Wetlands are the largest natural source of methane (CH4 ) to the atmosphere. The eddy covariance method provides robust measurements of net ecosystem exchange of CH4 , but interpreting its spatiotemporal variations is challenging due to the co-occurrence of CH4 production, oxidation, and transport dynamics. Here, we estimate these three processes using a data-model fusion approach across 25 wetlands in temperate, boreal, and Arctic regions. Our data-constrained model-iPEACE-reasonably reproduced CH4 emissions at 19 of the 25 sites with normalized root mean square error of 0.59, correlation coefficient of 0.82, and normalized standard deviation of 0.87. Among the three processes, CH4 production appeared to be the most important process, followed by oxidation in explaining inter-site variations in CH4 emissions. Based on a sensitivity analysis, CH4 emissions were generally more sensitive to decreased water table than to increased gross primary productivity or soil temperature. For periods with leaf area index (LAI) of ≥20% of its annual peak, plant-mediated transport appeared to be the major pathway for CH4 transport. Contributions from ebullition and diffusion were relatively high during low LAI (<20%) periods. The lag time between CH4 production and CH4 emissions tended to be short in fen sites (3 ± 2 days) and long in bog sites (13 ± 10 days). Based on a principal component analysis, we found that parameters for CH4 production, plant-mediated transport, and diffusion through water explained 77% of the variance in the parameters across the 19 sites, highlighting the importance of these parameters for predicting wetland CH4 emissions across biomes. These processes and associated parameters for CH4 emissions among and within the wetlands provide useful insights for interpreting observed net CH4 fluxes, estimating sensitivities to biophysical variables, and modeling global CH4 fluxes.

Wetland CH4 emissions are among the most uncertain components of the global CH4 budget. The complex nature of wetland CH4 processes makes it challenging to identify causal relationships for improving our understanding and predictability of CH4 emissions. In this study, we used the flux measurements of CH4 from eddy covariance towers (30 sites from 4 wetlands types: bog, fen, marsh, and wet tundra) to construct a causality-constrained machine learning (ML) framework to explain the regulative factors and to capture CH4 emissions at sub-seasonal scale. We found that soil temperature is the dominant factor for CH4 emissions in all studied wetland types. Ecosystem respiration (CO2) and gross primary productivity exert controls at bog, fen, and marsh sites with lagged responses of days to weeks. Integrating these asynchronous environmental and biological causal relationships in predictive models significantly improved model performance. More importantly, modeled CH4 emissions differed by up to a factor of 4 under a +1°C warming scenario when causality constraints were considered. These results highlight the significant role of causality in modeling wetland CH4 emissions especially under future warming conditions, while traditional data-driven ML models may reproduce observations for the wrong reasons. Our proposed causality-guided model could benefit predictive modeling, large-scale upscaling, data gap-filling, and surrogate modeling of wetland CH4 emissions within earth system land models.

Abstract. Methane (CH4) emissions from natural landscapes constitute roughly half of global CH4 contributions to the atmosphere, yet large uncertainties remain in the absolute magnitude and the seasonality of emission quantities and drivers. Eddy covariance (EC) measurements of CH4 flux are ideal for constraining ecosystem-scale CH4 emissions due to quasi-continuous and high-temporal-resolution CH4 flux measurements, coincident carbon dioxide, water, and energy flux measurements, lack of ecosystem disturbance, and increased availability of datasets over the last decade. Here, we (1) describe the newly published dataset, FLUXNET-CH4 Version 1.0, the first open-source global dataset of CH4 EC measurements (available at https://fluxnet.org/data/fluxnet-ch4-community-product/, last access: 7 April 2021). FLUXNET-CH4 includes half-hourly and daily gap-filled and non-gap-filled aggregated CH4 fluxes and meteorological data from 79 sites globally: 42 freshwater wetlands, 6 brackish and saline wetlands, 7 formerly drained ecosystems, 7 rice paddy sites, 2 lakes, and 15 uplands. Then, we (2) evaluate FLUXNET-CH4 representativeness for freshwater wetland coverage globally because the majority of sites in FLUXNET-CH4 Version 1.0 are freshwater wetlands which are a substantial source of total atmospheric CH4 emissions; and (3) we provide the first global estimates of the seasonal variability and seasonality predictors of freshwater wetland CH4 fluxes. Our representativeness analysis suggests that the freshwater wetland sites in the dataset cover global wetland bioclimatic attributes (encompassing energy, moisture, and vegetation-related parameters) in arctic, boreal, and temperate regions but only sparsely cover humid tropical regions. Seasonality metrics of wetland CH4 emissions vary considerably across latitudinal bands. In freshwater wetlands (except those between 20∘ S to 20∘ N) the spring onset of elevated CH4 emissions starts 3 d earlier, and the CH4 emission season lasts 4 d longer, for each degree Celsius increase in mean annual air temperature. On average, the spring onset of increasing CH4 emissions lags behind soil warming by 1 month, with very few sites experiencing increased CH4 emissions prior to the onset of soil warming. In contrast, roughly half of these sites experience the spring onset of rising CH4 emissions prior to the spring increase in gross primary productivity (GPP). The timing of peak summer CH4 emissions does not correlate with the timing for either peak summer temperature or peak GPP. Our results provide seasonality parameters for CH4 modeling and highlight seasonality metrics that cannot be predicted by temperature or GPP (i.e., seasonality of CH4 peak). FLUXNET-CH4 is a powerful new resource for diagnosing and understanding the role of terrestrial ecosystems and climate drivers in the global CH4 cycle, and future additions of sites in tropical ecosystems and site years of data collection will provide added value to this database. All seasonality parameters are available at https://doi.org/10.5281/zenodo.4672601 (Delwiche et al., 2021). Additionally, raw FLUXNET-CH4 data used to extract seasonality parameters can be downloaded from https://fluxnet.org/data/fluxnet-ch4-community-product/ (last access: 7 April 2021), and a complete list of the 79 individual site data DOIs is provided in Table 2 of this paper.

Abstract Wetland methane (CH 4 ) emissions ( $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> ) are important in global carbon budgets and climate change assessments. Currently, $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> projections rely on prescribed static temperature sensitivity that varies among biogeochemical models. Meta-analyses have proposed a consistent $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> temperature dependence across spatial scales for use in models; however, site-level studies demonstrate that $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> are often controlled by factors beyond temperature. Here, we evaluate the relationship between $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> and temperature using observations from the FLUXNET-CH 4 database. Measurements collected across the globe show substantial seasonal hysteresis between $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> and temperature, suggesting larger $${F}_{{{CH}}_{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> sensitivity to temperature later in the frost-free season (about 77% of site-years). Results derived from a machine-learning model and several regression models highlight the importance of representing the large spatial and temporal variability within site-years and ecosystem types. Mechanistic advancements in biogeochemical model parameterization and detailed measurements in factors modulating CH 4 production are thus needed to improve global CH 4 budget assessments.

• We evaluate methane flux gap-filling methods across 17 boreal-to-tropical wetlands • New methods for generating realistic artificial gaps and uncertainties are proposed • Decision tree algorithms perform slightly better than neural networks on average • Soil temperature and generic seasonality are the most important predictors • Open-source code is released for gap-filling steps and uncertainty evaluation Time series of wetland methane fluxes measured by eddy covariance require gap-filling to estimate daily, seasonal, and annual emissions. Gap-filling methane fluxes is challenging because of high variability and complex responses to multiple drivers. To date, there is no widely established gap-filling standard for wetland methane fluxes, with regards both to the best model algorithms and predictors. This study synthesizes results of different gap-filling methods systematically applied at 17 wetland sites spanning boreal to tropical regions and including all major wetland classes and two rice paddies. Procedures are proposed for: 1) creating realistic artificial gap scenarios, 2) training and evaluating gap-filling models without overstating performance, and 3) predicting half-hourly methane fluxes and annual emissions with realistic uncertainty estimates. Performance is compared between a conventional method (marginal distribution sampling) and four machine learning algorithms. The conventional method achieved similar median performance as the machine learning models but was worse than the best machine learning models and relatively insensitive to predictor choices. Of the machine learning models, decision tree algorithms performed the best in cross-validation experiments, even with a baseline predictor set, and artificial neural networks showed comparable performance when using all predictors. Soil temperature was frequently the most important predictor whilst water table depth was important at sites with substantial water table fluctuations, highlighting the value of data on wetland soil conditions. Raw gap-filling uncertainties from the machine learning models were underestimated and we propose a method to calibrate uncertainties to observations. The python code for model development, evaluation, and uncertainty estimation is publicly available. This study outlines a modular and robust machine learning workflow and makes recommendations for, and evaluates an improved baseline of, methane gap-filling models that can be implemented in multi-site syntheses or standardized products from regional and global flux networks (e.g., FLUXNET).

While wetlands are the largest natural source of methane (CH4) to the atmosphere, they represent a large source of uncertainty in the global CH4 budget due to the complex biogeochemical controls on CH4 dynamics. Here we present, to our knowledge, the first multi-site synthesis of how predictors of CH4 fluxes (FCH4) in freshwater wetlands vary across wetland types at diel, multiday (synoptic), and seasonal time scales. We used several statistical approaches (correlation analysis, generalized additive modeling, mutual information, and random forests) in a wavelet-based multi-resolution framework to assess the importance of environmental predictors, nonlinearities and lags on FCH4 across 23 eddy covariance sites. Seasonally, soil and air temperature were dominant predictors of FCH4 at sites with smaller seasonal variation in water table depth (WTD). In contrast, WTD was the dominant predictor for wetlands with smaller variations in temperature (e.g., seasonal tropical/subtropical wetlands). Changes in seasonal FCH4 lagged fluctuations in WTD by ~17 ± 11 days, and lagged air and soil temperature by median values of 8 ± 16 and 5 ± 15 days, respectively. Temperature and WTD were also dominant predictors at the multiday scale. Atmospheric pressure (PA) was another important multiday scale predictor for peat-dominated sites, with drops in PA coinciding with synchronous releases of CH4. At the diel scale, synchronous relationships with latent heat flux and vapor pressure deficit suggest that physical processes controlling evaporation and boundary layer mixing exert similar controls on CH4 volatilization, and suggest the influence of pressurized ventilation in aerenchymatous vegetation. In addition, 1- to 4-h lagged relationships with ecosystem photosynthesis indicate recent carbon substrates, such as root exudates, may also control FCH4. By addressing issues of scale, asynchrony, and nonlinearity, this work improves understanding of the predictors and timing of wetland FCH4 that can inform future studies and models, and help constrain wetland CH4 emissions.

A Correction to this paper has been published: https://doi.org/10.1038/s41597-021-00851-9.

• Large-scale eddy-covariance flux datasets need to be used with footprint-awareness • Using a fixed-extent target area across sites can bias model-data integration • Most sites do not represent the dominant land-cover type at a larger spatial extent • A representativeness index provides general guidance for site selection and data use Large datasets of greenhouse gas and energy surface-atmosphere fluxes measured with the eddy-covariance technique (e.g., FLUXNET2015, AmeriFlux BASE) are widely used to benchmark models and remote-sensing products. This study addresses one of the major challenges facing model-data integration: To what spatial extent do flux measurements taken at individual eddy-covariance sites reflect model- or satellite-based grid cells? We evaluate flux footprints—the temporally dynamic source areas that contribute to measured fluxes—and the representativeness of these footprints for target areas (e.g., within 250–3000 m radii around flux towers) that are often used in flux-data synthesis and modeling studies. We examine the land-cover composition and vegetation characteristics, represented here by the Enhanced Vegetation Index (EVI), in the flux footprints and target areas across 214 AmeriFlux sites, and evaluate potential biases as a consequence of the footprint-to-target-area mismatch. Monthly 80% footprint climatologies vary across sites and through time ranging four orders of magnitude from 10 3 to 10 7 m 2 due to the measurement heights, underlying vegetation- and ground-surface characteristics, wind directions, and turbulent state of the atmosphere. Few eddy-covariance sites are located in a truly homogeneous landscape. Thus, the common model-data integration approaches that use a fixed-extent target area across sites introduce biases on the order of 4%–20% for EVI and 6%–20% for the dominant land cover percentage. These biases are site-specific functions of measurement heights, target area extents, and land-surface characteristics. We advocate that flux datasets need to be used with footprint awareness, especially in research and applications that benchmark against models and data products with explicit spatial information. We propose a simple representativeness index based on our evaluations that can be used as a guide to identify site-periods suitable for specific applications and to provide general guidance for data use.

Abstract The FLUXNET2015 dataset provides ecosystem-scale data on CO 2 , water, and energy exchange between the biosphere and the atmosphere, and other meteorological and biological measurements, from 212 sites around the globe (over 1500 site-years, up to and including year 2014). These sites, independently managed and operated, voluntarily contributed their data to create global datasets. Data were quality controlled and processed using uniform methods, to improve consistency and intercomparability across sites. The dataset is already being used in a number of applications, including ecophysiology studies, remote sensing studies, and development of ecosystem and Earth system models. FLUXNET2015 includes derived-data products, such as gap-filled time series, ecosystem respiration and photosynthetic uptake estimates, estimation of uncertainties, and metadata about the measurements, presented for the first time in this paper. In addition, 206 of these sites are for the first time distributed under a Creative Commons (CC-BY 4.0) license. This paper details this enhanced dataset and the processing methods, now made available as open-source codes, making the dataset more accessible, transparent, and reproducible.

Abstract. Natural wetlands constitute the largest and most uncertain source of methane (CH4) to the atmosphere and a large fraction of them are found in the northern latitudes. These emissions are typically estimated using process (“bottom-up”) or inversion (“top-down”) models. However, estimates from these two types of models are not independent of each other since the top-down estimates usually rely on the a priori estimation of these emissions obtained with process models. Hence, independent spatially explicit validation data are needed. Here we utilize a random forest (RF) machine-learning technique to upscale CH4 eddy covariance flux measurements from 25 sites to estimate CH4 wetland emissions from the northern latitudes (north of 45∘ N). Eddy covariance data from 2005 to 2016 are used for model development. The model is then used to predict emissions during 2013 and 2014. The predictive performance of the RF model is evaluated using a leave-one-site-out cross-validation scheme. The performance (Nash–Sutcliffe model efficiency =0.47) is comparable to previous studies upscaling net ecosystem exchange of carbon dioxide and studies comparing process model output against site-level CH4 emission data. The global distribution of wetlands is one major source of uncertainty for upscaling CH4. Thus, three wetland distribution maps are utilized in the upscaling. Depending on the wetland distribution map, the annual emissions for the northern wetlands yield 32 (22.3–41.2, 95 % confidence interval calculated from a RF model ensemble), 31 (21.4–39.9) or 38 (25.9–49.5) Tg(CH4) yr−1. To further evaluate the uncertainties of the upscaled CH4 flux data products we also compared them against output from two process models (LPX-Bern and WetCHARTs), and methodological issues related to CH4 flux upscaling are discussed. The monthly upscaled CH4 flux data products are available at https://doi.org/10.5281/zenodo.2560163 (Peltola et al., 2019).