocessed, homogenized Lauder ozonesonde time series here, following the Ozonesonde Data Quality Assessment guidelines of . More details on the Lauder ozonesonde time series and the homogenization procedure can be found in Fig. 1, Table 1, and Appendix A of . The quoted overall precision and uncertainty of ozonesonde measurements are 3 %–5 % and 5 %–10 %, respectively see WMO/GAW;. The systematic uncertainties for the ozonesonde measurements in this study have presumably been removed thanks to the homogenization process. The random uncertainty in the measured ozone partial columns for the ozonesonde is shown in Table . A mean value of the uncertainties in the profile is taken to represent the uncertainty in the partial columns, which is likely an overestimation of the actual uncertainty, giving values between 4 % and 7 %.

In a worldwide ozonesonde comparison with satellite and ground‐based total column ozone and with satellite stratospheric O₃ profiles, mentioned a negative ozone bias in the homogenized Lauder ozonesonde time records in more recent years. This feature might be related to the so-called “post-2013 drop-off in total ozone” identified in a number of ozonesonde stations (not Lauder) in , but, as no clear cause has been determined yet, no correction strategy has been implemented in the WMO/GAW 2021 homogenization procedures applied here. While do not identify Lauder as a drop-off site, in this study we will discuss the implications of a potential 3 % post-2016 drop-off in TCO for the trend and drift values of the ozonesonde measurements. Our TCO measurements for the ozonesondes are shown in Fig.  where a post-2016 drop-off could be present, but it is better seen in a comparison to satellites at https://acd-ext.gsfc.nasa.gov/anonftp/acd/shadoz/nletter/stations_vs_satellites_timeseries.zip (last access: 18 November 2024).

Another TCO measurement available at Lauder is UV2 , which is based on a Bentham UV spectrometer. UV2 makes alternating measurements of UV global and direct-Sun irradiance, and the direct-Sun spectra are then combined with Dobson-like slit functions and used to calculate ozone using the Dobson method. In , UV2 ozone was shown to closely agree with Dobson TCO, with a mean bias between them of 2.57 DU and a standard deviation of 1.15 DU. The precision of UV2 is therefore assumed to be consistent with the Dobson TCO at 1 %; the accuracy, determined by the mean daily standard deviation, is also calculated to be approximately 5 %. UV2 observations are available from 2012–2022 and throughout the day.

Not all measurements share the same observation time, vertical extent, or vertical resolution. In order to perform a meaningful intercomparison between the various instruments, a consistent validation setup is necessary. For example, because the DOFS of several instruments are low, we do not have well-resolved information on the ozone concentration with altitude. Therefore, the vertical range is subdivided into altitude layers, where we measure “partial columns” of ozone. Similar to the approach in , these partial columns are defined by looking at the vertical information from the reference FTIR measurements as well as the altitude boundaries at which every other instrument measures. We disregard profiles from MWR, lidar, or ozonesonde if they stop in the middle of a partial column such that no discontinuity needs to be accounted for in the intercomparison. Ideally, the partial columns should have approximately 1 DOFS to ensure that the retrieved information comes mainly from the measurement and not from the a priori partial columns, meaning that for a total of ∼ 4.5 DOFS for the FTIR profile, we can define four altitude layers. The first layer is defined from the surface (∼ 0.5 km) to 11 km (corresponding to the mean tropopause height at Lauder; ), the second from 14 km (the onset of most lidar observations) to 22 km, the third from 22 to 29 km, and the last from 29 to 42 km. This upper limit is chosen such that the partial column covers all lidar observations and no extrapolation is needed, which would be the case if the upper limit were chosen to be higher. This way, all FTIR observations have around 1 DOFS per partial column. From the ozone profiles we then integrate the partial columns, ending up with one tropospheric column and three stratospheric columns (from now on labeled “lower”, “middle”, and “upper” stratosphere). In the troposphere we can compare FTIR, Umkehr, and ozonesonde measurements. In the lower stratosphere we additionally have the lidar measurements. In the middle stratosphere we can compare all measurements, and in the upper stratosphere we compare FTIR, Umkehr, MWR, and lidar observations. Because of the lower average DOFS of the Umkehr measurements, the DOFS of the defined partial layers do not always reach 1: we get on average 0.5, 0.6, 0.7, and 1.1 from the troposphere up to the upper stratosphere. For MWR, we can calculate the DOFS for the partial layers from the averaging kernels as well to get average values of 1.1 in the middle stratosphere and 2.2 in the upper stratosphere.

Table  summarizes this division of partial columns and provides information on the DOFS and the median instrument uncertainties between 2001–2022. These uncertainties are divided into systematic uncertainties and random uncertainties (which includes the random smoothing error), which capture the accuracy and the precision of the measurement, respectively. For the remote sounding measurements, the uncertainties within the partial column reported in Table  are obtained from the uncertainties contained in the error covariance matrix Sx of the measurement by 3UPC=hTSxh, where h​​​​​​​ transforms the volume mixing ratio profiles to the appropriate partial columns, having values of zero at altitudes outside the boundaries of the partial column. If a full error covariance matrix is not available, such as with the Umkehr observations, we use the available error estimates which we know as a function of altitude. These values are then used to calculate the errors for partial columns by taking a weighted average, similar to the process described above.

In order to perform a comparison between two measurements we need to take into account the different vertical resolution of the instruments. The passive, remote sounding instruments (FTIR, Umkehr, MWR) have different averaging kernels as well as a priori, which are both important to relate the retrieved state to the true state, as is seen in Eq. (). As already mentioned, we always perform the comparisons with respect to FTIR because these measurements provide total columns as well as partial columns from the surface up to 50 km. Before integrating the partial columns to be compared, we transform the vertical profiles according to the vertical resolution following . We can distinguish two cases depending on the resolution of the compared instrument.

The observations are not taken simultaneously, so a choice has to be made in constructing pairs of observations. The construction is done by considering each separate measurement of Umkehr, MWR, lidar, or ozonesonde and finding the FTIR measurement which lies within a time window around the observing time of the other instrument, where the window itself depends on the instrument we compare to. The choice of the time windows is elaborated on in Appendix . By choosing observation pairs as opposed to the full datasets, we automatically select the same time sampling of both instruments when calculating the bias and long-term drift. This leads to a time window of 6 h for Umkehr, ozonesondes, Dobson, and UV2; 12 h for lidar; and 3 h for MWR.

If more than one FTIR measurement falls within the time window of another observation, all these FTIR measurements are averaged. Because we do this, the random uncertainty associated with the measurements will be reduced. If there are N measurements within the comparison window, then the random error is reduced by N for this particular comparison. If both measurement techniques have multiple measurements in the same day that fall within the time window (for example, one or more FTIR measurements are taken within 3 h from two different MWR measurements), then the FTIR measurements that fall in this overlap are used for comparison in both observation pairs.

Now that we have defined the validation setup to perform the intercomparison, we can analyze the time series of the various ground-based measurements compared to FTIR. The first metric for our validation between the ground-based instruments is the bias. The bias M that we will report here is the median value (where we choose the median over the mean because of its robust nature with respect to outliers) of the full time series of the relative differences: 6Δrel=PCX-PCFTIRPCFTIR⋅100%,

7M=medΔrel, where we consider the total or partial column (PC) of FTIR and a second measurement X. Before we use the relative differences to produce the results, we filter for outliers which fall beyond the 3σ deviation. Additionally, to analyze the precision within the intercomparison, we use the MAD (median absolute deviation), which is the median of the absolute deviations from the overall median. 8MADs=1.4826⋅medabsΔrel-M Here it is seen that we always use the scaled MAD_s with a constant factor of 1.4826. This scaling factor makes the MAD representative as a deviation from the median, similarly as the standard deviation is to the average, in the case of a normal distribution . We are not dealing with perfect Gaussian distributions, but the factor still creates a reasonable value for the scatter. The MAD_s is thus similar to using the standard deviation but is more robust in the sense that it will be less affected by outliers. In order to put the bias and MAD_s in perspective, we will compare these to the combined systematic and random uncertainties of the two involved instruments, respectively. These combined uncertainties are calculated by 9σcomb=σFTIR2+σX2, where σ can signify either the systematic or random uncertainty. However, if we are dealing with the comparison of two remote sounding instruments (Umkehr and MWR), the simple combination of Eq. () is not sufficient because we also need to account for the smoothing error from the retrieval. Because the averaging kernels are not unit matrices, the total combined errors will be correlated. From , we find the covariance of the difference Scomb to be 10Scomb=AFTIR-AFTIRAXSaAFTIR-AFTIRAXT+SFTIR+AFTIRSXAFTIRT. This equation includes the separate errors in the covariances SFTIR and SX as the last two terms and includes the different averaging kernels AFTIR and AX, which account for the smoothing error of both retrievals in the a priori covariance matrix Sa.

For every pair of comparisons we give the numbers of the median and scaled MAD_s of the partial column relative differences as well as the combined random and systematic uncertainties in Table . Also, the Pearson correlation coefficient between the individual time series in time coincidence (see Sect. 3.3) is shown as a measure of the measurements' agreement and their capacity to capture the ozone variability. We also give the Pearson correlation between the monthly anomalies of each time series in order to remove strong seasonality, which could drive the correlation. The anomalies are constructed by taking a relative difference of the ozone column with the mean ozone column of the same month over the full time series. The last column shows the number of observation pairs that are used for the intercomparison, indicating the reduced sample size compared to the full time series of the observations. The results in this table will be discussed in the following sections where we consider the total column and each partial column defined above separately, reporting on these biases and dispersion.

In our study, we also want to obtain the difference in total and partial column trends between the measurements (drift). In the analysis of these relative differences between two measurements within one observation pair, we simply apply a linear fit to the time series. Deseasonalizing the time series is not necessary because we are dealing with differences of ozone measurements at the same location, so the ozone variability is canceled out. The slope of the linear trend in the relative differences quantifies the drift. We fit the relative differences between monthly means of data in coincidence Y(t) as 11Y(t)=A0+A1t, with A0 the intercept, A1 giving the drift, and time t being given in fractional years. The monthly means are first calculated from the two measurements separately, after which we take the relative difference, as in Eq. (). We have tested the possibility of including a seasonal cycle in the regression analysis, in the case that a seasonal cycle in the differences appears, but it turned out to be barely significant with no impact on the obtained drifts themselves. The 2σ trend error obtained from the fit is corrected with the autocorrelation of the residuals, according to . This results in a higher uncertainty if any correlation remains in the residuals of the fit. This trend uncertainty has the form 12Udrift=2σA1N-2Neff-2, with σA1 the standard deviation of the fit parameter A1, N the degrees of freedom (not to be confused with DOFS from a retrieval) representing the length of the monthly mean time series, and Neff=N1-R1+R in which R is the correlation coefficient between the residuals of two consecutive time steps. This error will be used to express our confidence in the drift values obtained in the results. Here “significant” actually refers to a high certainty of the drift value at a 95 % confidence interval. Similarly, “non-significant” refers to only medium to very low confidence in the obtained result. This terminology will be used from now on in the paper.

We summarize the obtained drift and uncertainty for each measurement with respect to FTIR in Table . Additionally, Figs.  and show the time series of the relative differences within the intercomparison together with the trend analysis. Figure  visualizes the obtained drifts in absolute units for the total column as well as all partial columns. These values are obtained by performing the same trend fitting procedure for the absolute differences of the monthly means in Dobson units (DU).