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Propane (C3H8) is an important trace gas in the atmosphere, as it is a proxy for oil and gas production and has a significant impact on atmospheric chemical reactions related to the hydroxyl radical and tropospheric ozone formation. In this study, solar direct absorption spectra near 2967 cm−1 recorded by a ground-based Fourier transform infrared spectrometer (FTIR) were applied to retrieve C3H8 total columns between June 2018 and July 2022 in Xianghe in north China. The systematic and random uncertainties of the C3H8 column retrieval are estimated to be 18.4 % and 18.1 %, respectively. The mean and standard deviation of the C3H8 columns derived from the FTIR spectra in Xianghe are 1.80 ± 0.81 (1σ) × 1015 molec. cm−2. Good correlations are found between C3H8 and other non-methane hydrocarbons, such as C2H6 (R=0.84) and C2H2 (R=0.79), as well as between C3H8 and CO (R=0.72). However, the correlation between C3H8 and CH4 is relatively weak (R=0.45). Moreover, the FTIR C3H8 measurements in Xianghe are also compared against MkIV measurements at several sites around the world. The new FTIR measurements in Xianghe provide us with insight into C3H8 column variations and the underlying processes in north China.

In this study, we carried out an independent validation of two methane retrieval algorithms using spectra from the Infrared Atmospheric Sounding Interferometer (IASI) that has been aboard the Meteorological Operational Satellite A (MetOp-A) since 2006. Both algorithms, one developed by the Laboratoire de Météorologie Dynamique (LMD), called the non-linear inference scheme (NLISv8.3), and the other by the Rutherford Appleton Laboratory (RAL), referred to as RALv2.0, provide long-term global CH4 concentrations using distinctively different retrieval approaches (neural network vs. optimal estimation, respectively). They also differ with respect to the vertical range covered, where LMD provides mid-tropospheric dry-air mole fractions (mtCH4), and RAL provides mixing ratio profiles from which we can derive total column-averaged dry-air mole fractions (XCH4) and potentially two partial column layers (qCH4). We compared both CH4 products using the Copernicus Atmospheric Monitoring Service (CAMS) model, in situ profiles (range extended using CAMS model data), and ground-based Fourier transform infrared (FTIR) remote-sensing measurements. The average difference (in mtCH4) with respect to in situ profiles for LMD ranges between −0.3 and 10.9 ppb, while for RAL the XCH4 difference ranges between −4.6 and −1.6 ppb. The standard deviation (SD) of the observed differences between in situ measurements and RAL retrievals is 14.1–21.9 ppb, which is consistently smaller than that between LMD retrievals and in situ measurements (15.2–30.6 ppb). By comparing with ground-based FTIR sites, the mean differences are within ±10 ppb for both RAL and LMD retrievals. However, the SD of the differences at the ground-based FTIR stations shows significantly lower values for RAL (11–15 ppb) than for LMD (about 25 ppb). The long-term trend and seasonal cycles of CH4 derived from the LMD and RAL products are further investigated and discussed. The seasonal variation in XCH4 derived from RAL is consistent with the seasonal variation observed by the ground-based FTIR measurements. However, the overall 2007–2015 XCH4 trend derived from RAL measurements is underestimated, if not adjusted, for an anomaly occurring on 16 May 2013 due to a L1 calibration change. For LMD, we see very good agreement at the (sub)tropics (° N–35° S) but notice deviations in the seasonal cycle (both in the amplitude and phase) and an underestimation of the long-term trend with respect to the RAL and reference data at higher-latitude sites.

The Copernicus Atmosphere Monitoring Service (CAMS) provides daily analyses and forecasts of the composition of the atmosphere, including the reactive gases such as O3, CO, NO2, HCHO and SO2; aerosol species; and greenhouse gases. The global CAMS analysis system (IFS-COMPO) is based on the ECMWF Integrated Forecasting System (IFS) for numerical weather prediction (NWP) and assimilates a large number of composition satellite products on top of the meteorological observations ingested in IFS. The CAMS system receives regular upgrades, following the upgrades of IFS. The last upgrade, Cy48R1, operational since 27 June 2023, was major with a large number of code changes, both for IFS-COMPO and for NWP. The main IFS-COMPO innovations include the introduction of full stratospheric chemistry; a major update of the emissions; a major update of the aerosol model, including the representation of secondary organic aerosol; several updates of the dust life cycle and optics; updates to the inorganic chemistry in the troposphere; and the assimilation of Visible Infrared Imaging Radiometer Suite (VIIRS) aerosol optical depth (AOD) and TROPOspheric Monitoring Instrument (TROPOMI) CO. The CAMS Cy48R1 upgrade was validated using a large number of independent measurement datasets, including surface in situ, surface remote sensing, routine aircraft, and balloon and satellite observations. In this paper we present the validation results for Cy48R1 by comparing them with the skill of the previous operational system (Cy47R3), with the independent observations as reference, for the period October 2022 to June 2023, during which daily forecasts from both cycles are available. Major improvements in skill are found for the ozone profile in the lower–middle stratosphere and for stratospheric NO2 due to the inclusion of full stratospheric chemistry. Stratospheric trace gases compare well with the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) observations between 10 and 200 hPa, with larger deviations between 1 and 10 hPa. The impact of the updated emissions is especially visible over East Asia and is beneficial for the trace gases O3, NO2 and SO2. The CO column assimilation is now anchored by the Infrared Atmospheric Sounding Interferometer (IASI) instead of the Measurements Of Pollution in The Troposphere (MOPITT) instrument, which is beneficial for most of the CO comparisons, and the assimilation of TROPOMI CO data improves the model CO field in the troposphere. In general the aerosol optical depth has improved globally, but the dust evaluation shows more mixed results. The results of the 47 comparisons are summarised in a scorecard, which shows that 83 % of the evaluation datasets show a neutral or improved performance of Cy48R1 compared to the previous operational CAMS system, while 17 % indicate a (slight) degradation. This demonstrates the overall success of this upgrade.

The Geostationary Environment Monitoring Spectrometer (GEMS) on board GEO-KOMPSAT-2B was launched in February 2020 and has been monitoring atmospheric chemical compositions over Asia. We present the first evaluation of the operational GEMS formaldehyde (HCHO) vertical column densities (VCDs) during and after the in-orbit test (IOT) period (August–October 2020) by comparing them with the products from the TROPOspheric Monitoring Instrument (TROPOMI) and Fourier-transform infrared (FTIR) and multi-axis differential optical absorption spectroscopy (MAX-DOAS) instruments. During the IOT, the GEMS HCHO VCDs reproduced the observed spatial pattern of TROPOMI VCDs over the entire domain (r= 0.62) with high biases (10 %–16 %). We found that the agreement between GEMS and TROPOMI was substantially higher in Northeast Asia (r= 0.90), encompassing the Korean Peninsula and east China. GEMS HCHO VCDs captured the seasonal variation in HCHO, primarily driven by biogenic emissions and photochemical activities, but showed larger variations than those of TROPOMI over coastal regions (Kuala Lumpur, Singapore, Shanghai, and Busan). In addition, GEMS HCHO VCDs showed consistent hourly variations with MAX-DOAS (r= 0.77) and FTIR (r= 0.86) but were 30–40 % lower than ground-based observations. Different vertical sensitivities of GEMS and ground-based instruments caused these biases. Utilizing the averaging kernel smoothing method reduces the low biases by approximately 10 % to 15 % (normalized mean bias (NMB): −47.4 % to −31.5 % and −38.6 % to −26.7 % for MAX-DOAS and FTIR, respectively). The remaining discrepancies are due to multiple factors, including spatial collocation and different instrumental sensitivities, requiring further investigation using inter-comparable datasets.

Spaceborne formaldehyde (HCHO) measurements constitute an excellent proxy for the sources of non-methane volatile organic compounds (NMVOCs). Past studies suggested substantial overestimations of NMVOC emissions in state-of-the-art inventories over major source regions. Here, the QA4ECV (Quality Assurance for Essential Climate Variables) retrieval of HCHO columns from OMI (Ozone Monitoring Instrument) is evaluated against (1) FTIR (Fourier-transform infrared) column observations at 26 stations worldwide and (2) aircraft in situ HCHO concentration measurements from campaigns conducted over the USA during 2012–2013. Both validation exercises show that OMI underestimates high columns and overestimates low columns. The linear regression of OMI and aircraft-based columns gives ΩOMI=0.651Ωairc+2.95×1015 molec.cm-2, with ΩOMI and Ωairc the OMI and aircraft-derived vertical columns, whereas the regression of OMI and FTIR data gives ΩOMI=0.659ΩFTIR+2.02×1015 molec.cm-2. Inverse modelling of NMVOC emissions with a global model based on OMI columns corrected for biases based on those relationships leads to much-improved agreement against FTIR data and HCHO concentrations from 11 aircraft campaigns. The optimized global isoprene emissions (∼445Tgyr-1) are 25 % higher than those obtained without bias correction. The optimized isoprene emissions bear both striking similarities and differences with recently published emissions based on spaceborne isoprene columns from the CrIS (Cross-track Infrared Sounder) sensor. Although the interannual variability of OMI HCHO columns is well understood over regions where biogenic emissions are dominant, and the HCHO trends over China and India clearly reflect anthropogenic emission changes, the observed HCHO decline over the southeastern USA remains imperfectly elucidated.

Nitrous oxide (N2O) and methane (CH4) are two important greenhouse gases in the atmosphere. In 2019, mid-infrared (MIR) solar absorption spectra were recorded by a Bruker VERTEX 70 spectrometer and a Bruker IFS 125HR spectrometer at Sodankylä, Finland, at spectral resolutions of 0.2 and 0.005 cm−1, respectively. The N2O and the CH4 retrievals from high-resolution MIR spectra have been well investigated within the Network for the Detection of Atmospheric Composition Change (NDACC) but not for MIR spectra gathered with instruments operating at low spectral resolution. In this study, N2O and CH4 retrieval strategies and retrieval uncertainties from the VERTEX 70 MIR low-resolution spectra are discussed and presented. The accuracy and precision of the VERTEX 70 N2O and CH4 retrievals are assessed by comparing them with the coincident 125HR retrievals and AirCore measurements. The relative differences between the N2O total columns retrieved from 125HR and VERTEX 70 spectra are −0.3 ± 0.7 (1σ) % with a correlation coefficient (R) of 0.93. Regarding the CH4 total column, we first used the same retrieval microwindows for 125HR and VERTEX 70 spectra, but there is an underestimation in the VERTEX 70 retrievals, especially in summer. The relative differences between the CH4 total columns retrieved from the 125HR and VERTEX 70 spectra are -1.3±1.1 (1σ) % with a R value of 0.77. To improve the VERTEX 70 CH4 retrievals, we propose alternative retrieval microwindows. The relative differences between the CH4 total columns retrieved from the 125HR and VERTEX 70 spectra in these new windows become 0.0±0.8 (1σ) %, along with an increase in the R value to 0.87. The coincident AirCore measurements confirm that the VERTEX 70 CH4 retrievals using the latter window choice are better, with relative mean differences between the VERTEX 70 CH4 retrievals and AirCore measurements of −1.9 % for the standard NDACC microwindows and of 0.13 % for the alternative microwindows. This study provides insight into the N2O and CH4 retrievals from the low-resolution (0.2 cm−1) MIR spectra observed with a VERTEX 70 spectrometer, and it demonstrates the suitability of this kind of instrument for contributing to satellite validation, model verification, and other scientific campaigns with the advantage of its transportability and lower cost compared to standard NDACC-type Fourier-transform infrared (FTIR) instruments.

The Copernicus Atmosphere Monitoring Service (CAMS) has recently produced a greenhouse gas reanalysis (version egg4) that covers almost 2 decades from 2003 to 2020 and which will be extended in the future. This reanalysis dataset includes carbon dioxide (CO2) and methane (CH4). The reanalysis procedure combines model data with satellite data into a globally complete and consistent dataset using the European Centre for Medium-Range Weather Forecasts' Integrated Forecasting System (IFS). This dataset has been carefully evaluated against independent observations to ensure validity and to point out deficiencies to the user. The greenhouse gas reanalysis can be used to examine the impact of atmospheric greenhouse gas concentrations on climate change (such as global and regional climate radiative forcing), assess intercontinental transport, and serve as boundary conditions for regional simulations, among other applications and scientific uses. The caveats associated with changes in assimilated observations and fixed underlying emissions are highlighted, as is their impact on the estimation of trends and annual growth rates of these long-lived greenhouse gases.

The availability of formaldehyde (HCHO) (a proxy for volatile organic compound reactivity) and nitrogen dioxide (NO2) (a proxy for nitrogen oxides) tropospheric columns from ultraviolet–visible (UV–Vis) satellites has motivated many to use their ratios to gain some insights into the near-surface ozone sensitivity. Strong emphasis has been placed on the challenges that come with transforming what is being observed in the tropospheric column to what is actually in the planetary boundary layer (PBL) and near the surface; however, little attention has been paid to other sources of error such as chemistry, spatial representation, and retrieval uncertainties. Here we leverage a wide spectrum of tools and data to quantify those errors carefully. Concerning the chemistry error, a well-characterized box model constrained by more than 500 h of aircraft data from NASA's air quality campaigns is used to simulate the ratio of the chemical loss of HO2 + RO2 (LROx) to the chemical loss of NOx (LNOx). Subsequently, we challenge the predictive power of HCHO/NO2 ratios (FNRs), which are commonly applied in current research, in detecting the underlying ozone regimes by comparing them to LROx/LNOx. FNRs show a strongly linear (R2=0.94) relationship with LROx/LNOx, but only on the logarithmic scale. Following the baseline (i.e., ln(LROx/LNOx) = −1.0 ± 0.2) with the model and mechanism (CB06, r2) used for segregating NOx-sensitive from VOC-sensitive regimes, we observe a broad range of FNR thresholds ranging from 1 to 4. The transitioning ratios strictly follow a Gaussian distribution with a mean and standard deviation of 1.8 and 0.4, respectively. This implies that the FNR has an inherent 20 % standard error (1σ) resulting from not accurately describing the ROx–HOx cycle. We calculate high ozone production rates (PO3) dominated by large HCHO × NO2 concentration levels, a new proxy for the abundance of ozone precursors. The relationship between PO3 and HCHO × NO2 becomes more pronounced when moving towards NOx-sensitive regions due to nonlinear chemistry; our results indicate that there is fruitful information in the HCHO × NO2 metric that has not been utilized in ozone studies. The vast amount of vertical information on HCHO and NO2 concentrations from the air quality campaigns enables us to parameterize the vertical shapes of FNRs using a second-order rational function permitting an analytical solution for an altitude adjustment factor to partition the tropospheric columns into the PBL region. We propose a mathematical solution to the spatial representation error based on modeling isotropic semivariograms. Based on summertime-averaged data, the Ozone Monitoring Instrument (OMI) loses 12 % of its spatial information at its native resolution with respect to a high-resolution sensor like the TROPOspheric Monitoring Instrument (TROPOMI) (> 5.5 × 3.5 km2). A pixel with a grid size of 216 km2 fails at capturing ∼ 65 % of the spatial information in FNRs at a 50 km length scale comparable to the size of a large urban center (e.g., Los Angeles). We ultimately leverage a large suite of in situ and ground-based remote sensing measurements to draw the error distributions of daily TROPOMI and OMI tropospheric NO2 and HCHO columns. At a 68 % confidence interval (1σ), errors pertaining to daily TROPOMI observations, either HCHO or tropospheric NO2 columns, should be above 1.2–1.5 × 1016 molec. cm−2 to attain a 20 %–30 % standard error in the ratio. This level of error is almost non-achievable with the OMI given its large error in HCHO. The satellite column retrieval error is the largest contributor to the total error (40 %–90 %) in the FNRs. Due to a stronger signal in cities, the total relative error (< 50 %) tends to be mild, whereas areas with low vegetation and anthropogenic sources (e.g., the Rocky Mountains) are markedly uncertain (> 100 %). Our study suggests that continuing development in the retrieval algorithm and sensor design and calibration is essential to be able to advance the application of FNRs beyond a qualitative metric.

Carbon monoxide (CO), acetylene (C2H2), ethane (C2H6), formaldehyde (H2CO), and hydrogen cyanide (HCN) are important trace gases in the atmosphere. They are highly related to biomass burning, fossil fuel combustion, and biogenic emissions globally, affecting air quality and climate change. However, the variations and correlations among these species are not well known in northern China due to limited measurements. In June 2018, we installed a new ground-based Fourier transform infrared (FTIR) spectrometer (Bruker IFS 125HR) recording mid-infrared high spectral resolution solar-absorption spectra at Xianghe (39.75∘ N, 116.96∘ E), China. In this study, we use the latest SFIT4 code, together with advanced a priori profiling and spectroscopy, to retrieve these five species from the FTIR spectra measured between June 2018 and November 2021. The retrieval strategies, retrieval information and retrieval uncertainties are presented and discussed. For the first time, the time series, variations, and correlations of these five species are analyzed at a typical polluted site in northern China. The seasonal variations in C2H2 and C2H6 total columns show a maximum in winter–spring and a minimum in autumn, whereas the seasonal variations in H2CO and HCN show a maximum in summer and a minimum in winter. Unlike the other four species, the FTIR measurements show that there is almost no seasonal variation in the CO column. The correlation coefficients (R) between the synoptic variations in CO and the other four species (C2H2, C2H6, H2CO, and HCN) are between 0.68 and 0.80, indicating that they are affected by common sources. Using the FLEXPART model backward simulations and satellite fire measurements, we find that the variations in CO, C2H2, C2H6, and H2CO columns are mainly dominated by the local anthropogenic emissions, while HCN column observed at Xianghe is a good tracer to identify fire emissions.

The Tropospheric Monitoring Instrument (TROPOMI) on the Copernicus Sentinel 5 Precursor (S5P) satellite, launched in October 2017, provides a wealth of atmospheric composition data, including total columns of carbon monoxide (TCCO) at high horizontal resolution (5.5 km × 7 km). Near-real-time TROPOMI TCCO data have been monitored in the global data assimilation system of the Copernicus Atmosphere Monitoring Service (CAMS) since November 2018 to assess the quality of the data. The CAMS system already routinely assimilates TCCO data from the Measurement of Pollution in the Troposphere (MOPITT) instrument and the Infrared Atmospheric Sounding Interferometer (IASI) outside the polar regions. The assimilation of TROPOMI TCCO data in the CAMS system was tested for the period 6 July to 31 December 2021, i.e. after the TROPOMI algorithm update to version 02.02.00 in July 2021. By assimilating TROPOMI TCCO observations, the CAMS CO columns increase by on average 8 %, resulting in an improved fit to independent observations (IAGOS aircraft profiles and NDACC Fourier transform infrared (FTIR) tropospheric and total-column CO data) compared to a version of the CAMS system where only TCCO from MOPITT and IASI is assimilated. The largest absolute and relative changes from the assimilation of TROPOMI CO are found in the lower and middle troposphere, i.e. that part of the atmosphere that is not already well constrained by the assimilated TIR MOPITT and IASI data. The largest impact near the surface comes from clear-sky TROPOMI data over land, and additional vertical information comes from the retrievals of measurements in cloudy conditions. July and August 2021 saw record numbers of boreal wildfires over North America and Russia, leading to large amounts of CO being released into the atmosphere. The paper assesses the impact of TROPOMI CO assimilation on selected CO plumes more closely. While the CO column can be well constrained by the assimilation of TROPOMI CO data, and the fit to individual IAGOS CO profiles in the lower and middle troposphere is considerably improved, the TROPOMI CO columns do not provide further constraints on individual plumes that are transported across continents and oceans at altitudes above 500 hPa.

Réunion Island is situated in the Indian Ocean and holds one of the very few atmospheric observatories in the tropical Southern Hemisphere. Moreover, it hosts experiments providing both ground-based surface and column observations of CO2, CH4, and CO atmospheric concentrations. This work presents a comprehensive study of these observations made in the capital Saint-Denis and at the high-altitude Maïdo Observatory. We used simulations of the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem), in its passive tracer option (WRF-GHG), to gain more insight to the factors that determine the observed concentrations. Additionally, this study provides an evaluation of the WRF-GHG performance in a region of the globe where it has not yet been applied. A comparison of the basic meteorological fields near the surface and along atmospheric profiles showed that WRF-GHG has decent skill in reproducing these meteorological measurements, especially temperature. Furthermore, a distinct diurnal CO2 cycle with values up to 450 ppm was found near the surface in Saint-Denis, driven by local anthropogenic emissions, boundary layer dynamics, and accumulation due to low wind speed at night. Due to an overestimation of local wind speed, WRF-GHG underestimates this nocturnal buildup. At Maïdo, a similar diurnal cycle is found but with much smaller amplitude. There, surface CO2 is essentially driven by the surrounding vegetation. The hourly column-averaged mole fractions of CO2 (XCO2) of WRF-GHG and the corresponding TCCON observations were highly correlated with a Pearson correlation coefficient of 0.90. These observations represent different air masses to those near the surface; they are influenced by processes from Madagascar, Africa, and further away. The model shows contributions from fires during the Southern Hemisphere biomass burning season but also biogenic enhancements associated with the dry season. Due to a seasonal bias in the boundary conditions, WRF-GHG fails to accurately reproduce the CH4 observations at Réunion Island. Furthermore, local anthropogenic fluxes are the largest source influencing the surface CH4 observations. However, these are likely overestimated. Furthermore, WRF-GHG is capable of simulating CO levels on Réunion Island with a high precision. As to the observed CO column (XCO), we confirmed that biomass burning plumes from Africa and elsewhere are important for explaining the observed variability. The in situ observations at the Maïdo Observatory can characterize both anthropogenic signals from the coastal regions and biomass burning enhancements from afar. Finally, we found that a high model resolution of 2 km is needed to accurately represent the surface observations. At Maïdo an even higher resolution might be needed because of the complex topography and local wind patterns. To simulate the column Fourier transform infrared (FTIR) observations on the other hand, a model resolution of 50 km might already be sufficient.

Nitric oxide (NO) is a key active trace gas in the atmosphere, which contributes to form harmful ozone in the troposphere and to the destruction of ozone in the stratosphere. In this study, we present the NO retrieval from ground-based Fourier-transform infrared (FTIR) solar absorption spectrometry measurements at a polluted site (Xianghe, China) and a background site (Maïdo, Reunion Island). The degree of freedom (DOF) of the NO retrieval is 2.3±0.4 (1σ) at Xianghe and 1.3±0.1 at Maïdo. By looking at the FTIR NO retrievals at Xianghe and Maïdo, we find that the stratospheric NO partial column is large in summer as compared to winter at both sites, and the seasonal variation in the FTIR stratospheric NO partial columns is consistent with that observed by the co-located Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite measurements. A large diurnal variation in the stratospheric NO partial column is observed by the FTIR measurements at Maïdo, with an increase from the early morning to about 14:00 local time and a decrease thereafter. Due to the low NO concentration near the surface, the FTIR NO retrieval is only sensitive to the stratosphere at Maïdo. The high NO mole fraction near the surface at Xianghe allows us to derive tropospheric and stratospheric NO partial columns separately, although the tropospheric column is very difficult to retrieve in summer (June–August) because of the high water vapor abundance. A good correlation is found between the NO observed by the FTIR measurements and other air pollutants (NO2 and CO) in the troposphere at Xianghe. It is the first study of a successful analysis of NO in the troposphere from a ground-based FTIR site. The tropospheric and stratospheric NO retrieval might be possible at other potential FTIR sites inside or near large cities with enhanced levels of NO near the surface.

The Sentinel-5 Precursor (S5P) mission with the TROPOspheric Monitoring Instrument (TROPOMI) on board has been measuring solar radiation backscattered by the Earth's atmosphere and surface since its launch on 13 October 2017. In this paper, we present for the first time the S5P operational methane (CH4) and carbon monoxide (CO) products' validation results covering a period of about 3 years using global Total Carbon Column Observing Network (TCCON) and Infrared Working Group of the Network for the Detection of Atmospheric Composition Change (NDACC-IRWG) network data, accounting for a priori alignment and smoothing uncertainties in the validation, and testing the sensitivity of validation results towards the application of advanced co-location criteria. We found that the S5P standard and bias-corrected CH4 data over land surface for the recommended quality filtering fulfil the mission requirements. The systematic difference of the bias-corrected total column-averaged dry air mole fraction of methane (XCH4) data with respect to TCCON data is -0.26±0.56 % in comparison to -0.68±0.74 % for the standard XCH4 data, with a correlation of 0.6 for most stations. The bias shows a seasonal dependence. We found that the S5P CO data over all surfaces for the recommended quality filtering generally fulfil the missions requirements, with a few exceptions, which are mostly due to co-location mismatches and limited availability of data. The systematic difference between the S5P total column-averaged dry air mole fraction of carbon monoxide (XCO) and the TCCON data is on average 9.22±3.45 % (standard TCCON XCO) and 2.45±3.38 % (unscaled TCCON XCO). We found that the systematic difference between the S5P CO column and NDACC CO column (excluding two outlier stations) is on average 6.5±3.54 %. We found a correlation of above 0.9 for most TCCON and NDACC stations. The study shows the high quality of S5P CH4 and CO data by validating the products against reference global TCCON and NDACC stations covering a wide range of latitudinal bands, atmospheric conditions and surface conditions.

The TROPOspheric Monitoring Instrument (TROPOMI), launched in October 2017 on board the Sentinel-5 Precursor (S5P) satellite, monitors the composition of the Earth's atmosphere at an unprecedented horizontal resolution as fine as 3.5 × 5.5 km2. This paper assesses the performances of the TROPOMI formaldehyde (HCHO) operational product compared to its predecessor, the OMI (Ozone Monitoring Instrument) HCHO QA4ECV product, at different spatial and temporal scales. The parallel development of the two algorithms favoured the consistency of the products, which facilitates the production of long-term combined time series. The main difference between the two satellite products is related to the use of different cloud algorithms, leading to a positive bias of OMI compared to TROPOMI of up to 30 % in tropical regions. We show that after switching off the explicit correction for cloud effects, the two datasets come into an excellent agreement. For medium to large HCHO vertical columns (larger than 5 × 1015 molec. cm−2) the median bias between OMI and TROPOMI HCHO columns is not larger than 10 % (< 0.4 × 1015 molec. cm−2). For lower columns, OMI observations present a remaining positive bias of about 20 % (< 0.8 × 1015 molec. cm−2) compared to TROPOMI in midlatitude regions. Here, we also use a global network of 18 MAX-DOAS (multi-axis differential optical absorption spectroscopy) instruments to validate both satellite sensors for a large range of HCHO columns. This work complements the study by Vigouroux et al. (2020), where a global FTIR (Fourier transform infrared) network is used to validate the TROPOMI HCHO operational product. Consistent with the FTIR validation study, we find that for elevated HCHO columns, TROPOMI data are systematically low (−25 % for HCHO columns larger than 8 × 1015 molec. cm−2), while no significant bias is found for medium-range column values. We further show that OMI and TROPOMI data present equivalent biases for large HCHO levels. However, TROPOMI significantly improves the precision of the HCHO observations at short temporal scales and for low HCHO columns. We show that compared to OMI, the precision of the TROPOMI HCHO columns is improved by 25 % for individual pixels and by up to a factor of 3 when considering daily averages in 20 km radius circles. The validation precision obtained with daily TROPOMI observations is comparable to the one obtained with monthly OMI observations. To illustrate the improved performances of TROPOMI in capturing weak HCHO signals, we present clear detection of HCHO column enhancements related to shipping emissions in the Indian Ocean. This is achieved by averaging data over a much shorter period (3 months) than required with previous sensors (5 years) and opens new perspectives to study shipping emissions of VOCs (volatile organic compounds) and related atmospheric chemical interactions.

In this study, we present O3 retrievals from ground-based Fourier transform infrared (FTIR) solar absorption measurements between June 2018 and December 2019 at Xianghe, China (39.75∘ N, 116.96∘ E). The FTIR spectrometer at Xianghe is operated with indium gallium arsenide (InGaAs) and indium antimonide (InSb) detectors, recording the spectra between 1800 and 11 000 cm−1. As the harmonized FTIR O3 retrieval strategy (Vigouroux et al., 2015) within the Network for the Detection of Atmospheric Composition Change (NDACC) uses the 1000 cm−1 spectral range, we apply the O3 retrieval in the 3040 cm−1 spectral range at Xianghe. The retrieved O3 profile is mainly sensitive to the vertical range between 10 and 40 km, and the degrees of freedom for signal is 2.4±0.3 (1σ), indicating that there are two individual pieces of information in partial columns between the surface and 20 km and between 20 and 40 km. According to the optimal estimation method, the systematic and random uncertainties of the FTIR O3 total columns are about 13.6 % and 1.4 %, respectively. The random uncertainty is consistent with the observed daily standard deviation of the FTIR retrievals. To validate the FTIR O3 total and partial columns, we apply the same O3 retrieval strategy at Maïdo, Réunion (a.k.a. Reunion Island; 21.08∘ N, 55.38∘ E). The FTIR O3 (3040 cm−1) measurements at Xianghe and Maïdo are then compared with the nearby ozonesondes at Beijing (39.81∘ N, 116.47∘ E) and at Gillot (20.89∘ S, 55.53∘ E), respectively, as well as with co-located TROPOspheric Monitoring Instrument (TROPOMI) satellite measurements at both sites. In addition at Maïdo, we compare the FTIR O3 (3040 cm−1) retrievals with the standard NDACC FTIR O3 measurements using the 1000 cm−1 spectral range. It was found that the total columns retrieved from the FTIR O3 3040 cm−1 measurements are underestimated by 5.5 %–9.0 %, which is mainly due to the systematic uncertainty in the partial column between 20 and 40 km (about −10.4 %). The systematic uncertainty in the partial column between surface and 20 km is relatively small (within 2.4 %). By comparison with other measurements, it was found that the FTIR O3 (3040 cm−1) retrievals capture the seasonal and synoptic variations of the O3 total and two partial columns very well. Therefore, the ongoing FTIR measurements at Xianghe can provide useful information on the O3 variations and (in the future) long-term trends.

The Total Carbon Column Observing Network (TCCON) is the baseline ground-based network of instruments that record solar absorption spectra from which accurate and precise column-averaged dry-air mole fractions of CO2 (XCO2), CH4 (XCH4), CO (XCO), and other gases are retrieved. The TCCON data have been widely used for carbon cycle science and validation of satellites measuring greenhouse gas concentrations globally. The number of stations in the network (currently about 25) is limited and has a very uneven geographical coverage: the stations in the Northern Hemisphere are distributed mostly in North America, Europe, and Japan, and only 20 % of the stations are located in the Southern Hemisphere, leaving gaps in the global coverage. A denser distribution of ground-based solar absorption measurements is needed to improve the representativeness of the measurement data for various atmospheric conditions (humid, dry, polluted, presence of aerosol), various surface conditions such as high albedo (>0.4) and very low albedo, and a larger latitudinal distribution. More stations in the Southern Hemisphere are also needed, but a further expansion of the network is limited by its costs and logistical requirements. For this reason, several groups are investigating supplemental portable low-cost instruments. The European Space Agency (ESA) funded campaign Fiducial Reference Measurements for Ground-Based Infrared Greenhouse Gas Observations (FRM4GHG) at the Sodankylä TCCON site in northern Finland aims to characterise the assessment of several low-cost portable instruments for precise solar absorption measurements of XCO2, XCH4, and XCO. The test instruments under investigation are three Fourier transform spectrometers (FTSs): a Bruker EM27/SUN, a Bruker IRcube, and a Bruker Vertex70, as well as a laser heterodyne spectroradiometer (LHR) developed by the UK Rutherford Appleton Laboratory. All four remote sensing instruments performed measurements simultaneously next to the reference TCCON instrument, a Bruker IFS 125HR, for a full year in 2017. The TCCON FTS was operated in its normal high-resolution mode (TCCON data set) and in a special low-resolution mode (HR125LR data set), similar to the portable spectrometers. The remote sensing measurements are complemented by regular AirCore launches performed from the same site. They provide in situ vertical profiles of the target gas concentrations as auxiliary reference data for the column retrievals, which are traceable to the WMO SI standards. The reference measurements performed with the Bruker IFS 125HR were found to be affected by non-linearity of the indium gallium arsenide (InGaAs) detector. Therefore, a non-linearity correction of the 125HR data was performed for the whole campaign period and compared with the test instruments and AirCore. The non-linearity-corrected data (TCCONmod data set) show a better match with the test instruments and AirCore data compared to the non-corrected reference data. The time series, the bias relative to the reference instrument and its scatter, and the seasonal and the day-to-day variations of the target gases are shown and discussed. The comparisons with the HR125LR data set gave a useful analysis of the resolution-dependent effects on the target gas retrieval. The solar zenith angle dependence of the retrievals is shown and discussed. The intercomparison results show that the LHR data have a large scatter and biases with a strong diurnal variation relative to the TCCON and other FTS instruments. The LHR is a new instrument under development, and these biases are currently being investigated and addressed. The campaign helped to characterise and identify instrumental biases and possibly retrieval biases, which are currently under investigation. Further improvements of the instrument are ongoing. The EM27/SUN, the IRcube, the modified Vertex70, and the HR125LR provided stable and precise measurements of the target gases during the campaign with quantified small biases. The bias dependence on the humidity along the measurement line of sight has been investigated and no dependence was found. These three portable low-resolution FTS instruments are suitable to be used for campaign deployment or long-term measurements from any site and offer the ability to complement the TCCON and expand the global coverage of ground-based reference measurements of the target gases.

Remote sensing of atmospheric state variables typically relies on the inverse solution of the radiative transfer equation. An adequately characterized retrieval provides information on the uncertainties of the estimated state variables as well as on how any constraint or a priori assumption affects the estimate. Reported characterization data should be intercomparable between different instruments, empirically validatable, grid-independent, usable without detailed knowledge of the instrument or retrieval technique, traceable and still have reasonable data volume. The latter may force one to work with representative rather than individual characterization data. Many errors derive from approximations and simplifications used in real-world retrieval schemes, which are reviewed in this paper, along with related error estimation schemes. The main sources of uncertainty are measurement noise, calibration errors, simplifications and idealizations in the radiative transfer model and retrieval scheme, auxiliary data errors, and uncertainties in atmospheric or instrumental parameters. Some of these errors affect the result in a random way, while others chiefly cause a bias or are of mixed character. Beyond this, it is of utmost importance to know the influence of any constraint and prior information on the solution. While different instruments or retrieval schemes may require different error estimation schemes, we provide a list of recommendations which should help to unify retrieval error reporting.

TROPOMI (the TROPOspheric Monitoring Instrument), on board the Sentinel-5 Precursor (S5P) satellite, has been monitoring the Earth's atmosphere since October 2017 with an unprecedented horizontal resolution (initially 7 km2×3.5 km2, upgraded to 5.5 km2×3.5 km2 in August 2019). Monitoring air quality is one of the main objectives of TROPOMI; it obtains measurements of important pollutants such as nitrogen dioxide, carbon monoxide, and formaldehyde (HCHO). In this paper we assess the quality of the latest HCHO TROPOMI products versions 1.1.(5-7), using ground-based solar-absorption FTIR (Fourier-transform infrared) measurements of HCHO from 25 stations around the world, including high-, mid-, and low-latitude sites. Most of these stations are part of the Network for the Detection of Atmospheric Composition Change (NDACC), and they provide a wide range of observation conditions, from very clean remote sites to those with high HCHO levels from anthropogenic or biogenic emissions. The ground-based HCHO retrieval settings have been optimized and harmonized at all the stations, ensuring a consistent validation among the sites. In this validation work, we first assess the accuracy of TROPOMI HCHO tropospheric columns using the median of the relative differences between TROPOMI and FTIR ground-based data (BIAS). The pre-launch accuracy requirements of TROPOMI HCHO are 40 %–80 %. We observe that these requirements are well reached, with the BIAS found below 80 % at all the sites and below 40 % at 20 of the 25 sites. The provided TROPOMI systematic uncertainties are well in agreement with the observed biases at most of the stations except for the highest-HCHO-level site, where it is found to be underestimated. We find that while the BIAS has no latitudinal dependence, it is dependent on the HCHO concentration levels: an overestimation (+26±5 %) of TROPOMI is observed for very low HCHO levels (<2.5×1015 molec. cm−2), while an underestimation (-30.8%±1.4 %) is found for high HCHO levels (>8.0×1015 molec. cm−2). This demonstrates the great value of such a harmonized network covering a wide range of concentration levels, the sites with high HCHO concentrations being crucial for the determination of the satellite bias in the regions of emissions and the clean sites allowing a small TROPOMI offset to be determined. The wide range of sampled HCHO levels within the network allows the robust determination of the significant constant and proportional TROPOMI HCHO biases (TROPOMI =+1.10±0.05 ×1015+0.64±0.03 × FTIR; in molecules per square centimetre). Second, the precision of TROPOMI HCHO data is estimated by the median absolute deviation (MAD) of the relative differences between TROPOMI and FTIR ground-based data. The clean sites are especially useful for minimizing a possible additional collocation error. The precision requirement of 1.2×1016 molec. cm−2 for a single pixel is reached at most of the clean sites, where it is found that the TROPOMI precision can even be 2 times better (0.5–0.8×1015 molec. cm−2 for a single pixel). However, we find that the provided TROPOMI random uncertainties may be underestimated by a factor of 1.6 (for clean sites) to 2.3 (for high HCHO levels). The correlation is very good between TROPOMI and FTIR data (R=0.88 for 3 h mean coincidences; R=0.91 for monthly means coincidences). Using about 17 months of data (from May 2018 to September 2019), we show that the TROPOMI seasonal variability is in very good agreement at all of the FTIR sites. The FTIR network demonstrates the very good quality of the TROPOMI HCHO products, which is well within the pre-launch requirements for both accuracy and precision. This paper makes suggestions for the refinement of the TROPOMI random uncertainty budget and TROPOMI quality assurance values for a better filtering of the remaining outliers.

The column-averaged dry-air mole fractions of CO2 (XCO2), CH4 (XCH4) and CO (XCO) have been measured with a Bruker IFS 125HR Fourier-transform infrared (FTIR) spectrometer at Xianghe (39.75∘ N, 116.96∘ E, north China) since June 2018. This paper presents the site, the characteristics of the FTIR system and the measurements. The instrumental setup follows the guidelines of the Total Carbon Column Observing Network (TCCON): the near-infrared spectra are recorded by an InGaAs detector together with a CaF2 beam splitter, and the HCl cell measurements are recorded regularly to derive the instrument line shape (ILS) showing that the instrument is correctly aligned. The TCCON standard retrieval code (GGG2014) is applied to retrieve XCO2, XCH4 and XCO. The resulting time series between June 2018 and July 2019 are presented, and the observed seasonal cycles and day-to-day variations in XCO2, XCH4 and XCO at Xianghe are discussed. In addition, the paper shows comparisons between the data products retrieved from the FTIR measurements at Xianghe and co-located Orbiting Carbon Observatory-2 (OCO-2) and Tropospheric Monitoring Instrument (TROPOMI) satellite observations. The comparison results appear consistent with validation results obtained at TCCON sites for XCO2 and XCH4, while for XCO they highlight the occurrence of frequent high-pollution events. As Xianghe lies in a polluted area in north China where there are currently no TCCON sites, this site can fill the TCCON gap in this region and expand the global coverage of the TCCON measurements. The Xianghe FTIR XCO2, XCH4 and XCO data can be obtained at https://doi.org/10.18758/71021049 (Yang et al., 2019).

We analyzed seasonality and interannual variability of tropospheric hydrogen cyanide (HCN) columns in densely populated eastern China for the first time. The results were derived from solar absorption spectra recorded with a ground-based high-spectral-resolution Fourier transform infrared (FTIR) spectrometer in Hefei (31∘54′ N, 117∘10′ E) between 2015 and 2018. The tropospheric HCN columns over Hefei, China, showed significant seasonal variations with three monthly mean peaks throughout the year. The magnitude of the tropospheric HCN column peaked in May, September, and December. The tropospheric HCN column reached a maximum monthly mean of (9.8±0.78)×1015 molecules cm−2 in May and a minimum monthly mean of (7.16±0.75)×1015 molecules cm−2 in November. In most cases, the tropospheric HCN columns in Hefei (32∘ N) are higher than the FTIR observations in Ny-Ålesund (79∘ N), Kiruna (68∘ N), Bremen (53∘ N), Jungfraujoch (47∘ N), Toronto (44∘ N), Rikubetsu (43∘ N), Izana (28∘ N), Mauna Loa (20∘ N), La Reunion Maido (21∘ S), Lauder (45∘ S), and Arrival Heights (78∘ S) that are affiliated with the Network for Detection of Atmospheric Composition Change (NDACC). Enhancements of tropospheric HCN column were observed between September 2015 and July 2016 compared to the same period of measurements in other years. The magnitude of the enhancement ranges from 5 % to 46 % with an average of 22 %. Enhancement of tropospheric HCN (ΔHCN) is correlated with the concurrent enhancement of tropospheric CO (ΔCO), indicating that enhancements of tropospheric CO and HCN were due to the same sources. The GEOS-Chem tagged CO simulation, the global fire maps, and the potential source contribution function (PSCF) values calculated using back trajectories revealed that the seasonal maxima in May are largely due to the influence of biomass burning in Southeast Asia (SEAS) (41±13.1 %), Europe and boreal Asia (EUBA) (21±9.3 %), and Africa (AF) (22±4.7 %). The seasonal maxima in September are largely due to the influence of biomass burnings in EUBA (38±11.3 %), AF (26±6.7 %), SEAS (14±3.3 %), and North America (NA) (13.8±8.4 %). For the seasonal maxima in December, dominant contributions are from AF (36±7.1 %), EUBA (21±5.2 %), and NA (18.7±5.2 %). The tropospheric HCN enhancement between September 2015 and July 2016 at Hefei (32∘ N) was attributed to an elevated influence of biomass burnings in SEAS, EUBA, and Oceania (OCE) in this period. In particular, an elevated number of fires in OCE in the second half of 2015 dominated the tropospheric HCN enhancement between September and December 2015. An elevated number of fires in SEAS in the first half of 2016 dominated the tropospheric HCN enhancement between January and July 2016.

The Total Carbon Column Observing Network (TCCON) column-averaged dry air mole fraction of CH4 (XCH4) measurements have been widely used to validate satellite observations and to estimate model simulations. The GGG2014 code is the standard TCCON retrieval software used in performing a profile scaling retrieval. In order to obtain several vertical pieces of information in addition to the total column, in this study, the SFIT4 retrieval code is applied to retrieve the CH4 mole fraction vertical profile from the Fourier transform spectrometer (FTS) spectrum at six sites (Ny-Ålesund, Sodankylä, Bialystok, Bremen, Orléans and St Denis) during the time period of 2016–2017. The retrieval strategy of the CH4 profile retrieval from ground-based FTS near-infrared (NIR) spectra using the SFIT4 code (SFIT4NIR) is investigated. The degree of freedom for signal (DOFS) of the SFIT4NIR retrieval is about 2.4, with two distinct pieces of information in the troposphere and in the stratosphere. The averaging kernel and error budget of the SFIT4NIR retrieval are presented. The data accuracy and precision of the SFIT4NIR retrievals, including the total column and two partial columns (in the troposphere and stratosphere), are estimated by TCCON standard retrievals, ground-based in situ measurements, Atmospheric Chemistry Experiment – Fourier Transform Spectrometer (ACE-FTS) satellite observations, TCCON proxy data and AirCore and aircraft measurements. By comparison against TCCON standard retrievals, it is found that the retrieval uncertainty of SFIT4NIR XCH4 is similar to that of TCCON standard retrievals with systematic uncertainty within 0.35 % and random uncertainty of about 0.5 %. The tropospheric and stratospheric XCH4 from SFIT4NIR retrievals are assessed by comparison with AirCore and aircraft measurements, and there is a 1.0 ± 0.3 % overestimation in the SFIT4NIR tropospheric XCH4 and a 4.0 ± 2.0 % underestimation in the SFIT4NIR stratospheric XCH4, which are within the systematic uncertainties of SFIT4NIR-retrieved partial columns in the troposphere and stratosphere respectively.

Column-averaged dry-air mole fraction of CO (XCO) measurements are obtained from two ground-based Fourier transform infrared (FTIR) spectrometer networks: the Total Carbon Column Observing Network (TCCON) and the Network for the Detection of Atmospheric Composition Change (NDACC). In this study, the differences between the TCCON and NDACC XCO measurements are investigated and discussed based on six NDACC–TCCON sites using data over the period 2007–2017. A direct comparison shows that the NDACC XCO measurements are about 5.5 % larger than the TCCON data at Ny-Ålesund, Bremen, and Izaña (Northern Hemisphere), and the absolute bias between the NDACC and TCCON data is within 2 % at Saint-Denis, Wollongong and Lauder (Southern Hemisphere). The hemispheric dependence of the bias is mainly attributed to their smoothing errors. The systematic smoothing error of the TCCON XCO data varies in the range between 0.2 % (Bremen) and 7.9 % (Lauder), and the random smoothing error varies in the range between 2.0 % and 3.6 %. The systematic smoothing error of NDACC data is between 0.1 % and 0.8 %, and the random smoothing error of NDACC data is about 0.3 %. For TCCON data, the smoothing error is significant because it is higher than the reported uncertainty, particularly at Southern Hemisphere sites. To reduce the influence from the a priori profiles and different vertical sensitivities, the scaled NDACC a priori profiles are used as the common a priori profiles for comparing TCCON and NDACC retrievals. As a result, the biases between TCCON and NDACC XCO measurements become more consistent (5.6 %–8.5 %) with a mean value of 6.8 % at these sites. To determine the sources of the remaining bias, regular AirCore measurements at Orléans and Sodankylä are compared to co-located TCCON measurements. It is found that TCCON XCO measurements are 6.1 ± 1.6 % and 8.0 ± 3.2 % smaller than the AirCore measurements at Orléans and Sodankylä, respectively, indicating that the scaling factor of TCCON XCO data should be around 1.0000 instead of 1.0672. Further investigations should be carried out in the TCCON community to determine the correct scaling factor to be applied to the TCCON XCO data. This paper also demonstrates that the smoothing error must be taken into account when comparing FTIR XCO data, and especially TCCON XCO data, with model or satellite data.

Climate change mitigation efforts require information on the current greenhouse gas atmospheric concentrations and their sources and sinks. Carbon dioxide (CO2) is the most abundant anthropogenic greenhouse gas. Its variability in the atmosphere is modulated by the synergy between weather and CO2 surface fluxes, often referred to as CO2 weather. It is interpreted with the help of global or regional numerical transport models, with horizontal resolutions ranging from a few hundreds of kilometres to a few kilometres. Changes in the model horizontal resolution affect not only atmospheric transport but also the representation of topography and surface CO2 fluxes. This paper assesses the impact of horizontal resolution on the simulated atmospheric CO2 variability with a numerical weather prediction model. The simulations are performed using the Copernicus Atmosphere Monitoring Service (CAMS) CO2 forecasting system at different resolutions from 9 to 80 km and are evaluated using in situ atmospheric surface measurements and atmospheric column-mean observations of CO2, as well as radiosonde and SYNOP observations of the winds. The results indicate that both diurnal and day-to-day variability of atmospheric CO2 are generally better represented at high resolution, as shown by a reduction in the errors in simulated wind and CO2. Mountain stations display the largest improvements at high resolution as they directly benefit from the more realistic orography. In addition, the CO2 spatial gradients are generally improved with increasing resolution for both stations near the surface and those observing the total column, as the overall inter-station error is also reduced in magnitude. However, close to emission hotspots, the high resolution can also lead to a deterioration of the simulation skill, highlighting uncertainties in the high-resolution fluxes that are more diffuse at lower resolutions. We conclude that increasing horizontal resolution matters for modelling CO2 weather because it has the potential to bring together improvements in the surface representation of both winds and CO2 fluxes, as well as an expected reduction in numerical errors of transport. Modelling applications like atmospheric inversion systems to estimate surface fluxes will only be able to benefit fully from upgrades in horizontal resolution if the topography, winds and prior flux distribution are also upgraded accordingly. It is clear from the results that an additional increase in resolution might reduce errors even further. However, the horizontal resolution sensitivity tests indicate that the change in the CO2 and wind modelling error with resolution is not linear, making it difficult to quantify the improvement beyond the tested resolutions. Finally, we show that the high-resolution simulations are useful for the assessment of the small-scale variability of CO2 which cannot be represented in coarser-resolution models. These representativeness errors need to be considered when assimilating in situ data and high-resolution satellite data such as Greenhouse gases Observing Satellite (GOSAT), Orbiting Carbon Observatory-2 (OCO-2), the Chinese Carbon Dioxide Observation Satellite Mission (TanSat) and future missions such as the Geostationary Carbon Observatory (GeoCarb) and the Sentinel satellite constellation for CO2. For these reasons, the high-resolution CO2 simulations provided by the CAMS in real time can be useful to estimate such small-scale variability in real time, as well as providing boundary conditions for regional modelling studies and supporting field experiments.

Nitrous oxide (N2O) is an important greenhouse gas and it can also generate nitric oxide, which depletes ozone in the stratosphere. It is a common target species of ground-based Fourier transform infrared (FTIR) near-infrared (TCCON) and mid-infrared (NDACC) measurements. Both TCCON and NDACC networks provide a long-term global distribution of atmospheric N2O mole fraction. In this study, the dry-air column-averaged mole fractions of N2O (XN2O) from the TCCON and NDACC measurements are compared against each other at seven sites around the world (Ny-Ålesund, Sodankylä, Bremen, Izaña, Réunion, Wollongong, Lauder) in the time period of 2007–2017. The mean differences in XN2O between TCCON and NDACC (NDACC–TCCON) at these sites are between −3.32 and 1.37 ppb (−1.1 %–0.5 %) with standard deviations between 1.69 and 5.01 ppb (0.5 %–1.6 %), which are within the uncertainties of the two datasets. The NDACC N2O retrieval has good sensitivity throughout the troposphere and stratosphere, while the TCCON retrieval underestimates a deviation from the a priori in the troposphere and overestimates it in the stratosphere. As a result, the TCCON XN2O measurement is strongly affected by its a priori profile. Trends and seasonal cycles of XN2O are derived from the TCCON and NDACC measurements and the nearby surface flask sample measurements and compared with the results from GEOS-Chem model a priori and a posteriori simulations. The trends and seasonal cycles from FTIR measurement at Ny-Ålesund and Sodankylä are strongly affected by the polar winter and the polar vortex. The a posteriori N2O fluxes in the model are optimized based on surface N2O measurements with a 4D-Var inversion method. The XN2O trends from the GEOS-Chem a posteriori simulation (0.97±0.02 (1σ) ppb yr−1) are close to those from the NDACC (0.93±0.04 ppb yr−1) and the surface flask sample measurements (0.93±0.02 ppb yr−1). The XN2O trend from the TCCON measurements is slightly lower (0.81±0.04 ppb yr−1) due to the underestimation of the trend in TCCON a priori simulation. The XN2O trends from the GEOS-Chem a priori simulation are about 1.25 ppb yr−1, and our study confirms that the N2O fluxes from the a priori inventories are overestimated. The seasonal cycles of XN2O from the FTIR measurements and the model simulations are close to each other in the Northern Hemisphere with a maximum in August–October and a minimum in February–April. However, in the Southern Hemisphere, the modeled XN2O values show a minimum in February–April while the FTIR XN2O retrievals show different patterns. By comparing the partial column-averaged N2O from the model and NDACC for three vertical ranges (surface–8, 8–17, 17–50 km), we find that the discrepancy in the XN2O seasonal cycle between the model simulations and the FTIR measurements in the Southern Hemisphere is mainly due to their stratospheric differences.

Atmospheric carbon monoxide (CO) and methane (CH4) mole fractions are measured by ground-based in situ cavity ring-down spectroscopy (CRDS) analyzers and Fourier transform infrared (FTIR) spectrometers at two sites (St Denis and Maïdo) on Reunion Island (21° S, 55° E) in the Indian Ocean. Currently, the FTIR Bruker IFS 125HR at St Denis records the direct solar spectra in the near-infrared range, contributing to the Total Carbon Column Observing Network (TCCON). The FTIR Bruker IFS 125HR at Maïdo records the direct solar spectra in the mid-infrared (MIR) range, contributing to the Network for the Detection of Atmospheric Composition Change (NDACC). In order to understand the atmospheric CO and CH4 variability on Reunion Island, the time series and seasonal cycles of CO and CH4 from in situ and FTIR (NDACC and TCCON) measurements are analyzed. Meanwhile, the difference between the in situ and FTIR measurements are discussed.The CO seasonal cycles observed from the in situ measurements at Maïdo and FTIR retrievals at both St Denis and Maïdo are in good agreement with a peak in September–November, primarily driven by the emissions from biomass burning in Africa and South America. The dry-air column averaged mole fraction of CO (XCO) derived from the FTIR MIR spectra (NDACC) is about 15.7 ppb larger than the CO mole fraction near the surface at Maïdo, because the air in the lower troposphere mainly comes from the Indian Ocean while the air in the middle and upper troposphere mainly comes from Africa and South America. The trend for CO on Reunion Island is unclear during the 2011–2017 period, and more data need to be collected to get a robust result.A very good agreement is observed in the tropospheric and stratospheric CH4 seasonal cycles between FTIR (NDACC and TCCON) measurements, and in situ and the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite measurements, respectively. In the troposphere, the CH4 mole fraction is high in August–September and low in December–January, which is due to the OH seasonal variation. In the stratosphere, the CH4 mole fraction has its maximum in March–April and its minimum in August–October, which is dominated by vertical transport. In addition, the different CH4 mole fractions between the in situ, NDACC and TCCON CH4 measurements in the troposphere are discussed, and all measurements are in good agreement with the GEOS-Chem model simulation. The trend of XCH4 is 7.6±0.4 ppb yr−1 from the TCCON measurements over the 2011 to 2017 time period, which is consistent with the CH4 trend of 7.4±0.5 ppb yr−1 from the in situ measurements for the same time period at St Denis.

Among the more than 20 ground-based FTIR (Fourier transform infrared) stations currently operating around the globe, only a few have provided formaldehyde (HCHO) total column time series until now. Although several independent studies have shown that the FTIR measurements can provide formaldehyde total columns with good precision, the spatial coverage has not been optimal for providing good diagnostics for satellite or model validation. Furthermore, these past studies used different retrieval settings, and biases as large as 50 % can be observed in the HCHO total columns depending on these retrieval choices, which is also a weakness for validation studies combining data from different ground-based stations.For the present work, the HCHO retrieval settings have been optimized based on experience gained from past studies and have been applied consistently at the 21 participating stations. Most of them are either part of the Network for the Detection of Atmospheric Composition Change (NDACC) or under consideration for membership. We provide the harmonized settings and a characterization of the HCHO FTIR products. Depending on the station, the total systematic and random uncertainties of an individual HCHO total column measurement lie between 12 % and 27 % and between 1 and 11×1014 molec cm−2, respectively. The median values among all stations are 13 % and 2.9×1014 molec cm−2 for the total systematic and random uncertainties.This unprecedented harmonized formaldehyde data set from 21 ground-based FTIR stations is presented and its comparison with a global chemistry transport model shows consistency in absolute values as well as in seasonal cycles. The network covers very different concentration levels of formaldehyde, from very clean levels at the limit of detection (few 1013 molec cm−2) to highly polluted levels (7×1016 molec cm−2). Because the measurements can be made at any time during daylight, the diurnal cycle can be observed and is found to be significant at many stations. These HCHO time series, some of them starting in the 1990s, are crucial for past and present satellite validation and will be extended in the coming years for the next generation of satellite missions.

SF6 total columns were successfully retrieved from FTIR (Fourier transform infrared) measurements (Saint Denis and Maïdo) on Reunion Island (21° S, 55° E) between 2004 and 2016 using the SFIT4 algorithm: the retrieval strategy and the error budget were presented. The FTIR SF6 retrieval has independent information in only one individual layer, covering the whole of the troposphere and the lower stratosphere. The trend in SF6 was analysed based on the FTIR-retrieved dry-air column-averaged mole fractions (XSF6) on Reunion Island, the in situ measurements at America Samoa (SMO) and the collocated satellite measurements (Michelson Interferometer for Passive Atmospheric Sounding, MIPAS, and Atmospheric Chemistry Experiment Fourier Transform Spectrometer, ACE-FTS) in the southern tropics. The SF6 annual growth rate from FTIR retrievals is 0.265 ± 0.013 pptv year−1 for 2004–2016, which is slightly weaker than that from the SMO in situ measurements (0.285 ± 0.002 pptv year−1) for the same time period. The SF6 trend in the troposphere from MIPAS and ACE-FTS observations is also close to the ones from the FTIR retrievals and the SMO in situ measurements.

A new IASI methane product developed at the Royal Belgian Institute for Space Aeronomy (BIRA-IASB) is presented. The retrievals are performed with the ASIMUT-ALVL software based on the optimal estimation method (OEM). This paper gives an overview of the forward model and retrieval concept. The usefulness of reconstructed principal component compressed (PCC) radiances is highlighted. The information content study carried out in this paper shows that most IASI pixels contain between 0.9 and 1.6 independent pieces of information about the vertical distribution of CH4, with a good sensitivity in the mid- to upper troposphere. A detailed error analysis was performed. The total uncertainty is estimated to be 3.73 % for a CH4 partial column between 4 and 17 km. An extended validation with ground-based CH4 observations at 10 locations was carried out. IASI CH4 partial columns are found to correlate well with the ground-based data for 6 out of the 10 Fourier transform infrared (FTIR) stations with correlation coefficients between 0.60 and 0.84. Relative mean differences between IASI and FTIR CH4 range between −2.31 and 4.04 % and are within the systematic uncertainty. For 6 out of the 10 stations the relative mean differences are smaller than ±1 %. The standard deviation of the difference lies between 1.76 and 2.97 % for all the stations.

In order to recognize the importance of ozone (O3) in the troposphere and lower stratosphere in the tropics, a DIAL (differential absorption lidar) tropospheric O3 lidar system (LIO3TUR) was developed and installed at the Université de la Réunion campus site (close to the sea) on Reunion Island (southern tropics) in 1998. From 1998 to 2010, it acquired 427 O3 profiles from the low to the upper troposphere and has been central to several studies. In 2012, the system was moved up to the new Maïdo Observatory facility (2160 m a.m.s.l. – metres above mean sea level) where it started operation in February 2013. The current system (LIO3T) configuration generates a 266 nm beam obtained with the fourth harmonic of a Nd:YAG laser sent into a Raman cell filled up with deuterium (using helium as buffer gas), generating the 289 and 316 nm beams to enable the use of the DIAL method for O3 profile measurements. The optimal range for the actual system is 6–19 km a.m.s.l., depending on the instrumental and atmospheric conditions. For a 1 h integration time, vertical resolution varies from 0.7 km at 6 km a.m.s.l. to 1.3 km at 19 km a.m.s.l., and mean uncertainty within the 6–19 km range is between 6 and 13 %. Comparisons with eight electrochemical concentration cell (ECC) sondes simultaneously launched from the Maïdo Observatory show good agreement between data sets with a 6.8 % mean absolute relative difference (D) between 6 and 17 km a.m.s.l. (LIO3T lower than ECC). Comparisons with 37 ECC sondes launched from the nearby Gillot site during the daytime in a ±24 h window around lidar shooting result in a 9.4 % D between 6 and 19 km a.m.s.l. (LIO3T lower than ECC). Comparisons with 11 ground-based Network for Detection of Atmospheric Composition Change (NDACC) Fourier transform infrared (FTIR) spectrometer measurements acquired during the daytime in a ±24 h window around lidar shooting show good agreement between data sets with a D of 11.8 % for the 8.5–16 km partial column (LIO3T higher than FTIR), and comparisons with 39 simultaneous Infrared Atmospheric Sounding Interferometer (IASI) observations over Reunion Island show good agreement between data sets with a D of 11.3 % for the 6–16 km partial column (LIO3T higher than IASI). ECC, LIO3TUR and LIO3T O3 monthly climatologies all exhibit the same range of values and patterns. In particular, the Southern Hemisphere biomass burning seasonal enhancement and the ozonopause altitude decrease in late austral winter–spring, as well as the sign of deep convection bringing boundary layer O3-poor air masses up to the middle–upper troposphere in late austral summer, are clearly visible in all data sets.

The Measurements of Pollution in the Troposphere (MOPITT) satellite instrument provides the longest continuous dataset of carbon monoxide (CO) from space. We perform the first validation of MOPITT version 6 retrievals using total column CO measurements from ground-based remote-sensing Fourier transform infrared spectrometers (FTSs). Validation uses data recorded at 14 stations, that span a wide range of latitudes (80° N to 78° S), in the Network for the Detection of Atmospheric Composition Change (NDACC). MOPITT measurements are spatially co-located with each station, and different vertical sensitivities between instruments are accounted for by using MOPITT averaging kernels (AKs). All three MOPITT retrieval types are analyzed: thermal infrared (TIR-only), joint thermal and near infrared (TIR–NIR), and near infrared (NIR-only). Generally, MOPITT measurements overestimate CO relative to FTS measurements, but the bias is typically less than 10 %. Mean bias is 2.4 % for TIR-only, 5.1 % for TIR–NIR, and 6.5 % for NIR-only. The TIR–NIR and NIR-only products consistently produce a larger bias and lower correlation than the TIR-only. Validation performance of MOPITT for TIR-only and TIR–NIR retrievals over land or water scenes is equivalent. The four MOPITT detector element pixels are validated separately to account for their different uncertainty characteristics. Pixel 1 produces the highest standard deviation and lowest correlation for all three MOPITT products. However, for TIR-only and TIR–NIR, the error-weighted average that includes all four pixels often provides the best correlation, indicating compensating pixel biases and well-captured error characteristics. We find that MOPITT bias does not depend on latitude but rather is influenced by the proximity to rapidly changing atmospheric CO. MOPITT bias drift has been bound geographically to within ±0.5 % yr−1 or lower at almost all locations.

Profiles of CFC-11 (CCl3F), CFC-12 (CCl2F2) and HCFC-22 (CHF2Cl) have been obtained from Fourier transform infrared (FTIR) solar absorption measurements above the Saint-Denis (St Denis) and Maïdo sites at Réunion Island (21° S, 55° E) with low vertical resolution. FTIR profile retrievals are performed by the well-established SFIT4 program and the detail retrieval strategies along with the systematic/random uncertainties of CFC-11, CFC-12 and HCFC-22 are discussed in this study. The FTIR data of all three species are sensitive to the whole troposphere and the lowermost stratosphere, with the peak sensitivity between 5 and 10 km. The ground-based FTIR data have been compared with the collocated Michelson Interferometer for Passive Atmospheric Sounding (MIPAS/ENVISAT) data and found to be in good agreement: the observed mean relative biases and standard deviations of the differences between the smoothed MIPAS and FTIR partial columns (6–30 km) are (−4.3 and 4.4 %), (−2.9 and 4.6 %) and (−0.7 and 4.8 %) for CFC-11, CFC-12 and HCFC-22, respectively, which are within the combined error budgets from both measurements. The season cycles of CFC-11, CFC-12 and HCFC-22 from FTIR measurements and MIPAS data show a similar variation: concentration is highest in February–April and lowest in August–October. The trends derived from the combined St Denis and Maïdo FTIR time series are −0.86 ± 0.12 and 2.84 ± 0.06 % year−1 for CFC-11 and HCFC-22, respectively, for the period 2004 to 2016, and −0.76 ± 0.05 % year−1 for CFC-12 for 2009 to 2016. These measurements are consistent with the trends observed by the National Oceanic and Atmospheric Administration (NOAA) Global Monitoring Division's (GMD) Halocarbons & other Atmospheric Trace Species Group (HATS) measurements at Samoa (14.2° S, 170.5° W) for CFC-11 (−0.87 ± 0.04 % year−1), but slightly weaker for HCFC-22 (3.46 ± 0.05 %) year−1 and stronger for CFC-12 (−0.60 ± 0.02 % year−1).

Knowing the spatial and seasonal distributions of nitric acid (HNO3) around the globe is of great interest and allows us to comprehend the processes regulating stratospheric ozone, especially in the polar regions. Due to its unprecedented spatial and temporal sampling, the nadir-viewing Infrared Atmospheric Sounding Interferometer (IASI) is capable of sounding the atmosphere twice a day globally, with good spectral resolution and low noise. With the Fast Optimal Retrievals on Layers for IASI (FORLI) algorithm, we are retrieving, in near real time, columns as well as vertical profiles of several atmospheric species, among which is HNO3. We present in this paper the first characterization of the FORLI-HNO3 profile products, in terms of vertical sensitivity and error budgets. We show that the sensitivity of IASI to HNO3 is highest in the lower stratosphere (10–20 km), where the largest amounts of HNO3 are found, but that the vertical sensitivity of IASI only allows one level of information on the profile (degrees of freedom for signal, DOFS; ∼ 1). The sensitivity near the surface is negligible in most cases, and for this reason, a partial column (5–35 km) is used for the analyses. Both vertical profiles and partial columns are compared to FTIR ground-based measurements from the Network for the Detection of Atmospheric Composition Change (NDACC) to characterize the accuracy and precision of the FORLI-HNO3 product. The profile validation is conducted through the smoothing of the raw FTIR profiles by the IASI averaging kernels and gives good results, with a slight overestimation of IASI measurements in the upper troposphere/lower stratosphere (UTLS) at the six chosen stations (Thule, Kiruna, Jungfraujoch, Izaña, Lauder and Arrival Heights). The validation of the partial columns (5–35 km) is also conclusive with a mean correlation of 0.93 between IASI and the FTIR measurements. An initial survey of the HNO3 spatial and seasonal variabilities obtained from IASI measurements for a 1-year (2011) data set shows that the expected latitudinal gradient of concentrations from low to high latitudes and the large seasonal variability in polar regions (cycle amplitude around 30 % of the seasonal signal, peak to peak) are well represented by IASI data.

We present a retrieval method for ammonia (NH3) total columns from ground-based Fourier transform infrared (FTIR) observations. Observations from Bremen (53.10° N, 8.85° E), Lauder (45.04° S, 169.68° E), Réunion (20.9° S, 55.50° E) and Jungfraujoch (46.55° N, 7.98° E) were used to illustrate the capabilities of the method. NH3 mean total columns ranging 3 orders of magnitude were obtained, with higher values at Bremen (mean of 13.47 × 1015 molecules cm−2) and lower values at Jungfraujoch (mean of 0.18 × 1015 molecules cm−2). In conditions with high surface concentrations of ammonia, as in Bremen, it is possible to retrieve information on the vertical gradient, as two layers can be distinguished. The retrieval there is most sensitive to ammonia in the planetary boundary layer, where the trace gas concentration is highest. For conditions with low concentrations, only the total column can be retrieved. Combining the systematic and random errors we have a mean total error of 26 % for all spectra measured at Bremen (number of spectra (N) = 554), 30 % for all spectra from Lauder (N = 2412), 25 % for spectra from Réunion (N = 1262) and 34 % for spectra measured at Jungfraujoch (N = 2702). The error is dominated by the systematic uncertainties in the spectroscopy parameters. Station-specific seasonal cycles were found to be consistent with known seasonal cycles of the dominant ammonia sources in the station surroundings. The developed retrieval methodology from FTIR instruments provides a new way of obtaining highly time-resolved measurements of ammonia burdens. FTIR-NH3 observations will be useful for understanding the dynamics of ammonia concentrations in the atmosphere and for satellite and model validation. It will also provide additional information to constrain the global ammonia budget.

The European MACC (Monitoring Atmospheric Composition and Climate) project is preparing the operational Copernicus Atmosphere Monitoring Service (CAMS), one of the services of the European Copernicus Programme on Earth observation and environmental services. MACC uses data assimilation to combine in situ and remote sensing observations with global and regional models of atmospheric reactive gases, aerosols, and greenhouse gases, and is based on the Integrated Forecasting System of the European Centre for Medium-Range Weather Forecasts (ECMWF). The global component of the MACC service has a dedicated validation activity to document the quality of the atmospheric composition products. In this paper we discuss the approach to validation that has been developed over the past 3 years. Topics discussed are the validation requirements, the operational aspects, the measurement data sets used, the structure of the validation reports, the models and assimilation systems validated, the procedure to introduce new upgrades, and the scoring methods. One specific target of the MACC system concerns forecasting special events with high-pollution concentrations. Such events receive extra attention in the validation process. Finally, a summary is provided of the results from the validation of the latest set of daily global analysis and forecast products from the MACC system reported in November 2014.

Daily global analyses and 5-day forecasts are generated in the context of the European Monitoring Atmospheric Composition and Climate (MACC) project using an extended version of the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). The IFS now includes modules for chemistry, deposition and emission of reactive gases, aerosols, and greenhouse gases, and the 4-dimensional variational data assimilation scheme makes use of multiple satellite observations of atmospheric composition in addition to meteorological observations. This paper describes the data assimilation setup of the new Composition-IFS (C-IFS) with respect to reactive gases and validates analysis fields of ozone (O3), carbon monoxide (CO), and nitrogen dioxide (NO2) for the year 2008 against independent observations and a control run without data assimilation. The largest improvement in CO by assimilation of Measurements of Pollution in the Troposphere (MOPITT) CO columns is seen in the lower troposphere of the Northern Hemisphere (NH) extratropics during winter, and during the South African biomass-burning season. The assimilation of several O3 total column and stratospheric profile retrievals greatly improves the total column, stratospheric and upper tropospheric O3 analysis fields relative to the control run. The impact on lower tropospheric ozone, which comes from the residual of the total column and stratospheric profile O3 data, is smaller, but nevertheless there is some improvement particularly in the NH during winter and spring. The impact of the assimilation of tropospheric NO2 columns from the Ozone Monitoring Instrument (OMI) is small because of the short lifetime of NO2, suggesting that NO2 observations would be better used to adjust emissions instead of initial conditions. The results further indicate that the quality of the tropospheric analyses and of the stratospheric ozone analysis obtained with the C-IFS system has improved compared to the previous "coupled" model system of MACC.

This paper evaluates and discusses the quality of the stratospheric ozone analyses delivered in near real time by the MACC (Monitoring Atmospheric Composition and Climate) project during the 3-year period between September 2009 and September 2012. Ozone analyses produced by four different chemical data assimilation (CDA) systems are examined and compared: the Integrated Forecast System coupled to the Model for OZone And Related chemical Tracers (IFS-MOZART); the Belgian Assimilation System for Chemical ObsErvations (BASCOE); the Synoptic Analysis of Chemical Constituents by Advanced Data Assimilation (SACADA); and the Data Assimilation Model based on Transport Model version 3 (TM3DAM). The assimilated satellite ozone retrievals differed for each system; SACADA and TM3DAM assimilated only total ozone observations, BASCOE assimilated profiles for ozone and some related species, while IFS-MOZART assimilated both types of ozone observations. All analyses deliver total column values that agree well with ground-based observations (biases < 5%) and have a realistic seasonal cycle, except for BASCOE analyses, which underestimate total ozone in the tropics all year long by 7 to 10%, and SACADA analyses, which overestimate total ozone in polar night regions by up to 30%. The validation of the vertical distribution is based on independent observations from ozonesondes and the ACE-FTS (Atmospheric Chemistry Experiment – Fourier Transform Spectrometer) satellite instrument. It cannot be performed with TM3DAM, which is designed only to deliver analyses of total ozone columns. Vertically alternating positive and negative biases are found in the IFS-MOZART analyses as well as an overestimation of 30 to 60% in the polar lower stratosphere during polar ozone depletion events. SACADA underestimates lower stratospheric ozone by up to 50% during these events above the South Pole and overestimates it by approximately the same amount in the tropics. The three-dimensional (3-D) analyses delivered by BASCOE are found to have the best quality among the three systems resolving the vertical dimension, with biases not exceeding 10% all year long, at all stratospheric levels and in all latitude bands, except in the tropical lowermost stratosphere. The northern spring 2011 period is studied in more detail to evaluate the ability of the analyses to represent the exceptional ozone depletion event, which happened above the Arctic in March 2011. Offline sensitivity tests are performed during this month and indicate that the differences between the forward models or the assimilation algorithms are much less important than the characteristics of the assimilated data sets. They also show that IFS-MOZART is able to deliver realistic analyses of ozone both in the troposphere and in the stratosphere, but this requires the assimilation of observations from nadir-looking instruments as well as the assimilation of profiles, which are well resolved vertically and extend into the lowermost stratosphere.

MACC-II,III, Monitoring Atmospheric Composition and Climate, is the current pre-operational Copernicus Atmosphere Monitoring Service (CAMS). It provides data records on atmospheric composition for recent years, present conditions and forecasts (a few days ahead). To support the quality assessment of the CAMS products, the EU FP7 project Network Of ground-based Remote-Sensing Observations (NORS) created a server to validate the gridded MACC-II,III/CAMS model data against remote-sensing observations from the Network for the Detection of Atmospheric Composition Change (NDACC), for a selected set of target species and pilot stations. This paper describes in detail the algorithms used in this validation server. Amongst others, the algorithms take into account the horizontal displacement of the measured profiles from the location of the instrument, the vertical averaging and uncertainty propagation.

Among spinning objects, the tippe top exhibits one of the most bizarre and counterintuitive behaviours. The commercially available tippe tops basically consist of a section of a sphere with a rod. After spinning on its rounded body, the top flips over and continues spinning on the stem. The commonly used simplified mathematical model for the tippe top is a sphere whose mass distribution is axially but not spherically symmetric, spinning on a flat surface subject to a small friction force that is due to sliding. Three main different dynamical behaviours are distinguished: tipping, nontipping, hanging, that is, the top rises but converges to an intermediate state instead of rising all the way to the vertical state. Subclasses according to the stability of relative equilibria can further be distinguished. Our concern is the degree of confidence in the mathematical model predictions, we applied 3D printing and rapid prototyping to manufacture a “3-in-1 toy” that could catch the three main characteristics defining the three main groups in the classification of spherical tippe tops as mentioned above. We propose three designs. This “toy” is suitable to validate the mathematical model qualitatively and quantitatively.

Abstract  Motivated by nonlinear control theory, we introduce the notion of conic distributions on a smooth manifold. We study topological and smoothness aspects of the set of accessible points associated with a conic distribution. We introduce the notion of abnormal paths and study their relation to boundary points of the accessible set. In particular, we provide sufficient conditions for the accessible set to be a maximal integral of the smallest integrable vector distribution containing the conic distribution. Under rather strong conditions, we are able to prove that the accessible set has the structure of a ‘manifold with corners’. [ABSTRACT FROM AUTHOR]

Abstract  We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states. [ABSTRACT FROM AUTHOR]

A coordinate-free proof of the maximum principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of integral curves of time-dependent vector fields with unit time component, and on the use of a concept of lift over a bundle map. We further derive necessary and sufficient conditions for the existence of so-called abnormal extremals. [ABSTRACT FROM AUTHOR]