Assessing Total and Tropospheric Ozone via IKFS-2 Infrared Measurements on Meteor-M No. 2

Abstract

Stratospheric ozone shields life on Earth from harmful ultraviolet radiation and plays a crucial role in climate formation, while tropospheric ozone is a pollutant and greenhouse gas. Satellite methods based on measurements of outgoing thermal radiation are the only methods that provide information on global ozone distribution, independent of solar illumination. Since about 90% of atmospheric ozone is concentrated in the stratosphere, ozone total column measurements can be used as stratospheric ozone measurements. We present techniques for deriving information on total ozone columns (TOCs) and tropospheric ozone columns (TrOCs) from spectra of outgoing thermal radiation measured by the IKFS-2 instrument aboard the Meteor-M No. 2 satellite. The techniques are based on principal component analysis and the artificial neural network approach, providing high accuracy in TOC (less than 3%) and TrOC (within 2–4 DU) retrieval in accordance with the WMO requirements for the quality of satellite measurements.

1. Introduction

Atmospheric ozone has a significant impact on the Earth’s climate and biosphere. Although its contribution to the total atmospheric composition is small and its maximum values are about 10⁻⁵, stratospheric ozone protects plant and animal life from dangerous ultraviolet (UV) radiation [1]. At the same time, tropospheric ozone is listed as one of the most critical pollutants detrimental to public health [2]. Ozone in the atmosphere was first detected in 1920 by Fabry and Buisson using the spectroscopic method [3]; systematic ozone measurements started with the invention of the famous Dobson spectrophotometer in the 1930s [4]. Attention to atmospheric ozone increased dramatically in the 1980s with the discovery of “ozone holes” caused by anthropogenic factors [1] and led to the development of various methods for observing changes in its content.

Stratospheric ozone is formed mainly in the middle stratosphere of tropical latitudes. During global circulation, this ozone content is transported to the lower stratosphere of high latitudes in the winter hemisphere. Due to global circulation, man-made chlorofluorocarbons are carried to the stratosphere and reach the polar regions. There, in photolysis reactions, they release active chlorine, which is usually converted into the inert gas reservoirs of HCl and ClONO₂ [5]. At low temperatures inside the polar stratospheric vortex, ozone is destroyed in heterogeneous reactions on the surface of the particles of the polar stratospheric clouds. With the appearance of the sunlight in spring, ozone can be dramatically depleted in chemical reactions with active chlorine. Ozone-depleting gases are still observed in the atmosphere; however, since the adoption of international agreements that limit and ban them, the atmospheric concentration of these gases has been decreasing, but with marked fluctuations [1].

The expected date of ozone recovery to pre-industrial levels is gradually being moved back to 2100. According to [1,6], predicting the variation in total ozone columns (TOCs) is difficult due to the influence of increasing greenhouse gas content. Thus, monitoring TOCs remains an urgent task, especially in the polar regions, where there is a maximum annual drop and variability in TOCs. At the same time, at low solar elevation angles and, even more so, in the absence of the Sun during the polar night, it is impossible to monitor ozone by methods that rely on solar radiation.

Attention to tropospheric ozone has recently been increasing for several reasons. Ozone determines the oxidation capacity of the troposphere. Ground-level ozone (surface ozone) harms the health of animals and humans [7] and depresses plants [8]. Ozone in the troposphere is one of the main greenhouse gases [9]. According to the 2021 IPCC report [10], the contribution of tropospheric ozone to the total anthropogenic influence on the radiation balance of the planet is 4–20%, which is also consistent with earlier data [11]. Models estimate the magnitude of tropospheric ozone column (TrOC) radiative forcing as +(0.40 ± 0.20) W m⁻² [12]. In particular, the large uncertainties in the TrOC contribution to the radiative forcing are caused by a lack of knowledge of the TrOC spatial distribution [13].

The main sources of tropospheric ozone are transport from the stratosphere and photochemical reactions with ozone precursors—NOx, CO, CH₄, OH, anthropogenic and biogenic volatile compounds, or VOCs. The significance of the latter source is greater than that of the former in terms of the number of molecules appearing in the troposphere [14]. However, the ozone molecules formed during photochemical reactions are actively destroyed; thus, both sources contribute approximately the same amount. The relative contribution of the second source depends on the emissions of ozone precursors and meteorological conditions [9,11], leading to significant spatio-temporal variability in TrOCs.

Both in situ and remote sensing methods are used to monitor atmospheric gases, particularly ozone. Contact methods provide high accuracy and precision (e.g., [15]), while remote satellite methods provide global spatial coverage. The satellite era of ozone monitoring began with the use of the IRIS (InfraRed Interferometer Spectrometer) Fourier Spectrometer on the Nimbus-3 satellite in 1969 [16]. The problems related to tropospheric ozone have been intensively investigated during the last decades.

Four main types of remote satellite methods for ozone monitoring can be distinguished as follows (see, e.g., [17]):

• Based on scattered and reflected solar radiation, e.g., Tropospheric Monitoring Instrument (TROPOMI) [18]; Ozone Monitoring Instrument (OMI) [19,20];
• Limb-based methods: Solar occultation, e.g., Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS) [21], SAGE III measurements [22], alter-natively inversion algorithm [23], or other natural sources of radiation (e.g., stars [24]);
• The atmosphere’s microwave or IR radiation, e.g., Microwave Limb Sounder (MLS) [25] or Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) [26]; and finally
• Nadir methods using outgoing thermal IR radiation, e.g., Infrared Atmospheric Sounding Interferometer (IASI) [27,28,29], Infra-Red Fourier Spectrometer (IKFS)-2 [30,31,32,33].

The methods based on the measurements of solar radiation cannot be used at night; for example, during a polar night in the Arctic and Antarctica. By using limb measurements, information on the gas composition vertical profile in the atmosphere can be obtained except for the lower atmospheric layers (only above 5–7 km). Hence, these methods do not provide information on TrOCs and, consequently, on TOCs. In addition, limb measurements have low horizontal resolution and gaps in the localisation of measurements. Thus, only satellite methods based on measurements of the outgoing thermal radiation, in particular, by the Russian IKFS-2 instrument, can provide information on TOCs and TrOCs during polar night periods.

Ground-based measurements of solar radiation in the UV, visible, and IR spectral ranges also provide information about atmospheric ozone. TOC retrievals based on measured direct and scattered solar radiation by the Dobson and Brewer instruments, the M-124 filter ozonometer [34], and IR Fourier spectrometers [35] are used to validate satellite methods as well as to detect a drift in satellite data.

In the frame of the international TOAR (Tropospheric Ozone Assessment Report) project (https://toar-data.org), the data on both surface ozone concentrations (SOCs) and TrOCs are collected from ground-based local and remote measurements, aircraft, satellite observations, etc. [36]. The first measurements of SOCs started in the 1870s, and ozonesondes were being launched from the 1930s to the 1940s, providing information on ozone content in the entire troposphere [37]. In the 1960s and 1970s, a widespread study of SOCs and ozone vertical profiles began. The WOUDC database (https://woudc.org/home.php, WMO/GAW, 2024) contains data from dozens of ozonesonde sites. These ozonesonde data, whose measurement accuracy has been recently increased, can also be used for the validation of TOCs satellite measurements [38]. At some observational sites, vertical profiles of ozone in the troposphere are measured regularly or during measurement campaigns by the lidar and Umkehr method using Brewer and Dobson spectrophotometers [39]. In addition, TrOCs in clear-sky conditions are obtained at stations of the IRWG-NDACC (InfraRed Working Group of Network for the Detection of Atmospheric Composition Change) (https://www2.acom.ucar.edu/irwg (accessed on 16 June 2025)) observational network equipped with the Fourier Transform InfraRed (FTIR) spectrometers of high spectral resolution [35]. Nowadays, ground-based measurements are used in studies of local variability in TrOCs, in validation of satellite measurements, and in adjusting the atmospheric numerical models on a regional scale.

In this paper, we present techniques for TOC and TrOC retrievals from the IR spectra of outgoing thermal radiation measured by the IKFS-2 instrument onboard the Meteor-M No. 2 satellite. For TrOC determination, we followed the recommendations of the TOAR project group [36], which defines the upper boundary of the tropospheric ozone layer as follows: from ground to 300 hPa in the midlatitudes (30–60°) and from ground to 400 hPa in the polar regions (>60°). Thus, to investigate the ozone content in the tropospheric layer, in this study, we consider TrOC as the ozone content in the layers below atmospheric pressure 300 and 400 hPa, which corresponds approximately to the altitudes of 9 and 7 km, respectively.

We suppose that it is not necessary to use multilayer neural networks, such as deep belief networks, to solve the inverse remote sensing problems. Simple networks, such as a three-layer perceptron that contains one hidden layer of neurons and coefficients determined during network training, allow for achieving a high accuracy in TOC and TrOC retrievals. At the same time, a feature of our approach is the use of the most statistically widest set of data pairs for the artificial neural network (ANN) training. For the ANN training of TOCs, the dataset consisted of approximately 2 × 10⁷ pairs, while for TrOCs, the dataset contained 5.6 × 10⁵ pairs. To support the generalizability of the ANNs, we used all available data that covered various geographical, seasonal, or cloud cover diversity in the training datasets.

In Section 2, we describe the sources of all the data used in the study, including spectra of outgoing IR radiation and TOC and TrOC values measured by different methods. Some of these data are used for the ANN training, while others are for validating the results obtained and demonstrating the advantages of the techniques proposed. The same section describes the ANNs, the procedure for training data, and the optimisation of the TrOC ANNs. The Section 3 presents the results of the ANN training, the extension of the ANN for the first 6 years of the IKFS-2 measurements to the whole measurement period of 8 years, and the optimisation of the structure of the ANN for TrOC determination. Finally, we show the comparison of the results obtained using the presented methods with independent data, their validation, and advantages. The most interesting cases of the observed TOC and TrOC values are also analysed.

2. Materials and Methods

2.1. Experimental Data

2.1.1. IKFS-2 Spectra

We use all available IKFS-2 spectral data from 2015 to 2022 for both training the ANNs and validation. The IR sounder IKFS-2 is part of the payload of the Meteor-M No. 2 spacecraft series [40], which was launched into a sun-synchronous orbit with an equator crossing time of 9:30 local time at the ascending node. The instrument shares basic characteristics with well-known instruments such as AIRS, IASI, and CrIS, as mentioned above. IKFS-2 measures the outgoing radiation by scanning a band up to 2500 km wide across the spacecraft’s orbit, with a spatial resolution of about 35 km. Details on the instrument and its use can be found in [30,41]. Although the main purpose of the instrument is meteorological sounding, the spectral range of measurements includes the ozone absorption band of 9.6 µm, which makes it possible to obtain information about atmospheric ozone. Scientific Research Centre Planeta provides access to the spectral data from the beginning of 2015 to the end of 2022. Up to December 2020, the swath width (SW) of the measurements was 1000 km. Since December 2020, the SW has been extended to 1500 km, which allowed daily scanning of the whole territory of the Russian Federation. Currently, the Meteor-M No. 2–4 spacecraft is in orbit with the IKFS-2 instrument aboard, measuring in a test mode.

Estimates of the IKFS-2 spectra informativity concerning the vertical ozone distribution show the sensitivity of the measurements to its content at different altitudes. We used the physics–mathematical (PM) approach based on the use of the optimal estimation method [42] to calculate the number of degrees of freedom for signal (DOFS) [42] of spectral measurements relative to ozone. An a priori ozone covariance matrix was constructed from ozonesonde measurements in 2015–2022—the years of IKFS-2 available spectral data. The diagonal elements of the error covariance matrix were taken from experimental estimates of measurement noise in the instrument’s spectral channels [43]. Using the LBLRTM (Line-By-Line Radiative Transfer Model) radiation model software code [44], we calculated the radiation derivative matrices. To simulate the measured spectra, we considered cloudless atmosphere conditions and a water/snow surface model with an emissivity equal to 1. We calculated averaging kernels (AK) and the DOFS for different atmospheric climate models, including tropics, mid-latitudes, and subarctic latitudes [45].

Figure 1 shows the AKs for the mid-latitude models. The IKFS-2 sensitivity to the ozone content is maximum at ~100 hPa. The AKs for the summer (Figure 1a) and winter (Figure 1b) mid-latitude models show that the sensitivity to the changes in tropospheric ozone content for the winter model is less than for the summer model. Thus, more information is expected in the lower atmosphere in the case of stronger temperature gradients (see Figure 2c). The information content for different climate models is estimated in

Table 1. Estimates of the DOFS number, TOC, and TrOC relative errors of the IKFS-2 measurements for different atmospheric climate models.

Climate Model	Tropics	Middle Latitudes		Subarctic
		Summer	Winter	Summer	Winter
DOFS	4.4	4.3	3.9	4.3	3.4
TOC error, %	0.6	0.6	0.7	0.6	1.1
TrOC error, %	9.9	8.3	9.8	8.2	12.3

. On average, we obtained four independent layers (DOFS is about 4) in the vertical ozone profile. Table 1 also presents estimates of the relative error of TOC and TrOC retrievals. The errors were obtained from the residual uncertainty matrix and include the smoothing error and the spectral measurement noise error components. These values are minimal potential errors, as the estimates do not consider a component due to errors in the forward model parameters.

Figure 2a,b show the sensitivity functions of the IKFS-2 measurements to the ozone content variability in TOCs and TrOCs. The ideal sensitivity is shown by a black line, which means that ozone content variations will contribute to the solution with a weight of 1.0 (100% sensitivity). Zero sensitivity means that there is no contribution of the corresponding altitudes to the solution; then, in the ideal case, ozone variations in the upper layers will contribute with a zero weight to the solution of the TrOCs determination. Figure 2b shows that the sensitivity to tropospheric ozone is relatively weak for the tropical climate model, although a large thermal gradient is observed there (see Figure 2c). This can be explained, firstly, by the higher tropopause in the model temperature profile, and secondly, by the smaller natural variability in the ozone content of the lower tropical atmosphere. The thermal contrast of the surface and near-surface layer in the present analyses totals 3 K for all climate models. The thermal contrast can reach 20 K, and then the sensitivity to the ozone variability in the near-surface layer will increase.

The IKFS-2 sensitivities related to TOCs are shown in Figure 2a. We can conclude that the sensitivity to the ozone variability is weak in the near-surface layer, which is caused by the shielding of the near-surface layer in satellite measurements.

2.1.2. Other Satellite Data

The ANN training for TOC retrieval is based on OMI TOC data. The OMI is a part of the payload of the Aura satellite, which provides measurements of TOCs with errors of 1–2% [19,20,46]. OMI data have been constantly validated; therefore, using an ANN trained on them does not require additional calibration of the results. OMI measurements provide a global distribution of TOCs, excluding only polar night regions. The OMI data were obtained from [47].

For comparisons, we used the results of independent TOC measurements by two other satellite instruments—TROPOMI and IASI. In May 2018, TROPOMI started TOC measurements on board the Sentinel 5 Precursor (S5P) satellite [18]. The spatial resolution of the instrument varies from 3.5 × 7 km [48] to 3.5 × 5.5 km [49]. Garane et al. [48] compared TOC data retrieved from TROPOMI with ground-based measurements by the Brewer, Dobson, and Differential Optical Absorption Spectroscopy (DOAS) instruments. Mean differences (MDs) ranged from 0 to 1.5%, with the standard deviation of the differences (SDDs) ranging from 2.5 to 4.5%. For TOC IKFS-2 validation, we used TROPOMI level 2 measurements [49], with a quality flag of at least 0.9. We used RPRO (reprocessed version) before and OFFL (results of the first offline processing) data after 26 August 2022, with data available on 5 March 2024. For comparison, we took TROPOMI and IKFS-2 TOC data pairs with 35 km and 6 h mismatch. Due to the orbital characteristics of two satellites, smaller time mismatches preclude comparison in the tropics and mid-latitudes. To exclude implausible TOC values, we limited TROPOMI data in the range of 100–650 DU.

Another satellite instrument, IASI [50], whose data were used to compare both the TOC and the TrOC results with those of IKFS-2, is quite like IKFS-2. The global TOC and TrOC datasets are based on IASI observations from the EUMETSAT MetOp-A, -B, and -C satellites (https://user.eumetsat.int/data/satellites/metop/data, accessed on 1 December 2022). We used MetOp-A and MetOp-B data because MetOp-C was launched later than IKFS-2. MetOp satellites operate in a sun-synchronous orbit with 07:50 and 9:31 local time of descending node equatorial crossing time for MetOp-A and MetOp-B, respectively. Spatial resolution of measurements constitutes 12 km. The main purpose of the instrument is temperature and humidity profile measurements, and as with IKFS-2, the IASI spectral region includes the 9.6 µm ozone absorption band, which provides information about ozone.

The FORLI-O3 (Fast Optimal Retrievals on Layers for IASI O3) software is used for the TOC and TrOC retrievals [51]. A good agreement between TOCs retrieved from IASI data and independent data was found in [52] for 2013–2017. The MDs between the data constituted 0.4 DU, growing in the polar regions up to 2 DU. Dufour et al. [50] analysed the results of TrOC measurements by IASI and showed for all comparisons in middle latitudes (320 days of comparisons) that MDs between satellite and ozonesonde data were +0.6 DU, and SDDs were 5.5 DU (IASI_LATMOS) and +1.0 DU with SDDs of 6.1 DU (IASI_LISA). IASI measurements of TrOC for 2008–2017 were also compared with FTIR measurements [52]. MDs varied from –4 to +0.5 DU; SDDs were 2.5–3.9 DU. Virolainen and co-authors [53,54] compared IASI data in the 0–8 km tropospheric layer with FTIR measurements at three IRWG-NDACC stations. The SDDs between satellite and ground-based measurements were 9–13%, within the total measurement errors of the compared data pairs.

2.1.3. Ground-Based Data

It is essential to compare TOCs retrieved from IKFS-2 measurements with data based on fundamentally different methods. Therefore, it is of great interest to compare IKFS-2 TOCs with ground-based measurements, such as direct measurements by ozonesondes, remote measurements of solar radiance by the Dobson and Brewer instruments, and FTIR measurements from the NDACC network.

Ozonesonde data are obtained using a specialised small sensor attached to a standard radiosonde to measure ozone content with high vertical resolution. These data have significant shortcomings: ozonesondes rarely rise above a pressure of 6 hPa, and the absolute measurement error reaches 5–10% [1,55].

However, ozonesonde data is available throughout the whole year, including the polar night period. Measurements are taken weekly, in most cases, on Wednesdays. A common practice is to integrate the ozonesonde data and to apply the McPeters and Labow [56] satellite ozone climatology above 6 hPa to calculate the TOCs. However, at some stations, only the integral ozone content from the ozonesonde profile (i.e., surface—6 hPa) is available. The Standard Operating Procedures (SOP) of Ozonesonde are constantly being improved and standardised, which allows us to expect an improvement in accuracy and a reduction in the errors of up to 5% [38,57].

Data from the WOUDC network is represented by separate measurements using Dobson and Brewer instruments. The Dobson spectrometer was developed in 1924 by British physicist and meteorologist Gordon Dobson. The Dobson spectrophotometer can be used to measure both TOCs and atmospheric ozone profiles. In this study, we only used the Dobson and Brewer TOCs retrieved from direct solar radiation measurements. According to [58], the accuracy of such measurements is 1–2%.

Within the NDACC, high-resolution solar absorption IR spectra have been continuously recorded since the 1990s by ground-based FTIR spectrometers (currently Bruker IFS 120/125HR). The FTIR instruments are distributed globally and provide high-quality measurements of TOCs and TrOCs at about 20 sites [59]. The total errors of TOC and TrOC retrievals are estimated as 2–4% and 6–10%, respectively [35,60,61].

In the framework of the TOAR-II project, an improved strategy for ozone content retrieval has been proposed. Most of the available data can be found at https://www-air.larc.nasa.gov/missions/ndacc/data.html# (accessed on 17 June 2025) with “IRWG2023” in ozone data file names. For spectra analysis, this strategy supposes to use (1) 4 micro-windows (991.25–993.8, 1001.47–1003.04, 1005–1006.9, 1007.348–1009 cm⁻¹) to avoid strong water vapour lines, (2) WACCM7 model [62] for a priori setup of ozone and other absorber gases profiles, and (3) HITRAN2020 database [63] for the fine structure of spectroscopic lines setup. This strategy allowed for to reduction of the bias between direct sun Dobson and FTIR measurements from 2.1% to 0.6% at the NDACC St. Petersburg site [53]. For the NDACC Lauder site [64], the bias between ozonesonde and FTIR TrOCs totals −1.9%, while the bias between Dobson direct sun and FTIR TOCs totals −2.9%.

2.2. Different Approaches for Solving the Inverse Problem: Discussion of Methods

As is well known, there are two main approaches to solving the inverse problems in remote sensing: (1) the PM (physical–mathematical) approach based on the numerical solution of the equation of radiation transfer in the atmosphere, and (2) the regression approach, an approximation of the solving operator of the inverse problem, based on a large sample of measured or modelled results. Usually, the PM approach, due to the nonlinearity of the problem, requires an iterative solution of the forward problem. In the case of the current study, calculating outgoing Earth radiation intensity usually requires substantial computational resources. In addition, the illness of most inverse problems of atmospheric optics leads to the necessity of using different regularisation schemes for the inverse problem, i.e., involving additional a priori information given in different forms [42]. With low informativity of measurements regarding the composition of the atmosphere, such as when measuring outgoing thermal radiation in near-polar regions with a near-isothermal atmosphere and low surface temperature, the contribution of a priori information to the solution increases. Nevertheless, at normal states of the atmosphere with a pronounced air temperature gradient, the PM method can provide reliable results even in cases that are not covered by a priori information.

The regression approach, relying on the approximation of a limited sample dataset, may give incorrect results for cases not included in this dataset, which is a recognised disadvantage of the regression approach. At the same time, the statistical completeness of the sample dataset allows for obtaining adequate solutions for almost any observed atmospheric state. Thus, we can conclude that both PM and regression approaches can give wrong solutions in certain situations not included in the a priori statistics. At the same time, when using nonlinear approximations, such as ANN, the relationships between different parameters are considered, not only linear but also nonlinear, while the optimal estimation method allows for considering only linear correlations. This is an advantage of the regression approach over PM. In any case, the applicability of each method for solving the inverse problem must be thoroughly tested, preferably on independent data, so that it can be applied to atmospheric research. In this paper, we consider a regression approach to form the inverse operator, which requires a sufficiently wide training dataset and comprehensive validation of the results.

We also note that, unlike the PM approach, the use of the regression approach takes insignificant computational resources, so it can be used to obtain an initial approximation or to quickly obtain preliminary results.

In our study, we consider the application of the regression nonlinear approach, using the simplest ANN, to retrieve TOCs and TrOCs.

2.3. The Technique for TOC and TrOC Retrieval

The technique for TOC retrieval has been previously presented in [31,32,65,66]. The algorithm uses the simplest types of ANN—a three-layer perceptron (see, for example, [67]), whose input parameters are zenith angle, the fraction of the year, the latitude, and principal components (PCs) of the IKFS-2 spectrum. Details of the algorithm are given in [31,33,66]. Based on the estimates of [65], 25 PCs of the 660–1210 cm⁻¹ spectral range, as well as 50 PCs of the 980–1080 cm⁻¹ spectral range, are used. The input parameters were also the satellite’s zenith angle and the day of the year, and the hidden layer of the ANN contained 40 neurons. A similar approach was previously used, for example, in [68,69] for the IASI. The main difference in the current study is the use of the widest possible dataset for the ANN training.

In detail, mathematically, the three-layer perceptron is represented by the Equation (1)

$$\mathit{y}=\mathit{f}\left({\mathit{b}}^{\mathbf{2}}+{{\displaystyle \sum }}_{\mathit{i}=\mathbf{1}}^{{\mathit{N}}_{\mathit{h}}}{\mathit{\omega }}_{\mathit{i}}^{\mathbf{2}}\mathit{f}\left({\mathit{b}}_{\mathit{i}}^{\mathbf{1}}+{{\displaystyle \sum }}_{\mathit{j}=\mathbf{1}}^{\mathit{N}}{\mathit{\omega }}_{\mathit{i},\mathit{j}}^{\mathbf{1}}{\mathit{x}}_{\mathit{j}}\right)\right)$$

(1)

Here $\mathit{f}$ is the activation function; $\overrightarrow{\mathit{X}}=\left\{{\mathit{x}}_{\mathit{j}}\right\}$ is a vector of input parameters; ${\mathit{b}}_{\mathit{i}}^{\mathbf{1}}, {\mathit{\omega }}_{\mathit{i},\mathit{j}}^{\mathbf{1}}, {\mathit{\omega }}_{\mathit{i}}^{\mathbf{2}}, \mathrm{and} {\mathit{b}}^{\mathbf{2}}$ are coefficients. Training of the ANN is the minimisation of approximation error ${\mathit{\sigma }}_{\mathit{a}\mathit{p}\mathit{p}}$ of the training data by the coefficients ${\mathit{b}}_{\mathit{i}}^{\mathbf{1}}, {\mathit{\omega }}_{\mathit{i},\mathit{j}}^{\mathbf{1}}, {\mathit{\omega }}_{\mathit{i}}^{\mathbf{2}}, {\mathit{b}}^{\mathbf{2}}$ (2),

$${\mathit{\sigma }}_{\mathit{a}\mathit{p}\mathit{p}}=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{\mathit{S}}{\left({\mathit{Y}}_{\mathit{s}}-\mathit{y}\left(\overrightarrow{{\mathit{X}}_{\mathit{s}}}\right)\right)}^{\mathbf{2}}}{{{\displaystyle \sum }}_{\mathit{S}}\mathbf{1}}}}\to \mathit{m}\mathit{i}\mathit{n},$$

(2)

where the set of pairs ${\left\{\overrightarrow{\mathit{X}}, \mathit{Y}\right\}}_{\mathit{s}}$, s—pair number, is the training dataset. The test and validation datasets are used to control the overfitting of the network. The training dataset contained about 2 × 10⁷ spectrum—TOC pairs; 20% of the data was randomly allocated to the test and validation sets. The approximation error during training was approximately 8.8 DU. We emphasise that we did not use the TensorFlow and Keras software libraries for working with ANNs, which have become widespread in recent years. The calculations used the original software developed by authors [70,71] for both training the ANN and for calculations.

For TrOC retrievals, we applied a similar approach, as it was well-established earlier for TOCs. As a first approximation, we repeated the fully developed ANN structure, only replacing TOCs with TrOCs.

For the ANN training, we used the integrated gas content in the layer below 300 hPa or 400 hPa calculated from the ozonesonde profiles. Although full information on TrOCs is not contained in the spectra in the presence of cloudiness due to clouds shielding IR radiation, it is possible to estimate TrOC under partial cloud cover, depending on the cloud cover index and the height of the clouds’ upper boundary. Therefore, for the ANN training, we considered both cloudless situations only (see [72,73] for the cloudless detection algorithm) and all IKFS-2 measurements, including cloudy situations. At the same time, situations with dense cloud cover could not affect the training result, since the TrOCs in these cases are not related to the recorded spectrum and are automatically discarded. The set of measurement pairs was split into three sets: training set (60%), test set, and validation set (20% each). For the TrOCs ANN training, the dataset contained 5.6 × 10⁵ pairs. As input parameters, we took satellite zenith angle, day of year, latitude, and 35 PCs of the whole spectrum; PCs in the ozone band were not included. There were 55 neurons in the hidden layer of the ANN, and the training error totalled 2.7 DU for the layer below 400 hPa and 3.7 DU for the layer below 300 hPa [32].

2.4. Optimisation of the ANNs for TOC Retrieval

First, we applied to the processing of the 2021–2022 spectra the method developed earlier based on the 2015–2020 data without any changes. We compared the obtained TOC values with the TROPOMI data and the ground-based ozonometric network WOUDC data [74].

Table 2. Results of comparison of TOC by IKFS-2 with other satellite (TROPOMI) and ground-based WOUDC measurements (Dobson, Brewer instruments). MDs and SDDs—mean difference and standard deviation of the difference, respectively; SW—swath width.

1	2	3	4		5
No.	ANN Training Period (SW)	Comparisons Period (SW)	Satellite Measurements		Ground-Based Measurements
			MD, %	SDD, %	MD, %	SDD, %
1	2015–2020 (1000)	2015–2020 (1000)	−2.05	2.63	−0.47	2.73
2		2021–2022 (1000)	−1.47	2.47	0.89	2.52
3		2021–2022 (1000–1500)	−1.73	3.49	−0.02	3.00
4	2015–2022 (1500)	2015–2020 (1000)	−2.02	2.58	−0.40	2.71
5		2015–2022 (1500)	−2.13	2.65	−0.41	2.67
6		2021–2022 (1000)	−1.86	2.20	0.21	2.28
7		2021–2022 (1000–1500)	−2.43	2.86	−1.02	2.30

shows the mean differences (MDs) and standard deviation of differences (SDDs) of the IKFS-2 data and the WOUDC data, the IKFS-2 data and the TROPOMI data, as well as the results of comparisons for the periods 2015–2020, 2021–2022, and 2015–2022. We do not indicate the confidence intervals for the obtained differences, as they are negligibly small due to the large number of compared data pairs.

We used the following matching criteria for data pairs: the IKFS-2 and the Dobson and Brewer measurements are within 1 h and 70 km; the IKFS-2 and the TROPOMI measurements are within 6 h and 35 km. The choice of acceptable mismatch parameters and the list of 21 stations whose data were used are justified by Polyakov et al. [31,66]. The ozonometric stations considered are located mostly in the Northern Hemisphere, in Europe and the USA. There are two stations that are north of the Arctic Circle, four in the tropical belt, and two in the Southern Hemisphere.

Row 1 of Table 2 presents the same results found in [66], but uses updated and supplemented independent data for comparisons. The values presented in row 1 of Table 2 differ slightly from the results of [66], where SDD was 2.9% for ground-based measurements and 2.75% for satellite measurements. The changes are due to their replenishment: TOCs at ground-based WOUDC stations are retrieved gradually over several years after the actual measurements of solar irradiance. Changes in differences for TROPOMI data are due to the replacement of preliminary OFFL versions of the processing with the final RPRO version.

Rows 2 and 3 of Table 2 show that the comparison for the last two years, only with data inside the 1000 km band (row 2), even decreases the SDDs for ground-based and slightly increases for satellite data. Measurements with SWs between 1000 and 1500 km (row 3) show a noticeable decrease in the SDDs: 3.0% for ground-based data and up to 3.5% for satellite data. We can conclude that the growth of the SDDs in 2021–2022 is caused by the expansion of the SW. Hence, the data for 2015–2020 fully describe the statistics of ozone changes in 2021–2022, which allows us to consider with high probability that these data describe the ozone statistics, and the ANN trained on them may be applied to the TOC retrievals in the future.

Rows 4–7 of Table 2 show the same, but for the entire 2015–2022 data. This part of Table 2 depicts that the ‘new’ ANN allows for obtaining the accuracy for the entire 8-year period of measurements no worse than that for the first 6 years.

Thus, the TOC variability for the first 6 and 8 years of measurements represents an ensemble of data that is wide enough and appropriate for the TOC estimation from spectral measurements in the subsequent period, already for the 1500 km SW.

3. Results and Discussions

3.1. Validation of the IKFS-2 Results

Without checking the accuracy and reliability of the measurement results, the development of the methodology cannot be considered complete. Therefore, validation of the ANN technique and its results based on a detailed and comprehensive quantitative and qualitative comparison by independent measurements is an obligatory and the most important stage in the development of the ANN. To avoid methodological errors, independent measurements should be based on methods and physical principles different from those used in the validated technique. Since our proposed methodology is based on satellite remote measurements of the IR radiation from the Earth’s atmosphere, for validation it is desirable to use (a) contact measurement methods, (b) in the case of remote measurements, another spectrum band such as UV and VIS, and (c) ground-based remote measurements. In addition, comparisons should cover the entire spatial and temporal range of measurements.

3.1.1. TOC Data Validation

Dobson and Brewer instruments’ data

In [33], the results of IKFS-2 were compared with the data of ground-based measurements by Dobson and Brewer spectrophotometers available at the WOUDC website https://woudc.org/home.php. It was shown that the average SDD for the 21 stations was 2.7%. The maximum SDD was observed for the Mauna Loa station located in the area of high variability of surface altitudes and, consequently, changes in the thickness of the TrOC layer.

Ozonesonde TOC Data

As noted above, measurements of solar radiation by satellite instruments such as TROPOMI, OMI, as well as by ground-based instruments, are impossible during the period of polar night. Apart from IR instruments, the only source of data on TOCs without solar radiation is ozonesondes. In [33], the correlations between IKFS-2 TOC and ozonesonde data harmonised by the HEGIFTOM working group within the framework of the TOAR-II project (https://hegiftom.meteo.be) were analysed. On 20 February 2024 (the last access), the database contained data from 57 ozonesonde stations with different degrees of readiness (harmonisation). Data from 40 stations were ready for use.

For quantitative comparisons, the IKFS-2 measurements data were selected in a 70 km circle around the location of the ozonesonde station and 1 h time mismatch. Due to the peculiarities of the satellite trajectory, the circle with a radius of about 150 km around the South Pole is inaccessible for measurements, even for a scanning band of 1500 km. Therefore, for comparison with data from the station not covered directly by IKFS-2 measurements, the IKFS-2 data at a distance of 200 km from the site were taken. Nevertheless, for such ozonesonde stations, comparisons are possible only from December 2020.

As mentioned above, the ozone profiles obtained by ozonesondes, supplemented above the sonde upper boundary with climate data [6], were used to calculate the TOC at ozonesonde stations. For comparison, we considered only measurements where the upper bound of the measurement profile was above the 10 hPa pressure level. The SDD between TOCs by IKFS-2 and ozonesondes were from 5.3 to 11% (17–33 DU) for different stations; the MD and SDD values averaged over all stations were 1.2 and 7.9%, which agrees with the uncertainty of the TOC derived from the ozonesonde data.

For qualitative comparison in the form of a graphical representation, we selected the stations that provide data on TOCs and for which both the number of measurements for 2015–2022 and the number of pairs of ozonesonde-IKFS-2 measurements exceed 100. There were 13 such stations in the HEGIFTOM database, located at different latitudes. To present the ozone variability in detail, we show values of the IKFS-2 measurement results averaged during the day, when the sonde was launched, in a circle around the station: 500 km for the South Pole station is 500 km and 70 km for other stations. For ozone-sounding data, single measurements are shown. Similar comparisons, but for all IKFS-2 measurements, were made by [33]. Below, we consider only those IKFS-2 measurements that were made on the same day as the ozone probe measurements, which allowed us to demonstrate more clearly the agreement between the two types of measurements.

Figure 3, Figure 4 and Figure 5 depict the TOCs from sondes and IKFS-2 data in the area of both poles and the tropical zone. Only some of the ozonesondes ascended to the 10 hPa level, which is determined by the balloon quality and weather conditions. Therefore, we highlighted in the figures the data obtained at the probe ascent above the 10 hPa level.

Figure 3 demonstrates a good qualitative agreement between the IKFS-2 and ozone-sounding data near the South Pole. Maximal TOCs are reached in December–July, accompanied by a large magnitude of variability of both IKFS-2 and sounding data. During the period of seasonal TOC decrease from July to November, the IKFS-2 and sonde data agree well. We note a peculiarity, which was less significant than in other years: a decrease in TOCs in spring 2019 registered by both types of measurements. Thus, the IKFS-2 TOCs in the South Pole area are in good qualitative agreement with the ozonesonde data.

Figure 4 shows similar comparisons for the Ny-Alesund observation station located at 79° N. Here, apparently, for some technical reasons, the number of measurements reaching the 10 hPa level sharply decreases during the polar night period. At the same time, an increase in the random variability of TOCs according to both types of measurements is observed. However, the tendency in TOC growth is consistently maintained throughout the polar night. Figure 3 and Figure 4 show satisfactory qualitative agreement of the two types of measurements during the polar night period.

Figure 5 shows the comparison for the Tenerife subtropical station. Due to the lower TOC variability near the tropical zone, we chose a large scale on the ordinate axis, and the agreement between the two types of measurements is less clear than in the polar regions. Considering this circumstance, Figure 5 also shows good agreement of both TOC variability and its seasonal variation.

3.1.2. TrOC Data Validation

For the period of IKFS-2 spectra measurements, the TrOC FTIR data are available at 19 NDACC sites, whose locations and geographical coordinates are presented in [33]. These sites are located in both hemispheres at different latitudes and altitudes. Therefore, the validation of the IKFS-2 TrOCs by NDACC measurements can be assumed global.

For comparison with daily averaged FTIR data, we used the following coincident criteria: IKFS-2 data were averaged daily within a 100 and 200 km radius with a centre at the site location. Some of the sites are located on isolated islands (e.g., Izaña, Mauna Loa, Maido), and some are elevated above sea level (e.g., Zugspitze, Jungfraujoch, etc.). Taking into account the spatial resolution of the averaged IKFS TrOCs, it can be assumed that for these sites, TrOCs derived from different layers are compared. For example, when the site is located in the mountains, especially on the isolated islands, some of the IKFS-2 data may cover not only the mountain area but also the area above the sea, with an additional layer of tropospheric ozone, which can influence the results of the comparison.

In [32], various ANN schemes were tested through the comparison with FTIR measurements at the NDACC sites mentioned above. On average, the absolute values of SDD do not change noticeably depending on the width of the tropospheric layer as well as on the radius of IKFS-2 TrOCs averaging, yielding agreement of about 3 DU (~15% of the mean FTIR TrOCs) for all considered data pairs. For separate sites, the SDDs vary from 2 DU (at mountain sites) to 4.5 DU (at sea-level sites located on isolated islands), mostly depending on the TrOC values. The IKFS-2 TrOCs overestimate FTIR TrOCs for the mountain NDACC sites, to a larger extent for Jungfraujoch, Zugspitze, and Altzomoni sites (10–12 DU), and underestimate FTIR TrOCs by 2–3 DU at Eureka, Thule, Tsukuba, and Wollongong sites. At all other sites, the mean differences between IKFS-2 and FTIR TrOCs do not exceed 1–2 DU. In these comparisons, TrOC FTIR measurements were derived using non-uniform retrieval strategies; thus, we cannot distinguish the influence of the retrieval strategy on the results of the comparison.

In the current study, we compare IKFS-2 retrievals with the results of the FTIR TrOCs derived using the IRWG2023 strategy (11 sites). The results of this comparison for two tropospheric layers and two radii of the IKFS-2 data averaging are presented in

Table 3. Differences between IKFS-2 and FTIR TrOCs (MDs, SDDs), N—the number of data pairs. SDDs in percentage are related to the FTIR values.

Site	100 km IKFS-2 Average						200 km IKFS-2 Average
	Up to 400 hPa			Up to 300 hPa			Up to 400 hPa			Up to 300 hPa
	N	Δ, DU	σ, DU (%)	N	Δ, DU	σ, DU (%)	N	Δ, DU	σ, DU (%)	N	Δ, DU	σ, DU (%)
Thule	513	−0.3	3.3 (15)	504	+0.4	3.9 (13)	554	−0.3	3.3 (14.6)	546	+0.4	3.9 (12.8)
St. Petersburg	209	−0.5	3.4 (13.5)	209	−0.8	4.0 (13)	249	−0.3	3.5 (13.9)	250	−0.6	4.3 (13.7)
Jungfraujoch	390	−12.9	2.2 (21)	390	−13.9	2.8 (18.8)	444	−13.1	2.4 (22)	444	−14.2	3.0 (19.9)
Toronto	544	−2.3	5.3 (23)	544	−2.5	6.0 (22)	681	−2.2	5.2 (23)	681	−2.4	5.8 (21)
Rikubetsu	81	−1.6	3.8 (16.5)	81	−1.7	4.7 (16.3)	94	−2.0	3.4 (15)	94	−2.2	4.3 (14.9)
Boulder	358	−2.8	2.3 (13.5)	359	−3.9	2.9 (13.9)	443	−2.5	2.5 (15)	443	−3.4	3.1 (14.8)
Tsukuba	112	+1.2	4.6 (17.7)	112	+1.6	4.7 (14.7)	166	+1.3	4.1 (15.5)	166	+1.5	4.5 (14.3)
Izaña	302	−8.5	2.0 (12.2)	302	−8.9	2.3 (10.9)	385	−8.6	1.9 (12)	386	−9.2	2.3 (11)
Mauna Loa	515	−8.6	2.2 (21)	515	−9.1	2.5 (18)	662	−8.5	2.1 (20)	662	−9.3	2.5 (18)
Altzomoni	206	−11.1	2.4 (30)	205	−9.9	2.6 (23)	283	−11.0	2.2 (27)	283	−10.2	2.5 (22)
Maido	332	−6.0	2.1 (13.8)	333	−7.5	2.5 (12.5)	424	−5.9	2.2 (14.1)	425	−7.5	2.6 (12.9)

.

The largest relative SDDs (~20 and more %) for both tropospheric layers are observed for the Altzomoni, Toronto, Mauna Loa, and Jungfraujoch sites. The smallest relative SDDs (11–15%) are obtained for the Izaña, Thule, St. Petersburg, Boulder, and Maido sites. On average, we derived the same agreement of ~15% between IKFS-2 and FTIR TrOC data as in [32]. Nearly the same estimates were obtained by [52] for the comparison of IASI TrOC data with ground-based measurements.

The smallest bias between satellite and ground-based measurements is observed for the Thule, St. Petersburg, and Tsukuba sites. In general, IKFS-2 and FTIR TrOCs correlate better and have a larger bias for a thicker layer—from surface to 300 hPa. The positive bias with ground-based measurements for mountain sites is explained by the ozone content in additional tropospheric layers for satellite measurements. For example, we receive ~8 DU mean difference for the Izaña site, which is very close to the difference between IASI and FTIR measurements for the same site [53], and which is recommended to be added to FTIR measurements based on the comparison of ozonesonde profiles launched at the site altitude and the sea level [60].

The examples of temporal variability of TrOCs derived from IKFS-2 and FTIR instruments for St. Petersburg (in the surface to 400 hPa layer) and Thule (from the surface to 300 hPa layer) sites are depicted in Figure 6. In general, IKFS-2 measurements reproduce the year-to-year variability detected from ground-based measurements well. For the tropospheric layer up to 400 hPa (St. Petersburg site), the IKFS-2 TrOC maximum is shifted from the spring to summer months. The same feature is observed for comparison between IASI and FTIR measurements [52,54].

For the tropospheric layer up to 300 hPa (Thule site), IKFS-2 measurements demonstrate the same character of the monthly/yearly variability as FTIR measurements, but with a smaller amplitude of changes.

Therefore, we suppose that taking into account the accuracy of IKFS-2 TrOC measurements (~15%), for both tropospheric layers, IKFS-2 measurements allow us to analyse the TrOC variability and estimate TrOC temporal variations at various scales.

3.2. IKFS-2 vs. TROPOMI and IASI TOCs

We compared the results of TOC measurements by the IKFS-2 instrument with the TROPOMI data obtained from the S5P satellite. Only the TOC values in the 100–650 DU range were used in the comparison, and the number of data pairs for comparison was about 10.7 × 10⁹. The MDs between the IKFS-2 and TROPOMI data relative to TROPOMI constitute 2.2% with an SDD of 2.7%. The large amount of compared data and global coverage allowed us to analyse the latitudinal and seasonal dependencies of differences between the measurements of two instruments that are shown in Figure 7.

The mean differences in the two types of measurements mostly fluctuate between −1 and −3%, around −2%. Their variability is minimal in the tropical zone, where the TOC variability is also minimal. An exception is observed in autumn in the northern polar zone, where TOCs based on TROPOMI measurements are higher than based on IKFS-2 by 4.5%. SDDs in the tropics are close to 2% regardless of the season, and increase towards the poles, especially in winter and spring (in each hemisphere), reaching 5% in the southern and 4% in the northern polar zones, in winter in the northern hemisphere and in winter–spring in the southern hemisphere.

Figure 8 shows the spatial distribution of MDs (a), SDDs (b), and Pearson correlation coefficient CCs (c) between IKFS-2 and IASI TOCs for 2015–2022 for daytime (Solar zenith angle < 90°) and night-time (Solar zenith angle > 90°) measurements, separately. Statistical t-test has demonstrated that all CC values for the period considered are statistically significant. Therefore, they are not highlighted in Figure 8c. The TOCs from IKFS-2 data are mostly lower than those from IASI data, except for some areas, some of which correspond to the position of deserts and mountains. Estimates of MDs and SDDs are given in % relative to the averaged IASI data. The lowest MDs and SDDs are observed in the latitude range 60 S–45 N. Their variability in this region is ~0–3%. The maximum MD and SDD are observed in the polar region of the southern hemisphere, as well as over the territories of deserts and mountains (e.g., the Sahara Desert in Africa). Thus, according to Figure 8, MDs and SDDs in the South Pole region exceed 15 and 10%, respectively. The CC is close to 1 almost on the whole territory of the Earth, except areas in the South Pole region, and above the surface of the Southern, Indian and Pacific Oceans. The latter territorially coincides with ENSO (El Niño–Southern Oscillation), which influences wind direction at the equator of the Pacific Ocean and the temperature of the water surface (https://oceanservice.noaa.gov/facts/ninonina.html (accepted 16 June 2025)). In addition, the lowest CCs (about 0.6) are also observed in the regions of deserts and mountains.

Thus, there is a connection between the increase in the differences and the decrease in the correlation coefficient of the two sets of measurements with the type of the underlying surface, apparently caused by inaccurate accounting of its optical properties in one or both processing algorithms.

The reasons for increasing discrepancies in specific areas can be partly explained by (a) the temperature profiles used in IASI TOC retrievals being less reliable at high latitudes and over elevated terrain, which leads to an increase in uncertainties in TOCs [52]; (b) areas with a lack of vegetation and high or low surface temperatures may lead to errors in thermal contrast and, consequently, to the limited information content in the remote sensing method—the same for both instruments [52,66]. The comparison of IASI FORLI-O3 retrieval vs. GOME-2A TOC product [52] demonstrated that IASI TOCs underestimated GOME-2A TOCs over deserts and mountains, whereas comparison of IKFS-2 TOC product vs. ERA5 re-analysis data based on various satellite retrievals showed that IKFS-2 TOCs overestimated ERA5 TOCs in these areas [66]. Thus, we may conclude that the errors of the satellite method based on measurements of thermal IR radiation are less reliable over elevated and desert areas.

3.3. IKFS-2 vs. IASI TrOCs

Figure 9 shows the spatial distribution of MDs, SDDs, and CCs on the territories of Eurasia and Eastern Europe between the TrOCs by IKFS-2 and IASI in the layer from the surface to altitudes of 300 (left) and 400 hPa (right) for 2015–2022. The crosses in Figure 9c (and in some further provided figures) demonstrate statistically insignificant CCs according to the t-test for a 95% confidence level. Such a choice is due to the locations of the ozonesonde measurements used to train the ANN. For example, in the Sahara Desert area, the differences between the tropospheric ozone content based on IKFS-2 and IASI measurements reach more than 10 DU (more than ~30%), which is (a) due to the absence of ozonesonde measurements in such extreme conditions; (b) due to the lack of information content of the considered remote sensing method (see Section 3.2).

In general, IKFS-2 TrOC values are greater than those of IASI up to ~60 N latitudes, but smaller in the north, which is especially noticeable in the layer up to 300 hPa (Figure 9a on the left). The smallest MDs are observed in Russia (about 0 DU), except for the Arctic part for TrOCs up to 300 hPa, where MDs reach 3–4 DU. This is probably due to the influence of the snow surface and, consequently, the influence of a lack of information with a small temperature gradient on the accuracy of satellite measurements. Nevertheless, in the layer up to 400 hPa (Figure 9a on the right), similar behaviour of MDs in the northern regions of Russia, where they reach ~1–2 DU, is not observed. Maximum MDs (up to 10 DU) are observed predominantly on the territories of eastern Europe, southwestern Russia, Kazakhstan, China, and Mongolia for both tropospheric layers. The spatial distribution of MDs has a vaguely pronounced zonation, resembling the distribution of the average land surface temperatures (see e.g., https://agroatlas.ru/en/content/Climatic_maps/Temperature_avg/Temperature_avg/index.html (accessed 16 June 2025)).

SDDs have a close spatial distribution in both layers (Figure 9b). The minimum values occur in the Arctic Ocean, eastern Europe, and western and central Russia (1–4 DU). The largest SDDs are observed in the same places as MDs—in the territories of Kazakhstan and Mongolia, but also in China and eastern Russia (6 DU and more). The latter territorially coincides with the centres of summer forest fires, which annually occur in this part of Russia [75].

In contrast to MDs and SDDs, the spatial distribution of CCs for TrOC in the two layers of the atmosphere is markedly different (Figure 9c). Thus, in the layer up to 300 hPa (Figure 9c on the left), the minimum CC values are close to 0 and are predominantly observed in the territories of Kazakhstan and eastern Russia. In the rest of the territory, the CC varies from about 0.5 to almost 1, with the highest values observed above the sea surface. In the layer up to 400 hPa, the CC is in the range from almost 0 to about −0.3 over almost the entire land surface area of the considered region (Kazakhstan and eastern Russia). At the same time, above the sea surface, the CC is relatively high and varies from 0.3 to 0.7. This is probably connected to the lower informativeness of spectral measurements in the 400 hPa layer with respect to the changes in tropospheric ozone content.

Figure 10 shows the same three characteristics but for the territory of North America. According to Figure 10a, MD has a pronounced zonal distribution. In the southern and central parts of the continent, TrOC values in the layer up to 300 hPa (Figure 10a on the left) based on IKFS-2 measurements are larger than IASI data by 3–6 DU, while they are smaller by 3–4 DU in northern regions. The smallest differences are observed in the northern continental part and over the Arctic Ocean. A similar spatial distribution of MDs is observed in the layer up to 400 hPa (Figure 10a on the right), but in the northern part of the continent, the MD values are close to 0 DU.

The spatial distribution of SDDa in the layers up to 300 and 400 hPa (Figure 10b) is close, having a minimum (about 0 DU) in the southern part of North America, and a maximum in the northeast and centre of the continent, namely in the territories of Canada and northern USA (up to 6 DU).

The minimum CC (Figure 10c) is observed in the central part of the continent, reaching about −0.2 (TrOC up to 300 hPa) and −0.4 (up to 400 hPa). At the same time, as for the territory of Eurasia (Figure 9), the largest area with negative CCs is observed for the TrOCs in the layer up to 400 hPa. Territorially, the areas of CC minimum coincide with the areas of maximum SDD. It can be assumed that, as in the previous case, these areas are territorially consistent with the centres of forest fires that periodically occur in the USA and Canada (Figure 9.1 in [76]). Again, on most of the land territory, CCs are statistically insignificant if considering a layer up to 400 hPa. This is related to low CCs.

Figure 11, Figure 12 and Figure 13 show the same as Figure 9, but for four separate seasons—winter (DJF), spring (MAM), summer (JJA), and autumn (SON), and only for the layer up to 300 hPa. In winter, the largest MDs (up to 10 DU), when IKFS-2 TrOCs underestimate IASI TrOCs, are observed over the entire territory of Russia (Figure 11a). In autumn, MDs on the territory of Russia decrease and on average reach about 0 DU (Figure 11d). In summer, mainly in the south and east of Russia, and in the territories of Kazakhstan and Mongolia, the TrOCs by IKFS-2, on average, overestimate that of IASI (in some places up to more than 10 DU).

The SDDs do not show such pronounced seasonal variations, but the minimum values (1–2 DU) are observed in winter over the land surface (Figure 12a), and the maximum values are observed in spring and summer (Figure 12c,d) (4–6 DU). In summer, the eastern part of Russia stands out, where the highest SDDs are observed, spatially correlating with the forest fires. In this case, TrOCs by IKFS-2 are larger than those by IASI. This confirms the fact that the data on TrOCs in the layer up to 300 hPa, based on IASI FORLI-O3 retrieval, lacks a signal associated with hydrocarbon emissions from biomass burning.

The maximum CC, reaching almost 1, is observed in spring, over the land and is probably related to the maximum values of TrOCs in this season. The lowest CC (up to 0.5–0.6) occurs in autumn and is probably, on the contrary, connected with the lowest TrOCs over this territory. However, in all seasons, CCs are mostly statistically insignificant above the land surface. This is related to a smaller number of values filtered by a season and low CC values. Only in spring (Figure 13b), about half of the land territory is covered with statistically significant CCs.

Figure 14a shows the results for an area with relatively good agreement (60 N, 90 E, region of the Taimyrskii Avtonomnii Okrug). There is a pronounced correlation between the TrOCs, the CC is about 0.6, and the MDs and SDDs are of the order of 2 and 11% relative to the mean ozone content from IASI data. The agreement between the satellite data at the second selected site, 60 N, 120 E (Figure 14b), is noticeably worse; the CC is about 0.3, with MD and SDD of 7.7 and 19%, respectively. Another interesting feature at the site with poor agreement is that the maxima and minima of IKFS-2 TrOCs are observed in spring and autumn, while IASI TrOCs—in summer and winter.

The study [53,54] presents the seasonal variations in ozone content in the layer up to 8 km at the St Petersburg NDACC site (59.88° N, 29.82° E, 20 m above sea level) based on ground-based spectroscopic measurements for 2009–2022. According to the study, the maximum of TrOCs is reached in April and the minimum in October–November, which is closer to the results from this paper based on satellite measurements of IKFS-2. At the same time, the study [54] shows that the seasonal variations in tropospheric ozone in the layer up to 300 hPa from IASI data for 2009–2017, reconstructed by scientists from the LISA laboratory, have a close resemblance to ground-based spectroscopic measurements. It is suggested that the shift in the seasonal variations in the tropospheric ozone content based on IASI FORLI-O3 data is due to incorrect a priori information on the variability of ozone in the atmosphere in some months, which is used to reconstruct the ozone profile from IASI measurements.

An example of a pronounced shift in the seasonal variability of TrOCs between IKFS-2 and IASI data is shown in Figure 15 for an observational site in the USA (see Figure 10, approximately 42 N and 95 W). In this case, the offset of ozone maxima and minima is about 2 months, and again, the IKFS-2 data are ahead of IASI data.

4. Conclusions

We presented new TOC and TrOC products obtained from the measurements of the Russian IKFS-2 instrument aboard the Meteor-M No. 2 in 2015–2022. The advantage of these products is their global distribution, including periods of polar nights. The retrieval algorithms for both products are based on a simple 3-layer perceptron ANNs approach, which provides the accuracy of measurements in accordance with the WMO requirements for the satellite ozone monitoring in various scientific research tasks. We validated the quality of the TOC and TrOC products by comparison vs. reference ground-based measurements and compared them with independent satellite measurements. The main results of the study are as follows:

• After the IKFS-2 swath width changed to 1500 km in 2021–2022 and the ANN retraining, the TOC retrieval errors have not changed compared to the period 2015–2020. In general, the TOC errors from the IKFS-2 spectra measurements do not exceed 3%.
• The estimate of the TrOC retrieval errors is less than 2.8 and 3.8 DU for the layers below 400 hPa and 300 hPa, respectively.
• Comparison of the TOC variability measured by IKFS-2 and ozonesondes demonstrated good qualitative agreement, including the polar night period.
• Comparison of the IKFS-2 TOC results vs. the ozonesondes data also showed good quantitative agreement: MDs are 1.2% and SDDs are 7.9%, which is close to the errors of TOC measurements by ozonesondes.
• The results of TrOC satellite measurements were validated against data from 19 sites of the IRWG-NDACC network, with SDDs ranging from 2 to 4 DU, which is consistent with the results of other authors for similar measurement methods.
• Monthly mean TOC values by IKFS-2 and IASI correlate spatially well with the largest differences in polar regions (up to 10–15%), where both instruments have the largest measurement errors. Examples of the obtained TOC and TrOC distribution fields over the entire globe are given, compared with similar data from the IASI instrument.
• Monthly mean IKFS-2 TrOCs are larger than those of IASI, with the maximum differences in lower latitudes (up to ~6 DU) of most of Eurasia and North America. Correlation between TrOCs is significantly higher if a thicker atmospheric layer is considered (up to 300 hPa vs. 400 hPa). The observed lowest correlation partially coincides with the territories of annual forest fires. The best agreement between monthly mean IKFS-2 and IASI data was found in spring and autumn.

The results obtained demonstrate that for solving the inverse problem of both TOC and TrOC retrieval, it is sufficient to use the simplest ANN—a three-layer perceptron. There is no need to use more complex approaches and other types of ANNs. At the same time, the statistical completeness of the dataset for the ANN training is fundamentally important. If this condition is met, the results of using ANN for solving the inverse problem show good quality and applicability in various conditions.

In the future, we plan to study in more detail the problem related to the discrepancies between IKFS-2 TOC and TrOC products and independent satellite measurements over deserts and mountains to increase the reliability of the IKFS-2 products.