The Tropospheric Monitoring Instrument (TROPOMI) on board the Sentinel-5 Precursor (S5P) satellite is part of the latest generation of trace gas monitoring satellites and provides a new level of spatio-temporal information with daily global coverage, which enables the calculation of daily globally averaged

Methane (

While the concentrations have risen in total, the trend, i.e. the rate of change in the background level without seasonal or short-term variations, has evolved non-linearly. Global methane concentrations have been observed to increase in the period from the 1980s to 2000 and from 2007 to the present. However, a plateau between 2000 and 2007 was observed. This is referred to as “stabilization”. Whether to define the stabilization period or the period of renewed growth (2007–present) as anomalous has been a subject of debate. There have been a variety of explanations for the observed behaviour in the literature

The Arctic contains large amounts of soil organic carbon (SOC), which is stored in the permafrost regions (ca. 1300

In this paper we present methane growth rates and annual methane increases (AMIs) derived from Sentinel-5P TROPOMI

The S5P satellite was launched on 13 October 2017 and has since delivered high-quality data from its only scientific instrument, TROPOMI, which is a nadir-viewing passive grating imaging spectrometer. Combined with a near-polar, sun-synchronous orbit, the swath width of 2600

The CAMS/INV dataset provides data for carbon dioxide, nitrous oxide, and methane. The methane data are produced using the CAMS

The marine boundary layer reference (MBLR) is a two-dimensional matrix (time vs. latitude) created from weekly air samples from the Cooperative Air Sampling Network

Annual methane increases are published by the Copernicus Climate Change Service (C3S,

The

The combined C3S/CAMS

The Method section is split into four parts. First, we describe how the data are prepared for the DLM, meaning how we get from single observations to a time series we can fit our model to. Next, we briefly introduce DLMs and provide information on the specific types of models we are using. In the third subsection we explain how we use an ensemble of DLMs and cross-validation to select the best model. Lastly, we describe how we estimate the bias related to imperfect satellite sampling.

The

In Eq. (

We first calculate the temporal inhomogeneity (

We determine a limit,

Finally, we compute the area-weighted average of the chosen sub-grid, generating a time series for the analysis. To further mitigate sampling bias in the global average, we first average over longitudes and subsequently over latitudes. This approach assumes a faster mixing of background methane levels within zonal bands while acknowledging greater latitudinal disparities. A more detailed description is given in Sect.

To extract information about the methane growth rate from the time series we first need to calculate the underlying

A dynamic linear model is a regression model that can handle observations of varying accuracy, missing data, non-uniform sampling, and non-stationary processes. It allows some of its parameters to change over time and directly models the observed variability using unobserved state variables

A DLM can be formulated as a special case of a state-space model, i.e. a model which consists of some unobserved components (represented by a state vector) and the observation vector. The evolution of the state vector and the relation between observation and state vectors are modelled by a set of equations. If these equations are linear, we have a so-called dynamic linear model. The DLM we use consists of three main components: first, a slowly changing background level, which captures the long-term trend of the methane concentration; second, a seasonal component included to model variations arising from seasonal cycles. This component enables variations in the phase and amplitude of the seasonal cycle to be accounted for. Third, an autoregressive component is incorporated to model noise and residual correlations in the data, accounting for short-term effects. Additionally, Gaussian noise can be included to model part of the errors. The ability of DLMs to capture changing components over time is achieved by modelling these changes as Gaussian random walks, allowing for smooth transitions and adjustments. The variances of these Gaussian random walks determine the overall variability of a certain parameter (e.g. trend). A detailed description of the model set-up and the different DLM components can be found in Appendix

DLM fit for daily area-weighted global WFMDv1.8 data. Panel

In general, the model parameters (e.g. variances; see Table

DLMs have been previously used to successfully model stratospheric ozone

The choice of model configuration is a non-trivial problem, which is impacted by prior knowledge, empirical testing, and different quality measures. From prior knowledge the inclusion of a seasonal component is inferred, because the existence of a seasonality in atmospheric methane concentrations is known. Empirical testing can show that the inclusion of an autoregressive component is necessary, because the data contain residual short-term variations. The term “quality measures” refers to measures that facilitate model selection, such as the mean squared error (MSE), which is defined as the mean of squared differences between the model and data. Additionally, the DLM provides variances (squared standard deviations) for each component which can be used to compare models; models with lower uncertainty in the level and seasonality are preferable to models with high uncertainties for these terms.

To avoid the need for manual model selection, we employ an ensemble approach, fitting a range of DLMs to the data and automatically selecting the best model. The ensemble consists of different DLM configurations, with varying components as described in Appendix

The inclusion of the variances ensures that the uncertainty of the level and seasonal components is considered in the selection criterion. This approach aims to select DLMs that provide good estimates of the underlying methane signal while avoiding overfitting and reliance on expert knowledge.

Different methods and measures can be used for model selection and may yield different results. We want to emphasize that the problem of model selection is non-trivial, and different approaches may be suitable for different data and use cases. Here we select the model which yields the highest certainty fit of the level and seasonal component (i.e. the

To quantify the impact of model selection, we calculate a model selection bias

The contribution of the model selection bias to the error budget can be seen in Table

Error budget for global AMIs.

All values are in parts per billion.

Sampling and model error for zonal growth rates.

All values are given in parts per billion per year.

The spatio-temporal coverage of S5P

We therefore compare AMIs (for global data) and growth rates (for zonal data) calculated using different samplings and/or methods. To simulate the spatio-temporal pattern of S5P sampling, we created a daily mask from gridded WFMDv1.8 data and applied it to the model data. To only simulate the systematic effect of the polar nights, we created a daily mask using the average solar zenith angle (SZA) per grid cell with a cut-off value of 75

Global AMIs derived from CAMS/INV-SRF

First, we investigate the effect of the averaging method. We compare standard averaging, which is defined in this study as the area-weighted mean of all grid cells in a region, with an approach we call zonal-first averaging. Zonal-first averaging takes into account the inhomogeneous sampling at each latitude, which is influenced by the distribution of land mass and seasonal coverage. Since zonal transport occurs within weeks

Zonal growth rates derived from CAMS/INV-SRF

Figure

The different growth rates for Fig.

Table

In this section, we discuss the global AMIs calculated using WFMDv1.8 data from May 2018 to February 2023. The results are shown in Fig.

Global annual methane increases derived from Sentinel-5P TROPOMI WFMDv1.8 data. The error bars show the 1

Comparison of global AMIs using different data and methods.

All values are in parts per billion. Uncertainties reflect 1 standard deviation.

Global annual methane increases derived from CAMS global inversion-optimized greenhouse gas concentrations including only surface observations. The error bars show the 1

Comparison of global AMIs listed in Table

To validate our findings, we compared our results with AMIs determined by

Additionally, we used our DLM approach on monthly WFMDv1.8 data to better compare our method to the method used by

The AMIs for 2020 and 2021 are the largest observed since the NOAA began systematic records in 1983. The drivers contributing to these record increases have been the subject of recent debate and can be attributed to a rise in emissions, a reduction in the

In addition to our global analysis, we investigated 20

Zonal growth rates for 20

The results are shown in Fig.

Zonal growth rate anomalies for the 20

Overall growth rates derived from WFMD data are close to growth rates derived from CAMS/INV-SRF

Recent studies, which discuss the record methane increases in 2020 and 2021, can help with interpreting the structures of zonal growth rates.

As mentioned before, zonal growth rates provide information about the change in methane concentration in a given zonal band, including changes in sources, sinks and transport patterns. These transport patterns would average out for global AMIs given a perfect coverage. In Sect.

Difference between total surface fluxes from the CAMS/INV-SRF data.

Difference between wetland surface fluxes from the CAMS/INV-SRF data.

Difference between other surface fluxes from the CAMS/INV-SRF data.

Difference between total surface fluxes from the CAMS/INV-SRF-SAT data. No flux difference is available for 2022–2021, since the dataset currently ends in 2021.

The agreement within 1

Large changes in fluxes are identified between all the years investigated. The wetland flux difference between 2019 and 2020 indicate a strong increase in the NH as indicated by

In this study, we presented a DLM-based approach to calculate methane growth rates and AMIs from S5P/TROPOMI data. We addressed sampling-related biases by comparing AMIs and growth rates derived from CAMS/INV

In addition to global AMIs, we investigated growth rates for 20

We further investigated these inter-hemispheric differences by investigating the surface fluxes available from CAMS/INV data. We argue that this is possible since (a) growth rates derived from WFMDv1.8 data are similar to growth rates from CAMS/INV data and (b) no significant sampling bias is present, as we showed in Sect.

In addition to the confirmation of known results, new conclusions are also drawn. Most notably, the decrease in the global AMI in 2022 is caused by reduced NH zonal growth rates. This is clearly visible in zonal growth rates derived from S5P

In summary, our DLM-based approach allows calculation of growth rates or AMIs for global and zonal S5P/TROPOMI data. This approach is computationally inexpensive and readily allows for the constant integration of new data, enabling timely assessments of global methane concentration changes. Importantly, no additional prior information about the atmospheric state is required. We believe that our approach provides an additional valuable tool for investigating atmospheric methane concentrations, enabling rapid identification of regions of interest, such as the 2022 NH. Furthermore, our approach can be readily applied to other datasets facing similar challenges, such as inhomogeneous sampling, non-linear trends, and data gaps. For the 70–90

Future research could aim to improve this approach, especially for high-latitude regions, to identify smaller changes in growth rates. Better estimates of the impact of meridional transport on zonal growth rates could help to provide better error estimates for our method. The 2022 decrease in NH growth rates could be investigated in more detail and this approach be extended to include datasets of other atmospheric constituents. Data from future satellite missions, with lower uncertainties and increased data coverage, could enable the investigation of sub-annual changes in growth rates, which are presently not detectable. Finally, zonal growth rates of long-lived gases (e.g. HF) without any significant sources or sinks could possibly enable the quantification of atmospheric transport patterns.

The structure of our DLMs assumes that the measured methane signal can be separated into a slowly changing background level, a seasonal component and noise term. This section closely follows the more detailed description in

The level component can be described by the following formulas:

The seasonal part of the signal is modelled by a truncated Fourier series with

DLM parameters.

The noise term accounts for residual correlations as well as random Gaussian noise in the signal. Residual correlations can be modelled by an autoregressive component which includes a serial dependence between the observations. An autoregressive noise of order

An additional Gaussian noise can be included:

The complete signal can then be written as the sum of these components:

The ensemble size is determined by the number of possible model configurations. In our case this is determined by whether to allow variability of the seasonal cycle or whether to include a Gaussian error term and the number of harmonics:

To investigate the effect of the fitting method on AMIs we replicated AMIs calculated by the NOAA–GML and C3S in Figs.

Comparison of global annual methane increases derived from the NOAA–GML MBLR data using different methods.

Comparison of global annual methane increases derived from C3S XCH4_OBS4MIPS v4.4 data which are extended by CAMS NRT data after 2021 using different methods.

Here we present global AMIs and zonal growth rates for CAMS/INV-SRF-SAT data which includes satellite measurements from GOSAT in its optimization (see Figs.

Global annual methane increases derived from CAMS global inversion-optimized greenhouse concentrations including both surface and satellite observations.

Zonal growth rates for 20

Figure

Area-normalized coverage of S5P/TROPOMI WFMDv1.8 data for 30

CAMS global inversion-optimized greenhouse gas fluxes and concentrations are available from

JH developed the methodology and conducted the formal analysis. OS provided information on the WFMDv1.8 data. MiB provided information on the UB–C3S–CAMS data. JPB provided valuable input on atmospheric transport effects. MaB provided supervision and helped with the conceptualization. JH wrote the initial draft of this paper. All the authors contributed significantly to the conception of the analysis, jointly discussed the results, and provided constructive comments to improve the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This publication uses and contains modified Copernicus Atmosphere Monitoring Service information (2018–2022) and modified Copernicus Sentinel data (2018–2023). Sentinel-5 Precursor is an ESA mission implemented on behalf of the European Commission. The TROPOMI payload is a joint development by the European Space Agency (ESA) and the Netherlands Space Office (NSO). The Sentinel-5 Precursor ground-segment development has been funded by the ESA and with national contributions from the Netherlands, Germany, and Belgium. The pre-operational TROPOMI data processing was carried out on the Dutch national e-infrastructure with the support of the SURF cooperative. Scientific colour maps

This project is funded by the State and University of Bremen. In particular, the University of Bremen funding for the junior research group “Greenhouse gases in the Arctic” is acknowledged by Jonas Hachmeister and Michael Buchwitz. We gratefully acknowledge the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant no. 268020496 – TRR 172, within the Transregional Collaborative Research Center “ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe Processes, and Feedback Mechanisms (AC)

This paper was edited by Bryan N. Duncan and reviewed by two anonymous referees.