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Optical resonators are used in spectroscopic measurements of atmospheric trace gases to establish long optical path lengths L with enhanced absorption in compact instruments. In cavity-enhanced broad-band methods, the exact knowledge of both the magnitude of L and its spectral dependency on the wavelength λ is fundamental for the correct retrieval of trace gas concentrations. L(λ) is connected to the spectral mirror reflectivity R(λ), which is often referred to instead. L(λ) is also influenced by other quantities like broad-band absorbers or alignment of the optical resonator. The established calibration techniques to determine L(λ), e.g. introducing gases with known optical properties or measuring the ring-down time, all have limitations: limited spectral resolution, insufficient absolute accuracy and precision, inconvenience for field deployment, or high cost of implementation. Here, we present two new methods that aim to overcome these limitations: (1) the narrow-band cavity ring-down (NB-CRD) method uses cavity ring-down spectroscopy and a tunable filter to retrieve spectrally resolved path lengths L(λ); (2) integrated calibration by means of optical modulation (ICOM) allows the determination of the optical path length at the spectrometer resolution with high accuracy in a relatively simple setup. In a prototype setup we demonstrate the high accuracy and precision of the new approaches. The methods facilitate and improve the determination of L(λ), thereby simplifying the use of cavity-enhanced absorption spectroscopy.

Knowledge of the atmospheric boundary layer state and evolution is important for understanding air pollution and low-level cloud development, among other things. There are a number of instruments and methods that are currently used to estimate boundary layer height (BLH). However, no single instrument is capable of providing BLH measurements in all weather conditions. We proposed a method to derive a daytime convective BLH using clear air echoes in radar observations and investigated the consistency of these retrievals between different radar frequencies. We utilized data from three vertically pointing radars that are available at the SMEAR II station in Finland, i.e. the C band (5 GHz), Ka band (35 GHz) and W band (94 GHz). The Ka- or W-band cloud radars are an integral part of cloud profiling stations of pan-European Aerosol, Clouds and Trace Gases Research Infrastructure (ACTRIS). Our method will be utilized at ACTRIS stations to serve as an additional estimate of the BLH during summer months. During this period, insects and Bragg scatter are often responsible for clear air echoes recorded by weather and cloud radars. To retrieve a BLH, we suggested a mechanism to separate passive and independently flying insects that works for all analysed frequency bands. At the lower frequency (the C band) insect scattering has been separated from Bragg scattering using a combination of the radar reflectivity factor and linear depolarization ratio. Retrieved values of the BLH from all radars are in a good agreement when compared to the BLH obtained with the co-located HALO Doppler lidar and ERA5 reanalysis data set. Our method showed some underestimation of the BLH after nighttime heavy precipitation yet demonstrated a potential to serve as a reliable method to obtain a BLH during clear-sky days. Additionally, the entrainment zone was observed by the C-band radar above the CBL in the form of a Bragg scatter layer. Aircraft observations of vertical profiles of potential temperature and water vapour concentration, collected in the vicinity of the radar, demonstrated some agreement with the Bragg scatter layer.

The second Cabauw Intercomparison of Nitrogen Dioxide measuring Instruments (CINDI-2) took place in Cabauw (the Netherlands) in September 2016 with the aim of assessing the consistency of multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements of tropospheric species (NO2, HCHO, O3, HONO, CHOCHO and O4). This was achieved through the coordinated operation of 36 spectrometers operated by 24 groups from all over the world, together with a wide range of supporting reference observations (in situ analysers, balloon sondes, lidars, long-path DOAS, direct-sun DOAS, Sun photometer and meteorological instruments). In the presented study, the retrieved CINDI-2 MAX-DOAS trace gas (NO2, HCHO) and aerosol vertical profiles of 15 participating groups using different inversion algorithms are compared and validated against the colocated supporting observations, with the focus on aerosol optical thicknesses (AOTs), trace gas vertical column densities (VCDs) and trace gas surface concentrations. The algorithms are based on three different techniques: six use the optimal estimation method, two use a parameterized approach and one algorithm relies on simplified radiative transport assumptions and analytical calculations. To assess the agreement among the inversion algorithms independent of inconsistencies in the trace gas slant column density acquisition, participants applied their inversion to a common set of slant columns. Further, important settings like the retrieval grid, profiles of O3, temperature and pressure as well as aerosol optical properties and a priori assumptions (for optimal estimation algorithms) have been prescribed to reduce possible sources of discrepancies. The profiling results were found to be in good qualitative agreement: most participants obtained the same features in the retrieved vertical trace gas and aerosol distributions; however, these are sometimes at different altitudes and of different magnitudes. Under clear-sky conditions, the root-mean-square differences (RMSDs) among the results of individual participants are in the range of 0.01–0.1 for AOTs, (1.5–15) ×1014molec.cm-2 for trace gas (NO2, HCHO) VCDs and (0.3–8)×1010molec.cm-3 for trace gas surface concentrations. These values compare to approximate average optical thicknesses of 0.3, trace gas vertical columns of 90×1014molec.cm-2 and trace gas surface concentrations of 11×1010molec.cm-3 observed over the campaign period. The discrepancies originate from differences in the applied techniques, the exact implementation of the algorithms and the user-defined settings that were not prescribed. For the comparison against supporting observations, the RMSDs increase to a range of 0.02–0.2 against AOTs from the Sun photometer, (11–55)×1014molec.cm-2 against trace gas VCDs from direct-sun DOAS observations and (0.8–9)×1010molec.cm-3 against surface concentrations from the long-path DOAS instrument. This increase in RMSDs is most likely caused by uncertainties in the supporting data, spatiotemporal mismatch among the observations and simplified assumptions particularly on aerosol optical properties made for the MAX-DOAS retrieval. As a side investigation, the comparison was repeated with the participants retrieving profiles from their own differential slant column densities (dSCDs) acquired during the campaign. In this case, the consistency among the participants degrades by about 30 % for AOTs, by 180 % (40 %) for HCHO (NO2) VCDs and by 90 % (20 %) for HCHO (NO2) surface concentrations. In former publications and also during this comparison study, it was found that MAX-DOAS vertically integrated aerosol extinction coefficient profiles systematically underestimate the AOT observed by the Sun photometer. For the first time, it is quantitatively shown that for optimal estimation algorithms this can be largely explained and compensated by considering biases arising from the reduced sensitivity of MAX-DOAS observations to higher altitudes and associated a priori assumptions.

We present the inter-comparison of delta slant column densities (SCDs) and vertical profiles of nitrous acid (HONO) derived from measurements of different multi-axis differential optical absorption spectroscopy (MAX-DOAS) instruments and using different inversion algorithms during the Second Cabauw Inter-comparison campaign for Nitrogen Dioxide measuring Instruments (CINDI-2) in September 2016 at Cabauw, the Netherlands (51.97∘ N, 4.93∘ E). The HONO vertical profiles, vertical column densities (VCDs), and near-surface volume mixing ratios are compared between different MAX-DOAS instruments and profile inversion algorithms for the first time. Systematic and random discrepancies of the HONO results are derived from the comparisons of all data sets against their median values. Systematic discrepancies of HONO delta SCDs are observed in the range of ±0.3×1015 molec. cm−2, which is half of the typical random discrepancy of 0.6×1015 molec. cm−2. For a typical high HONO delta SCD of 2×1015 molec. cm−2, the relative systematic and random discrepancies are about 15 % and 30 %, respectively. The inter-comparison of HONO profiles shows that both systematic and random discrepancies of HONO VCDs and near-surface volume mixing ratios (VMRs) are mostly in the range of ∼±0.5×1014 molec. cm−2 and ∼±0.1 ppb (typically ∼20 %). Further we find that the discrepancies of the retrieved HONO profiles are dominated by discrepancies of the HONO delta SCDs. The profile retrievals only contribute to the discrepancies of the HONO profiles by ∼5 %. However, some data sets with substantially larger discrepancies than the typical values indicate that inappropriate implementations of profile inversion algorithms and configurations of radiative transfer models in the profile retrievals can also be an important uncertainty source. In addition, estimations of measurement uncertainties of HONO dSCDs, which can significantly impact profile retrievals using the optimal estimation method, need to consider not only DOAS fit errors, but also atmospheric variability, especially for an instrument with a DOAS fit error lower than ∼3×1014 molec. cm−2. The MAX-DOAS results during the CINDI-2 campaign indicate that the peak HONO levels (e.g. near-surface VMRs of ∼0.4 ppb) often appeared in the early morning and below 0.2 km. The near-surface VMRs retrieved from the MAX-DOAS observations are compared with those measured using a co-located long-path DOAS instrument. The systematic differences are smaller than 0.15 and 0.07 ppb during early morning and around noon, respectively. Since true HONO values at high altitudes are not known in the absence of real measurements, in order to evaluate the abilities of profile inversion algorithms to respond to different HONO profile shapes, we performed sensitivity studies using synthetic HONO delta SCDs simulated by a radiative transfer model with assumed HONO profiles. The tests indicate that the profile inversion algorithms based on the optimal estimation method with proper configurations can reproduce the different HONO profile shapes well. Therefore we conclude that the features of HONO accumulated near the surface derived from MAX-DOAS measurements are expected to represent the ambient HONO profiles well.

In September 2016, 36 spectrometers from 24 institutes measured a number of key atmospheric pollutants for a period of 17 d during the Second Cabauw Intercomparison campaign for Nitrogen Dioxide measuring Instruments (CINDI-2) that took place at Cabauw, the Netherlands (51.97∘ N, 4.93∘ E). We report on the outcome of the formal semi-blind intercomparison exercise, which was held under the umbrella of the Network for the Detection of Atmospheric Composition Change (NDACC) and the European Space Agency (ESA). The three major goals of CINDI-2 were (1) to characterise and better understand the differences between a large number of multi-axis differential optical absorption spectroscopy (MAX-DOAS) and zenith-sky DOAS instruments and analysis methods, (2) to define a robust methodology for performance assessment of all participating instruments, and (3) to contribute to a harmonisation of the measurement settings and retrieval methods. This, in turn, creates the capability to produce consistent high-quality ground-based data sets, which are an essential requirement to generate reliable long-term measurement time series suitable for trend analysis and satellite data validation. The data products investigated during the semi-blind intercomparison are slant columns of nitrogen dioxide (NO2), the oxygen collision complex (O4) and ozone (O3) measured in the UV and visible wavelength region, formaldehyde (HCHO) in the UV spectral region, and NO2 in an additional (smaller) wavelength range in the visible region. The campaign design and implementation processes are discussed in detail including the measurement protocol, calibration procedures and slant column retrieval settings. Strong emphasis was put on the careful alignment and synchronisation of the measurement systems, resulting in a unique set of measurements made under highly comparable air mass conditions. The CINDI-2 data sets were investigated using a regression analysis of the slant columns measured by each instrument and for each of the target data products. The slope and intercept of the regression analysis respectively quantify the mean systematic bias and offset of the individual data sets against the selected reference (which is obtained from the median of either all data sets or a subset), and the rms error provides an estimate of the measurement noise or dispersion. These three criteria are examined and for each of the parameters and each of the data products, performance thresholds are set and applied to all the measurements. The approach presented here has been developed based on heritage from previous intercomparison exercises. It introduces a quantitative assessment of the consistency between all the participating instruments for the MAX-DOAS and zenith-sky DOAS techniques.

Cavity-enhanced differential optical absorption spectroscopy (CE-DOAS or BB-CEAS DOAS) allows us to make in situ measurements while maintaining the kilometre-long light paths required by DOAS. This technique has been successfully used for several years to measure in situ atmospheric trace gases. A property of optical cavities is that in the presence of strong absorbers or scatterers the light path is reduced, in contrast to classical long-path DOAS measurements where the light path is fixed. Typical CE-DOAS or BB-CEAS evaluation schemes correct this effect using the measured total light intensity attenuation. This makes them sensitive to any variations in the light intensity not arising from the trace gas absorption. That means an important DOAS advantage, to be independent of total light intensity, is actually lost. In order to cope with this problem, the instrument setup would require a thorough stabilisation of the light source and a very rigid mechanical setup, which would make instrumentation more complex and error prone. We present a new approach to cavity-enhanced (CE) DOAS based on an iterative algorithm (ICAD) which actually models the light path reduction from the derived absorbers in the optical resonator. It allows a sensitive and robust data analysis that does not depend on the total light intensity, allowing a simpler and more compact instrument setup. The algorithm is discussed and simulated measurements demonstrate its sensitivity and robustness. Furthermore, a new ICAD NO2 instrument is presented. It takes advantage of the advanced data evaluation to build a compact (50 cm cavity) and lightweight instrument ( kg) with low power consumption (25 W) for sensitive measurements of NO2 with a detection limit of 0.02 ppbv at an averaging time of 7 min. The instrument is characterised with a NO2 calibration source and good long-term stability is demonstrated in a comparison with a commercial chemiluminescence detector. As a new application of ICAD we show measurements on an automobile platform to investigate the two-dimensional NO2 distribution in an urban area. The instrument is so robust that even strong vibrations do not lead to any measurement problems.

In this study the consistency between MAX-DOAS measurements and radiative transfer simulations of the atmospheric O4 absorption is investigated on 2 mainly cloud-free days during the MAD-CAT campaign in Mainz, Germany, in summer 2013. In recent years several studies indicated that measurements and radiative transfer simulations of the atmospheric O4 absorption can only be brought into agreement if a so-called scaling factor () is applied to the measured O4 absorption. However, many studies, including those based on direct sunlight measurements, came to the opposite conclusion, that there is no need for a scaling factor. Up to now, there is no broad consensus for an explanation of the observed discrepancies between measurements and simulations. Previous studies inferred the need for a scaling factor from the comparison of the aerosol optical depths derived from MAX-DOAS O4 measurements with that derived from coincident sun photometer measurements. In this study a different approach is chosen: the measured O4 absorption at 360 nm is directly compared to the O4 absorption obtained from radiative transfer simulations. The atmospheric conditions used as input for the radiative transfer simulations were taken from independent data sets, in particular from sun photometer and ceilometer measurements at the measurement site. This study has three main goals: first all relevant error sources of the spectral analysis, the radiative transfer simulations and the extraction of the input parameters used for the radiative transfer simulations are quantified. One important result obtained from the analysis of synthetic spectra is that the O4 absorptions derived from the spectral analysis agree within 1 % with the corresponding radiative transfer simulations at 360 nm. Based on the results from sensitivity studies, recommendations for optimised settings for the spectral analysis and radiative transfer simulations are given. Second, the measured and simulated results are compared for 2 selected cloud-free days with similar aerosol optical depths but very different aerosol properties. On 18 June, measurements and simulations agree within their (rather large) uncertainties (the ratio of simulated and measured O4 absorptions is found to be 1.01±0.16). In contrast, on 8 July measurements and simulations significantly disagree: for the middle period of that day the ratio of simulated and measured O4 absorptions is found to be 0.82±0.10, which differs significantly from unity. Thus, for that day a scaling factor is needed to bring measurements and simulations into agreement. Third, recommendations for further intercomparison exercises are derived. One important recommendation for future studies is that aerosol profile data should be measured at the same wavelengths as the MAX-DOAS measurements. Also, the altitude range without profile information close to the ground should be minimised and detailed information on the aerosol optical and/or microphysical properties should be collected and used. The results for both days are inconsistent, and no explanation for a O4 scaling factor could be derived in this study. Thus, similar but more extended future studies should be performed, including more measurement days and more instruments. Also, additional wavelengths should be included.

We present a new MAX-DOAS profiling algorithm for aerosols and trace gases, BOREAS, which utilizes an iterative solution method including Tikhonov regularization and the optimal estimation technique. The aerosol profile retrieval is based on a novel approach in which the absorption depth of O4 is directly used in order to retrieve extinction coefficient profiles instead of the commonly used perturbation theory method. The retrieval of trace gases is done with the frequently used optimal estimation method but significant improvements are presented on how to deal with wrongly weighted a priori constraints and for scenarios in which the a priori profile is inaccurate. Performance tests are separated into two parts. First, we address the general sensitivity of the retrieval to the example of synthetic data calculated with the radiative transfer model SCIATRAN. In the second part of the study, we demonstrate BOREAS profiling accuracy by validating the results with the help of ancillary measurements carried out during the CINDI-2 campaign in Cabauw, the Netherlands, in 2016. The synthetic sensitivity tests indicate that the regularization between measurement and a priori constraints is insufficient when knowledge of the true state of the atmosphere is poor. We demonstrate a priori pre-scaling and extensive regularization tests as a tool for the optimization of retrieved profiles. The comparison of retrieval results with in situ, ceilometer, NO2 lidar, sonde and long-path DOAS measurements during the CINDI-2 campaign always shows high correlations with coefficients greater than 0.75. The largest differences can be found in the morning hours, when the planetary boundary layer is not yet fully developed and the concentration of trace gases and aerosol, as a result of a low night-time boundary layer having formed, is focused in a shallow, near-surface layer.

Experience of differential atmospheric absorption spectroscopy (DOAS) shows that a spectral shift between measurement spectra and reference spectra is frequently required in order to achieve optimal fit results, while the straightforward calculation of the optical density proves inferior. The shift is often attributed to temporal instabilities of the instrument but implicitly solved the problem of the tilt effect discussed/explained in this paper. Spectral positions of Fraunhofer and molecular absorption lines are systematically shifted for different measurement geometries due to an overall slope – or tilt – of the intensity spectrum. The phenomenon has become known as the tilt effect for limb satellite observations, where it is corrected for in a first-order approximation, whereas the remaining community is less aware of its cause and consequences. It is caused by the measurement process, because atmospheric absorption and convolution in the spectrometer do not commute. Highly resolved spectral structures in the spectrum will first be modified by absorption and scattering processes in the atmosphere before they are recorded with a spectrometer, which convolves them with a specific instrument function. In the DOAS spectral evaluation process, however, the polynomial (or other function used for this purpose) accounting for broadband absorption is applied after the convolution is performed. In this paper, we derive that changing the order of the two modifications of the spectra leads to different results. Assuming typical geometries for the observations of scattered sunlight and a spectral resolution of 0.6 nm, this effect can be interpreted as a spectral shift of up to 1.5 pm, which is confirmed in the actual analysis of the ground-based measurements of scattered sunlight as well as in numerical radiative transfer simulations. If no spectral shift is allowed by the fitting routine, residual structures of up to 2.5 × 10−3 peak-to-peak are observed. Thus, this effect needs to be considered for DOAS applications aiming at an rms of the residual of 10−3 and below.

In order to promote the development of the passive DOAS technique the Multi Axis DOAS – Comparison campaign for Aerosols and Trace gases (MAD-CAT) was held at the Max Planck Institute for Chemistry in Mainz, Germany, from June to October 2013. Here, we systematically compare the differential slant column densities (dSCDs) of nitrous acid (HONO) derived from measurements of seven different instruments. We also compare the tropospheric difference of SCDs (delta SCD) of HONO, namely the difference of the SCDs for the non-zenith observations and the zenith observation of the same elevation sequence. Different research groups analysed the spectra from their own instruments using their individual fit software. All the fit errors of HONO dSCDs from the instruments with cooled large-size detectors are mostly in the range of 0.1 to 0.3 × 1015 molecules cm−2 for an integration time of 1 min. The fit error for the mini MAX-DOAS is around 0.7 × 1015 molecules cm−2. Although the HONO delta SCDs are normally smaller than 6 × 1015 molecules cm−2, consistent time series of HONO delta SCDs are retrieved from the measurements of different instruments. Both fits with a sequential Fraunhofer reference spectrum (FRS) and a daily noon FRS lead to similar consistency. Apart from the mini-MAX-DOAS, the systematic absolute differences of HONO delta SCDs between the instruments are smaller than 0.63 × 1015 molecules cm−2. The correlation coefficients are higher than 0.7 and the slopes of linear regressions deviate from unity by less than 16 % for the elevation angle of 1°. The correlations decrease with an increase in elevation angle. All the participants also analysed synthetic spectra using the same baseline DOAS settings to evaluate the systematic errors of HONO results from their respective fit programs. In general the errors are smaller than 0.3 × 1015 molecules cm−2, which is about half of the systematic difference between the real measurements.The differences of HONO delta SCDs retrieved in the selected three spectral ranges 335–361, 335–373 and 335–390 nm are considerable (up to 0.57 × 1015 molecules cm−2) for both real measurements and synthetic spectra. We performed sensitivity studies to quantify the dominant systematic error sources and to find a recommended DOAS setting in the three spectral ranges. The results show that water vapour absorption, temperature and wavelength dependence of O4 absorption, temperature dependence of Ring spectrum, and polynomial and intensity offset correction all together dominate the systematic errors. We recommend a fit range of 335–373 nm for HONO retrievals. In such fit range the overall systematic uncertainty is about 0.87 × 1015 molecules cm−2, much smaller than those in the other two ranges. The typical random uncertainty is estimated to be about 0.16 × 1015 molecules cm−2, which is only 25 % of the total systematic uncertainty for most of the instruments in the MAD-CAT campaign. In summary for most of the MAX-DOAS instruments for elevation angle below 5°, half daytime measurements (usually in the morning) of HONO delta SCD can be over the detection limit of 0.2 × 1015 molecules cm−2 with an uncertainty of ∼ 0.9 × 1015 molecules cm−2.

The differential optical absorption spectroscopy (DOAS) method is a well-known remote sensing technique that is nowadays widely used for measurements of atmospheric trace gases, creating the need for harmonization and characterization efforts. In this study, an intercomparison exercise of DOAS retrieval codes from 17 international groups is presented, focusing on NO2 slant columns. The study is based on data collected by one instrument during the Multi-Axis DOAS Comparison campaign for Aerosols and Trace gases (MAD-CAT) in Mainz, Germany, in summer 2013. As data from the same instrument are used by all groups, the results are free of biases due to instrumental differences, which is in contrast to previous intercomparison exercises.While in general an excellent correlation of NO2 slant columns between groups of > 99.98 % (noon reference fits) and > 99.2 % (sequential reference fits) for all elevation angles is found, differences between individual retrievals are as large as 8 % for NO2 slant columns and 100 % for rms residuals in small elevation angles above the horizon.Comprehensive sensitivity studies revealed that absolute slant column differences result predominantly from the choice of the reference spectrum while relative differences originate from the numerical approach for solving the DOAS equation as well as the treatment of the slit function. Furthermore, differences in the implementation of the intensity offset correction were found to produce disagreements for measurements close to sunrise (8–10 % for NO2, 80 % for rms residual). The largest effect of ≈ 8 % difference in NO2 was found to arise from the reference treatment; in particular for fits using a sequential reference. In terms of rms fit residual, the reference treatment has only a minor impact. In contrast, the wavelength calibration as well as the intensity offset correction were found to have the largest impact (up to 80 %) on rms residual while having only a minor impact on retrieved NO2 slant columns.

Knowledge of the field of view (FOV) of a remote sensing instrument is particularly important when interpreting their data and merging them with other spatially referenced data. Especially for instruments in space, information on the actual FOV, which may change during operation, may be difficult to obtain. Also, the FOV of ground-based devices may change during transportation to the field site, where appropriate equipment for the FOV determination may be unavailable. This paper presents an independent, simple and robust method to retrieve the FOV of an instrument during operation, i.e. the two-dimensional sensitivity distribution, sampled on a discrete grid. The method relies on correlated measurements featuring a significantly higher spatial resolution, e.g. by an imaging instrument accompanying a spectrometer. The method was applied to two satellite instruments, GOME-2 and OMI, and a ground-based differential optical absorption spectroscopy (DOAS) instrument integrated in an SO2 camera. For GOME-2, quadrangular FOVs could be retrieved, which almost perfectly match the provided FOV edges after applying a correction for spatial aliasing inherent to GOME-type instruments. More complex sensitivity distributions were found at certain scanner angles, which are probably caused by degradation of the moving parts within the instrument. For OMI, which does not feature any moving parts, retrieved sensitivity distributions were much smoother compared to GOME-2. A 2-D super-Gaussian with six parameters was found to be an appropriate model to describe the retrieved OMI FOV. The comparison with operationally provided FOV dimensions revealed small differences, which could be mostly explained by the limitations of our IFR implementation. For the ground-based DOAS instrument, the FOV retrieved using SO2-camera data was slightly smaller than the flat-disc distribution, which is assumed by the state-of-the-art correlation technique. Differences between both methods may be attributed to spatial inhomogeneities. In general, our results confirm the already deduced FOV distributions of OMI, GOME-2, and the ground-based DOAS. It is certainly applicable for degradation monitoring and verification exercises. For satellite instruments, the gained information is expected to increase the accuracy of combined products, where measurements of different instruments are integrated, e.g. mapping of high-resolution cloud information, incorporation of surface climatologies. For the SO2-camera community, the method presents a new and efficient tool to monitor the DOAS FOV in the field.

The instrumental spectral response function (ISRF) is a key quantity in DOAS analysis, as it is needed for wavelength calibration and for the convolution of trace gas cross sections to instrumental resolution. While it can generally be measured using monochromatic stimuli, it is often parameterized in order to merge different calibration measurements and to plainly account for its wavelength dependency. For some instruments, the ISRF can be described appropriately by a Gaussian function, while for others, dedicated, complex parameterizations with several parameters have been developed.Here we propose to parameterize the ISRF as a super-Gaussian, which can reproduce a variety of shapes, from point-hat to boxcar shape, by just adding one parameter to the classical Gaussian. The super-Gaussian turned out to describe the ISRF of various DOAS instruments well, including the satellite instruments GOME-2, OMI, and TROPOMI.In addition, the super-Gaussian allows for a straightforward parameterization of the effect of ISRF changes, which can occur on long-term scales as well as, for example, during one satellite orbit and impair the spectral analysis if ignored. In order to account for such changes, spectral structures are derived from the derivatives of the super-Gaussian, which are afterwards just scaled during spectral calibration or DOAS analysis. This approach significantly improves the fit quality compared to setups with fixed ISRF, without drawbacks on computation time due to the applied linearization. In addition, the wavelength dependency of the ISRF can be accounted for by accordingly derived spectral structures in an easy, fast, and robust way.

Scanning spectrometer networks using scattered solar radiation in the ultraviolet spectral region have become an increasingly important tool for monitoring volcanic sulfur dioxide (SO2) emissions. Often measured spectra are evaluated using the differential optical absorption spectroscopy (DOAS) technique. In order to obtain absolute column densities (CDs), the DOAS evaluation requires a Fraunhofer reference spectrum (FRS) that is free of absorption structures of the trace gas of interest. For measurements at volcanoes such a FRS can be readily obtained if the scan (i.e. series of measurements at different elevation angles) includes viewing directions where the plume is not seen. In this case, it is possible to use these viewing directions (e.g. zenith) as FRS. Possible contaminations of the FRS by the plume can then be corrected by calculating and subtracting an SO2 offset (e.g. the lowest SO2 CD) from all viewing directions of the respective scan. This procedure is followed in the standard evaluations of data from the Network for Observation of Volcanic and Atmospheric Change (NOVAC). While this procedure is very efficient in removing Fraunhofer structures and instrumental effects it has the disadvantage that one can never be sure that there is no SO2 from the plume in the FRS. Therefore, using a modelled FRS (based on a high-resolution solar atlas) has a great advantage. We followed this approach and investigated an SO2 retrieval algorithm using a modelled FRS. In this paper, we present results from two volcanoes that are monitored by NOVAC stations and which frequently emit large volcanic plumes: Nevado del Ruiz (Colombia) recorded between January 2010 and June 2012 and from Tungurahua (Ecuador) recorded between January 2009 and December 2011. Instrumental effects were identified with help of a principal component analysis (PCA) of the residual structures of the DOAS evaluation. The SO2 retrieval performed extraordinarily well with an SO2 DOAS retrieval error of 1 − 2 × 1016 [molecules cm−2]. Compared to a standard evaluation, we found systematic differences of the differential slant column density (dSCD) of only up to ≈ 15 % when looking at the variation of the SO2 within one scan. The major advantage of our new retrieval is that it yields absolute SO2 CDs and that it does not require complicated instrumental calibration in the field (e.g. by employing calibration cells or broadband light sources), since the method exploits the information available in the measurements.We compared our method to an evaluation that is similar to the NOVAC approach, where a spectrum that is recorded directly before the scan is used as an FRS and an SO2 CD offset is subtracted from all retrieved dSCD in the scan to correct for possible SO2 contamination of the FRS. The investigation showed that 21.4 % of the scans (containing significant amounts of SO2) at Nevado del Ruiz and 7 % of the scans at Tungurahua showed much larger SO2 CDs when evaluated using modelled FRS (more than a factor of 2). For standard evaluations the overall distribution of the SO2 CDs in a scan can in some cases indicate whether the plume affects all viewing directions and thus these scans need to be discarded for NOVAC emission rate evaluation. However, there are other cases where this is not possible and thus the reported SO2 emission rates would be underestimated. The new method can be used to identify these cases and thus it can considerably improve SO2 emission budgets.

In recent updates of the HITRAN water vapour H2O spectroscopic compilation covering the blue spectral region (here: 394–480 nm) significant changes for the absorption bands at 416 and 426 nm were reported. In order to investigate the consistency of the different cross-sections calculated from these compilations, H2O vapour column density ratios for different spectral intervals were retrieved from long-path and multi-axis differential optical absorption spectroscopy (DOAS) measurements. We observed a significant improvement of the DOAS evaluation when using the updated HITRAN water vapour absorption cross-sections for the calculation of the reference spectra. In particular the magnitudes of the residual spectra as well as the fit errors were reduced. However, we also found that the best match between measurement and model is reached when the absorption cross-section of groups of lines are scaled by factors ranging from 0.5 to 1.9, suggesting that the HITRAN water vapour absorption compilation still needs significant corrections. For this spectral region we present correction factors for HITRAN 2009, HITRAN 2012, HITEMP and BT2 derived from field measurements. Additionally, upper limits for water vapour absorption in the UV-A range from 330 to 390 nm are given.

In remote sensing applications, such as differential optical absorption spectroscopy (DOAS), atmospheric scattering processes need to be considered. After inelastic scattering on N2 and O2 molecules, the scattered photons occur as additional intensity at a different wavelength, effectively leading to "filling-in" of both solar Fraunhofer lines and absorptions of atmospheric constituents, if the inelastic scattering happens after the absorption. Measured spectra in passive DOAS applications are typically corrected for rotational Raman scattering (RRS), also called Ring effect, which represents the main contribution to inelastic scattering. Inelastic scattering can also occur in liquid water, and its influence on DOAS measurements has been observed over clear ocean water. In contrast to that, vibrational Raman scattering (VRS) of N2 and O2 has often been thought to be negligible, but it also contributes. Consequences of VRS are red-shifted Fraunhofer structures in scattered light spectra and filling-in of Fraunhofer lines, additional to RRS. At 393 nm, the spectral shift is 25 and 40 nm for VRS of O2 and N2, respectively. We describe how to calculate VRS correction spectra according to the Ring spectrum. We use the VRS correction spectra in the spectral range of 420–440 nm to determine the relative magnitude of the cross-sections of VRS of O2 and N2 and RRS of air. The effect of VRS is shown for the first time in spectral evaluations of Multi-Axis DOAS data from the SOPRAN M91 campaign and the MAD-CAT MAX-DOAS intercomparison campaign. The measurements yield in agreement with calculated scattering cross-sections that the observed VRS(N2) cross-section at 393 nm amounts to 2.3 ± 0.4 % of the cross-section of RRS at 433 nm under tropospheric conditions. The contribution of VRS(O2) is also found to be in agreement with calculated scattering cross-sections. It is concluded, that this phenomenon has to be included in the spectral evaluation of weak absorbers as it reduces the measurement error significantly and can cause apparent differential optical depth of up to 3 ×10−4. Its influence on the spectral retrieval of IO, glyoxal, water vapour and NO2 in the blue wavelength range is evaluated for M91. For measurements with a large Ring signal a significant and systematic bias of NO2 dSCDs (differential slant column densities) up to (−3.8 ± 0.4) × 1014 molec cm−2 is observed if this effect is not considered. The effect is typically negligible for DOAS fits with an RMS (root mean square) larger than 4 × 10−4.

Remote sensing via differential optical absorption spectroscopy (DOAS) has become a standard technique to identify and quantify trace gases in the atmosphere. Due to the wide range of measurement conditions, atmospheric compositions and instruments used, a specific challenge of a DOAS retrieval is to optimize the retrieval parameters for each specific case and particular trace gas of interest. Of these parameters, the retrieval wavelength range is one of the most important ones. Although for many trace gases the overall dependence of common DOAS retrieval on the evaluation wavelength interval is known, a systematic approach for finding the optimal retrieval wavelength range and quantitative assessment is missing. Here we present a novel tool to visualize the effect of different evaluation wavelength ranges. It is based on mapping retrieved column densities in the retrieval wavelength space and thus visualizing the consequences of different choices of spectral retrieval ranges caused by slightly erroneous absorption cross sections, cross correlations and instrumental features. Based on the information gathered, an optimal retrieval wavelength range may be determined systematically. The technique is demonstrated using examples of a theoretical study of BrO retrievals for stratospheric BrO and BrO measurements in volcanic plumes. However, due to the general nature of the tool, it is applicable to any type of DOAS retrieval (active or passive).