LPJ-GUESS is a dynamic global vegetation model (DGVM), designed to simulate the interactions between vegetation, soil, and their responses to environmental changes and management . The model can simulate vegetation dynamics, carbon and water cycles, and soil biogeochemistry from local to global scales, including the simulation of methane fluxes from natural wetlands.

For this study, we used the Arctic-enabled version 4.1 of the model , which differs from previous versions for having detailed representation of wetland CH₄ emission. The process descriptions of the CH₄ module were mostly adopted from the LPJ-WHyMe model , and are described in detail in . It is based on a “potential carbon pool”, which is then decomposed to soil organic carbon distributed vertically in the soil layers. Methanogens use this decomposed organic carbon and produce CH₄. A part of this produced CH₄ gets oxidized by O₂ and the remainder is transported to the atmosphere by diffusion, ebullition, or plant-mediated transport (see for more details). The model is driven by daily climate data including air temperature, precipitation, and shortwave radiation taken from the Climatic Research Unit-Japanese Reanalysis (CRU-JRA; dataset. Annual atmospheric CO₂ concentrations, as additional model input for LPJ-GUESS, are obtained from the Global Monitoring Laboratory (https://gml.noaa.gov/ccgg/trends, last access: 23 October 2025), and the soil property data was extracted from WISE5min, V1.2 Soil Property Database .

Model simulations covering the area north of 45° N are produced using PEATMAP , which combines geospatial information from various sources to create a global map of wetland extent. PEATMAP has been used in several studies mainly because it is an updated quantification of peat land extend, and it focuses on mapping peatlands, such as marshes and swamps, which are the dominant wetlands in northern latitudes .

To optimize the methane module of LPJ-GUESS, developed the GRaB-AM data assimilation framework, which seeks to optimize the value of ten highly sensitive parameters in the methane module of LPJ-GUESS (connected to production, transport and consumption pathways of CH₄), based on the model fit to eddy-covariance (EC) flux observations. The minimization is performed using an adaptive scheme of the Markov Chain Monte Carlo Metropolis-Hastings algorithm . In , observations from 14 natural wetlands distributed across the Northern Hemisphere above 40° and over a total period of 20 years (from 2000 to 2020 with individual sites contributing observations over different years within this time period) were assimilated. The number of sites used for the GRaB-AM optimization exceeds the indicated sites shown in Fig.  (a full list of the sites is given in ).

In this study we computed two ensembles of hundred gridded LPJ-GUESS simulations each, randomizing the values of the LPJ-GUESS parameters adjusted by the GRaB-AM algorithm. In the first ensemble (LPJ-GUESS-unopt) the parameter values were draw from a log transform distribution, such that 90 % of the prior samples fall within their assumed ±40% uncertainty range. In the second ensemble (LPJ-GUESS-opt), the ensemble members were drawn from the corresponding 90 % confidence interval, to maintain consistency.

LUMIA is a regional atmospheric inversion setup developed initially to estimate European CO₂ inversions using in-situ concentration measurements such as those provided by the ICOS network . This study is the first application to a non-CO₂ tracer.

The inversion seeks to determine the set of regional CH₄ emissions that is the most consistent with a dataset of observed in-situ CH₄ mixing ratios. The impact of emissions outside the regional domain is provided through a prescribed background term. The link between emissions and volume mixing ratio given by: 1y+εo=Hx+ybg+εm with y the observations vector contains observations of the atmospheric CH₄ mixing ratio, and x the control vector contains the variables that we seek to optimise: in our case, the daily CH₄ emissions, grouped in two categories (wetlands and non-wetlands), at a 0.25° resolution over a regional domain ranging from 15° W, 33° N to 35° E, 73° N (Fig. ). The regional transport operator H contains the sensitivity of the observations y to the (regional) emissions x (Hi,j=∂yi/∂xj). The background concentrations (ybg) are provided as timeseries of baseline concentrations directly at the observation sites, following the two step approach of (see Sect. ). The error terms εo and εm represent respectively the measurement error and the model error.

The optimal control vector x^ is given as the one that minimises a cost function J(x), such that 2J(x)=12x-xbTB-1x-xb+12Hx+ybg-yTR-1Hx+ybg-y The first part evaluates the goodness of fit of the estimated control vector x to its prior estimate xb, normalised by the prior error-covariance matrix B, which contains the uncertainty of xb. The right hand side term evaluates the model fit to the observations y, normalised by the observation error-covariance matrix R, which combines the model (εm) and measurement (εo) uncertainties (i.e. it is the total uncertainty on the model-data mismatch).

The optimal control vector x^, which satisfies ∇xJ(x^)=0, is the set of CH₄ emissions that represents the best compromise between fitting the observations and limiting the departures from the prior estimate (which implicitly carries the knowledge of the models and data used to construct the prior emissions).

The solution is searched for iteratively, using a conjugate gradient algorithm provided by the python “scipy.optimize” package (which employs a nonlinear conjugate gradient algorithm by Polak and Ribiere, a variant of the Fletcher-Reeves method described in Nocedeal and Wright (2006). This solver is not optimal for our setup (a linear CG algorithm would be better suited, since our optimization problem is strictly linear), but turned out to be more practical and I/O efficient than the linear solver used in previous LUMIA papers (e.g. ), while giving similar results.

The regional transport operator H was computed using the FLEXPART 10.4 Lagrangian particle dispersion model . FLEXPART is not called directly within the inversion, but is used before, to pre-compute observation footprints, i.e. rows of the H matrix from Eq. (). These footprints are stored on disk and simply read during the successive phases of the inversion. Each footprint was obtained by simulating the dispersion, backward in time starting from the observation time and position, of ten thousand virtual air particles, based on meteorological fields from the ECMWF ERA5 reanalysis (at a 0.25°, hourly resolution), and limited to the aforementioned European domain: the particles are destroyed when they reach the edge of the domain. The aggregated residence time of the particles near the surface (below 100 m above ground) is used as a proxy for the sensitivity of the observations to the emissions.

The background vector ybg accounts for all the contributions to the observed CH₄ mixing ratio that are not adjusted by the inversions: the impact of the initial condition, the impact of CH₄ emissions from outside the regional domain, the impact of European CH₄ emissions having left the domain on the CH₄ mixing ratio of air masses (re-)entering it, and the impact of the various CH₄ sinks (reactions with OH, and, in the stratosphere, with Cl and O(¹D).

The background concentrations were taken from the CAMS v19r1 global CH₄ reanalysis of surface observations , which relies on the TM5-4DVAR global atmospheric inversion system. The concentrations baselines were extracted using the two-step scheme of (see also for the CAMS implementation, and for the usage in LUMIA). These baselines were provided as part of the CoCO2 CH₄ inversion intercomparison, therefore they are purely an external input to our modeling setup.

The inversions solve for CH₄ emissions grouped in two “super-categories”: wetland and non-wetlands. The latter groups the contributions of all remaining categories, both anthropogenic (mainly agriculture, waste management and fossil fuel emissions), and natural (geological emissions, termites, lakes and oceans). Anthropogenic emissions are taken from the EDGAR v6.0 emission inventory , wetland emissions are taken from the LPJ-GUESS simulations described in Sect. , with or without the parameters optimization described in Sect.  (depending on the simulation). Natural emissions are taken from various climatological estimates, reported in Table . All the emissions were regridded from their original resolution to the 0.25°, daily resolution of the FLEXPART footprints.

The spatial distribution of the emissions is shown in Fig. , while their temporal distribution is shown in Fig. . Wetland emissions are the only category that exhibits a strong seasonality (biomass burning emissions are seasonal as well, but very low overall, so their contribution to the seasonality of total emissions is negligible). There is also a geographical separation between emissions from wetlands, which are concentrated in Northern Europe, and emissions from the other categories, which are more significant in the rest of the continent, and tend to overlap in time and space. This, and the fact that the observation network is relatively dense in Northern Europe (Fig. ), where wetland emissions are important, justify resolving wetland emissions separately from the other CH₄ sources in the inversions.

The emission uncertainties are stored in the prior error-covariance matrix B, which is composed, for each category c, of four components: the vector σxc containing the standard deviations of the emission themselves, two correlation matrices, Cch and Cct, storing respectively the prescribed correlations in the spatial and in the temporal dimension, and a scalar scaling factor γc, which is used to enforce a specified total annual uncertainty. No cross-category correlations are assumed, therefore the error-covariance matrix is written, for each category, as: 3Bc=(Cct⊗Cch)TσxcTγc2σxc(Cct⊗Cch) For wetland emissions, the standard deviations σxc are set to the standard deviation of the LPJ-GUESS ensembles (Sect. ), whereas for non-wetland emissions, they are set to the absolute value of the emissions. The scaling factor γc is then determined such that ∑ijBcij-1/2 equals the desired annual uncertainty for category c. This facilitates comparisons between simulations with different correlation structure, as their overall uncertainty remain identical.

The uncertainties on non-wetland emissions were set to 5 Tg CH₄ yr⁻¹ (≈15 % of the annual emissions), with Ct and Ch constructed as correlation-decay functions (corr(x)=e-x/L), with horizontal correlation length of 500 km and temporal correlation length of 30 d. For wetlands, the annual uncertainty was set to 0.5 Tg CH₄ yr⁻¹, with temporal correlation length of 30 d. The spatial correlations were either constructed using the same approach, with spatial correlation lengths of 1000 km, in the main inversions (LUMIA-Lprior and LUMIA-Lpost), or directly using the error correlation structure from the LPJ-GUESS ensembles (see Sect. ).

The LUMIA inversions were constrained by observations from 43 European in-situ and flask measurement sites, from various observation networks (see Table  and Fig. ), most of which are now part of the ICOS network of atmospheric in-situ measurements. The observations were taken from a quality controlled dataset prepared for a CH₄ inverse modeling intercomparison conducted within the CoCO2 project (https://coco2-project.eu/, last access: 23 October 2025, ).

The observation frequency is typically hourly, but we filtered the observations to avoid assimilating observations close to the transition between the planetary boundary layer (PBL) and the free troposphere, as this is where model errors on the PBL height would have the largest impact. For most sites, afternoon data was selected (from 11:00 to 17:00, local time), when the PBL is expected to be the most developed. For high altitude sites (above 1000 m altitude a.m.s.l), night time data was used instead (from 00:00 to 04:00, local time), when the observations are expected to be well above the PBL. At a few sites (Hohenpeissenberg, Hegyhatsal, Ispra, Mace Hear and Pallas), there are also a some observations from flask measurements, for these, no specific filter was applied.

The uncertainties (diagonal of R in Eq. ) are set as the quadratic sum of the measurement uncertainty εobs, provided by the atmospheric observations dataset, and of the model uncertainty εmod. The model uncertainty should in theory be set close to the random component of the error that the model would make when simulating the observations based on the “true” emissions, and excluding systematic component of that error. In practice, that true error is unknown. Here we constructed it as site-specific weekly uncertainty, based on the mismatch between the observed and modelled short term CH₄ variability. The procedure is conducted for each site, in four steps:

Compute the prior model estimate for the observations, yapri, corresponding to the prior emissions described in Sect. .

The rationale behind this approach is that the inversions should be able to efficiently reduce the mismatch between the baselines by adjusting the CH₄ emissions, but will likely struggle more with reducing the model-data mismatches between the modelled and observed sub-weekly variability. In practice this results in a larger uncertainty at sites close to large CH₄ emitters, such as Ispra, Saclay and Norunda, reducing their relative weight in the inversion. The last step (4) ensures that the weight of a site doesn't depend on the observation frequency (if there are more observations within a given week, the individual weight of each observation will be reduced accordingly).

The non-optimized LPJ-GUESS model (LPJ-GUESS-unopt) points to an emission total of 8.7 Tg CH₄ yr⁻¹ from natural wetlands, including 4.3 Tg CH₄ yr⁻¹ in the Nordic sub-domain. All three observation-informed estimates point to emission reductions ranging from -37 % (LPJ-GUESS-opt, 5.5 Tg CH₄ yr⁻¹) to -51 % (LUMIA-Lpost, 4.3 Tg CH₄ yr⁻¹) at the European scale, and from -42 % (LPJ-GUESS-opt, 2.5 Tg CH₄ yr⁻¹) to -60 % (LUMIA-Lpost, 1.7 Tg CH₄ yr⁻¹) in the Nordic subdomain (Fig. ). The two sensitivity inversions also lead to very similar results (See full results in Table S1).

In contrast, the inversions lead to much lower adjustments to non-wetland emissions, both in relative and absolute terms. The priors (i.e. LPJ-GUESS-unopt and LPJ-GUESS-opt in Fig. ) are 35 Tg CH₄ for the full domain, and 34.3 Tg CH₄ yr⁻¹ (-2.8 %) and 35.2 Tg CH₄ yr⁻¹ (-0.1 %) respectively in LUMIA-Lprior and LUMIA-Lpost. The contribution of the Nordic region to this is very small, with 3.3 Tg CH₄ yr⁻¹ in the prior (comparable in magnitude to the wetland emissions in that region). The inversions reduce these to 2.2 Tg CH₄ yr⁻¹ (-33 %) and 2.5 Tg CH₄ yr⁻¹ (-25 %), respectively in LUMIA-Lprior and LUMIA-Lpost. Here again, the difference between the reference inversions and their sensitivity run counterparts is very small.

Temporal emission adjustments are shown in Fig.  (note the different y-ranges in the figure). For the figure clarity, results from the LUMIA-Lprior+corr and LUMIA-Lpost+corr inversions are shown in Fig. S1.

For wetlands, the patterns are very similar between the full-domain and the Nordic region (which reflects the fact that this region accounts for more than half of the European wetland emissions). In LPJ-GUESS-unopt, the emissions remain close to zero in the first quarter of the year, except for two small peaks at the end of January and of March. The emissions then follow a “double-peak” pattern, with a first peak around late May, particularly pronounced in the Nordics, and the main peak in August, after which the emissions decline steadily to reach nearly zero at the end of the year.

The assimilation of in-situ flux data in LPJ-GUESS-opt leads to roughly a halving of the emissions, mainly during the May to October period. Within the Nordic region, the emission peak in May is almost fully preserved, whereas the remaining part of the summer variability is smoothed. Outside the Nordics, the temporal structure of the emissions is better preserved. LPJ-GUESS-opt points to a reduction of the amplitude of the emission peaks in January-February (mostly visible outside the Nordics). On the other hand, the emissions after October remain similar to LPJ-GUESS-unopt.

The two LUMIA inversions lead to emission reduction in the Nordic region that are overall consistent with those obtained in LPJ-GUESS-opt, in particular during the summer months (June-August). Both inversions further attenuate the May emission peak compared to both LPJ-GUESS estimates, and also point to lower emissions than the LPJ-GUESS simulations after August. LUMIA-Lprior essentially retains the seasonal cycle shape of its prior (LPJ-GUESS-unopt), but with a reduced amplitude, whereas LUMIA-Lpost infers corrections to its prior (LPJ-GUESS-opt) only during some parts of the year (May and August–November).

Outside the Nordics (lower left plot in Fig. ), LUMIA-Lprior also leads to a rather annually uniform scaling down of the wetland emissions, compared to its prior (LPJ-GUESS-unopt). LUMIA-Lpost infers almost no adjustment to its prior (LPJ-GUESS-opt) during most of the year, except during the last months (October to December), when it leads to a signfificant (a third to a half) reduction of the baseline emissions, and also completely erases small emission peaks that LPJ-GUESS simulated at the end of October and beginning of December.

The two sensitivity inversions LUMIA-Lprior+corr and LUMIA-Lpost+corr lead to comparable results, on multi-day averages. However, LUMIA-Lprior+corr displays an extremely high short-term variability (much more that LPJ-GUESS-unopt, its prior). We hypothesize that this is due to the very high uncertainty on wetland emissions used in that simulation (6.4 Tg CH₄, i.e. ≈13 times more than in the other inversions), which, associated to the fact that LPJ-GUESS-unopt tends to alternate (at the grid cell level) between days with strong emissions and days with near zero emissions, makes that inversion very under-constrained. However, on a multi-day average, it is remarkably similar to LPJ-GUESS-opt within the Nordic region, until August, and to LUMIA-Lprior for the rest of the year, and also in the rest of Europe.

Compared to LUMIA-Lprior, LUMIA-Lprior+corr follows very closely the seasonal variability of their prior (LPJ-GUESS-opt), shifting it only by a seemingly constant scaling factor. This is a consequence of the very long distance correlations from the LPJ-GUESS ensemble (see Fig. ), which reduces drastically the degrees of freedom of the inversion, even though the observations provide sufficient constraint to resolve finer scale patterns.

The temporal adjustments of the “non-wetland” emission category groups contributions from many source processes, mainly anthropogenic, which makes them difficult to interpret at the domain-scale. In the Nordics, the LUMIA inversions infer, on average, a reduction of the non-wetland emission of 25 % (LUMIA-Lpost) to 32 % (LUMIA-Lprior), with large variations throughout the year, with a peak increase of up to 35 % (LUMIA-Lpost, in August), and a reduction to near zero towards the end of the year.

A part of this variability is likely caused by misattributions of emission corrections between the two emission categories. For instance, from April to July, the non-wetland emissions of LUMIA-Lprior in the Nordics are significantly lower than those inferred in LUMIA-Lpost, which compensates for an opposite sign difference between these two inversions in the wetland emission category. However, while the reduction in non-wetland emissions towards the end of the year doesn't appear probable given the expected stability of anthropogenic emissions over the year, re-allocating it entirely to the wetland emission category would lead to (significantly) negative wetland emissions, which isn't realistic either.

A possible alternative (or complementary) explanation could be error in the CAMS boundary condition: the background concentrations (ybg in Eq. ) explains nearly 100 % of the observed mixing ratio on several days towards the end of the year, especially at Hyytiälä (SMR) and Birkenes (BIR). The situation is also similar in the two sensitivity inversions.

The emission adjustments inferred in GRaB-AM and LUMIA optimizations are shown in Fig. . To facilitate the comparison, wetland adjustments in LUMIA-Lpost are shown relative to the unoptimized LPJ-GUESS estimate (LPJ-GUESS-unopt). Maps for the sensitivity inversions are can be found in Figs. S2, and S3 shows the maps relative to LPJ-GUESS-opt.

The spatial distribution of wetland emission adjustments is very similar in the five data-informed products, and largely proportional to the LPJ-GUESS-unopt emission estimate itself. The long error-correlations imposed on the LUMIA inversions (and intrinsic to the GRaB-AM optimization), combined with the relative concentration of wetland emissions in Northern Europe, ensure a convergence between the localization of flux corrections.

Among the most marked features in the adjustment to the “non-wetland” category, we note a doubling of the emissions in the Bretagne region of France, and in the Northern part of the Netherlands. This could point to underestimated agricultural emissions, which are important in these two regions. Another marked feature is an important (≈80 %) reduction of the emissions in Northern Italy, which is well correlated with both high natural emissions (mainly geological) and high agricultural emissions.

We, however, need to ascertain a level of care when interpreting these emission adjustments: For instance emissions in the west of the continent can also result from the need to correct an inaccurate boundary condition. There can also be compensating effects between adjustments of emission hotspots, such as the city of Paris or the Po Valley, and their surroundings. These emission corrections should be investigated, but fall outside the scope of our study.

CH₄ emissions can be estimated locally on wetland scales using flux measurement techniques such as Eddy-covariance measurements, which involve capturing the covariance between the vertical wind speed and the concentration of methane, providing high-resolution data on gas exchange over wetlands. Such observations are for instance provided by the ICOS network in Europe , and the FLUXNET-CH₄ dataset globally , which offers aggregates of high-quality CH₄ flux measurements from wetlands. These networks try to offer a comprehensive coverage of the different types of wetlands (with differences in physiological features such as hydrology, soil characteristics, vegetation types, etc., and in spatial features, such as geographical distribution, size, landscape position and topography).

However, a direct comparison with gridded emissions is difficult, as the latter accounts for average conditions over the grid cells, which can be very different from the local ones. This is illustrated in Fig. , which shows a comparison between our four main emission estimates and in-situ flux measurements at three sites in the Nordic region (Zarnekow is slightly outside the Nordic domain used for the emission comparisons, see Fig. ), along with the site-level LPJ-GUESS simulations which were used to train the GRaB-AM optimization (see Sect. ).

The fit of the modelled emissions against the observations is improved for most sites (clearly shown for e.g. Siikaneva and Degero) but since the GRaB-AM optimization is seeking for an optimal parameter set fitting multiple sites simultaneously it is not surprising that there are still larger differences between simulated emissions and observations for any given individual site (as is the case for Zarnekov where the calibrated LPJ-GUESS model fails to simulate the observed peak values during August 2018).

The site-level simulations achieve systematically a better fit to the observations than their corresponding gridded products. Among the gridded products, the best fit is obtained by LUMIA-Lpost, at Siikaneva and Degero, with RMSE reduction above 61 % (Table ), whereas the error reduction is lower at Zarnekow, with all the data-informed product in a 17 % to 21 % RMSE reduction range. The two sensitivity inversions using ensemble-derived covariances lead to slightly worse fit than the base LUMIA inversions. We also note a tendency of the LUMIA inversions using LPJ-GUESS-unopt as a prior to infer significant negative emissions on some days (Fig. S4): LUMIA adjusts the emissions but preserves most of their original day-to-day variability, which results in days with negative emissions.

The CH₄ concentrations corresponding to the four methane emission estimates are shown in Fig. , for the six sites in the Nordic region. These sites are also among the ones where the relative contribution of wetland emissions to the foreground concentrations (i.e. the part of the concentrations that can be adjusted by LUMIA) is the highest. For figure clarity, a two-days rolling average has been applied to the the modelled timeseries, while the data without weekly averaging is shown in Fig. S5.

LPJ-GUESS-unopt leads to an overestimation of the concentrations throughout the summer (with a mean bias of up to 18 ppb at Norunda, and peak model-data mismatches exceeding 200 ppb). The fit obtained using LPJ-GUESS-opt emissions is more in line with the observations, with mean biases ranging from -2.1 ppb at Hyltemossa to +14.1 ppb at Hyytiälla. However, the CH₄ concentrations are still significantly overestimated towards the end of the year at Pallas, Norunda and Hytiälla.

Both LUMIA inversions lead to very comparable results in terms of mean bias, with a tendency to underestimate the observations (with biases ranging from -0.5 ppb at Utö, down to -5.4 ppb at Hyltemossa). However, they lead to a significant RMSE reduction compared to the LPJ-GUESS simulations, with RMSE values in a 12.8 to 17 ppb range (slightly lower in LUMIA-Lpost).

The slightly worse statistics of the LUMIA inversions in terms of bias compared to LPJ-GUESS-opt at the Hyltemossa site (and to a lesser degree also at Birkenes) is likely due to a misfit of observations during the first two weeks of the year, when there is very little flux adjustments that the inversions can infer since the prior emissions start on 1st January. However, the bias is well below the typical prescribed model-data mismatches (which are on the order of 30 ppb), and the RMSEs are reduced as expected. Nonetheless, this points to a possible slight underestimation of the emissions by the inversions.

On the other hand, the overestimation of the observations in the LPJ-GUESS-unopt simulation is very large and a clear indication that the emissions modelled by the non-optimized LPJ-GUESS in the summer are refuted by the atmospheric observations (and to a lesser extent, for the optimized LPJ-GUESS simulation). Other sources of uncertainties (transport model error, uncertainty on the background concentrations, uncertainty in non-wetland emissions) don't seem large enough to account for such an overestimation of the observed data.