To determine the gaps in physical research infrastructure for ecosystem-scale CH4 fluxes, we need to understand how the current infrastructure is distributed across the US. We focus here on EC flux towers given their capabilities for continuous measurements and use in upscaling flux estimates and are therefore a useful basis for identifying gaps in the current network of CH4 observations. The AmeriFlux network of EC towers was launched in 1996 and grew from about 15 sites in 1997 to more than 110 active sites registered today. It was originally a network of PI-managed sites measuring ecosystem CO2, H2O, and energy fluxes. The network was established to connect research on field sites representing major climatic and ecological biomes, including tundra, grasslands, savanna, crops, and coniferous, deciduous, and tropical forests. The AmeriFlux community tailored instrumentation to suit each unique ecosystem but now also includes towers that are a part of the standardized network, the National Ecological Observatory Network (NEON). In 2012, the US Department of Energy established the AmeriFlux Management Project (AMP) at Lawrence Berkeley National Laboratory (LBNL) to support the broad AmeriFlux community and the AmeriFlux sites. The AMP standardizes, post-processes, and makes flux data available to the research community. More recently, flux towers began measuring CH4 in freshwater, coastal, upland, natural, and managed ecosystems. Although we have information on the location of existing EC tower infrastructure that is a part of AmeriFlux (n=223), NEON (n=47), and known, independent PI-managed sites (n=141), we focus this analysis on the towers measuring CH4 (n=100) and we distinguish between towers providing data to AmeriFlux (yes = 49, no = 51) and tower activity (active = 70; inactive = 30). We understand that additional towers exist within the US, but because these towers are not reporting or providing data to the flux community, we cannot include them in this analysis.

To understand the landscape representativeness across geographic clusters, we measured dissimilarity based on climate and land cover type, as these two factors together are characteristic of regional resource availability and disturbance regimes. First, we developed a dissimilarity matrix that was condensed down to a two-dimensional ordination to determine regional clusters and calculate cluster dissimilarity for each location within a cluster (Fig. 1). It is important to note that a tower should be representative of the ecosystem type and the region where it is stationed (Desai, 2010; Jung et al., 2011; Xiao et al., 2012; Chu et al., 2021); however, the landscape representativeness analysis done here uses a coarser classification of land cover types that are more emblematic of resource availability and factors that influence how ecosystems function, not the specific ecosystem type where the tower is situated. Chu et al. (2021) examined the land-cover composition and vegetation characteristics of 214 AmeriFlux tower site footprints. They found that most sites do not represent the dominant land-cover type of the ecosystems they exist within, and when paired with common model–data integration approaches this mismatch introduces biases on the order of 4 %–20 % for the enhanced vegetation index (EVI) and 6 %–20 % for the dominant land cover percentage (Chu et al., 2021), making it essential to consider landscape characteristics in the design and evaluation of network infrastructure. Infrastructure representativeness at the landscape scale is indicative of the capacity to upscale information by climate and the dominant ecosystems of locations within a landscape.

We used the National Land Cover Database (NLCD; https://www.mrlc.gov, last access: 1 October 2021) to create a land cover layer for the contiguous US (Jin et al., 2019). The NLCD has a 30 m resolution with a 16-class legend based on a modified Anderson Level II classification system. We reclassified the NLCD into eight major land cover types (water, developed, barren, forest, scrub, herbaceous, crop, and wetland). Where the NLCD was not available (Alaska, Hawaii, and Puerto Rico), we used the Moderate Resolution Imaging Spectroradiometer (MODIS; 1 km) land cover (type 5 – vegetation functional types) for vegetation functional type (MCD12Q1.006) (Sulla-Menashe and Friedl, 2018), which was also reclassified to the eight major land cover types (Table 1). The crop land cover type was expanded to non-irrigated and irrigated classes using agricultural information from the US Department of Agriculture's CropScape and Cropland Data layer (Boryan et al., 2011), and the wetland class was expanded using information from the US Fish and Wildlife Service's National Wetland Inventory. Expanded wetland classes were emergent coastal, emergent freshwater, and forest freshwater (Wilen and Bates, 1995). Climate data were obtained from DAYMET (Thornton et al., 2017). We used five climate variables to characterize the climatic conditions across the US: annual mean daily minimum, daily average, and daily maximum temperatures, annual total precipitation, and mean annual daily vapor pressure deficit from 2010–2020. Understanding that these patterns are changing with climate change, we chose a shorter time period than the commonly used 30-year climate normal to better represent current conditions (Bessembinder et al., 2021). Land cover was resampled to match the DAYMET climate data (1 km), and all pre-processing was done in R version 4.0.4 (R Core Team, 2021) with the raster package (Hijmans, 2021). This approach allowed us to create a land cover layer of the dominant land cover types at 1 km resolution that was expanded in categories of interest for CH4. The land cover and climate layers were chosen to represent the primary environmental conditions that are often indicative of a combination of resource availability and disturbance regimes. These coarse layers are essential for considering the landscape and large-scale climate effects that can influence how ecosystems within landscapes function. While the available land cover information is appropriate for the coarse, landscape-scale analysis done here, it is important to note that the products used here are not designed to estimate the potential CH4 source/sink status, particularly from the aquatic, wetland, and agricultural land cover types.

Climate, land cover, and location (latitude/longitude) were used in a multivariate distance analysis (Venables and Ripley, 2002; Ripley, 2007; Cox and Cox, 2008) to measure the dissimilarity across the US (all 50 states and Puerto Rico) at the landscape scale and divide it into ecological clusters. The purpose of this is to identify the interrelatedness of ecological components within a landscape (Ippoliti et al., 2019). We included location (latitude/longitude) to incorporate the interaction between climate, land cover, and most importantly, seasonality. The US was subsampled because of limitations in the maximum number of points that can be evaluated in the cluster analysis. To measure dissimilarity, we first randomly sampled (n = 20 000 1 km pixels) the US, maintaining the distribution of land cover and climate to define dissimilarity between observations. Although there were more than 8 million 1 km pixels available for the US, there are limits to the number of samples that can be analyzed by the functions used for the multidimensional scaling (MDS) analysis. We first developed a dissimilarity matrix by calculating Gower dissimilarity (Gower, 1971; Huang, 1997; Podani, 1999; Ahmad and Dey, 2007; Harikumar and Pv, 2015) using the function distmix from the package kmed in R. We used Gower dissimilarity because it can handle mixed data types. For each variable type in the data set, the dissimilarity metric that works well for that type is used and scaled to fall between 0 and 1. Then, a linear combination featuring user-specified weights (most simply an average) is calculated to create the final dissimilarity matrix. This approach measures the dissimilarity for each location within the US using land cover, climate, and location information (land cover, five climate variables, and location) and creates a dissimilarity matrix (20 000 × 20 000) that indicates dissimilarity for a location to every other location in the US.

Once we created the dissimilarity matrix, we used MDS to generate a two-dimensional ordination showing landscape dissimilarity with the MASS package in R (Venables and Ripley, 2002). The MDS makes it possible to evaluate dissimilarity in two dimensions, which is essential to our goal to evaluate representativeness. We used the Kruskal method of non-metric scaling with the IsoMDS function in the MASS package (Venables and Ripley, 2002). IsoMDS works best when applied to metric variables (Torgerson, 1958). Torgerson (1958) initially developed this method, which assumes that the data obey distance axioms. It uses eigendecomposition of the dissimilarity to identify major components and axes and represents any point as a linear combination of dimensions. This is very similar to principal component analysis (PCA) or factor analysis, but it uses the dissimilarity matrix rather than a correlation matrix as input. Furthermore, the included dimensions are the most important dimensions produced, like PCA which is able to identify all of the dimensions that exist in the original data up to N-1, but will retain only the most important ones.

Knowing that regional patterns in climate and land cover will be important for scaling CH4 to the regional and national scale, we divided the US into clusters to evaluate representativeness using the first and second dimension from the MDS. Cluster analysis has been used to assess the spatial representativeness of network infrastructure and to suggest arrangements of study sites (Sulkava et al., 2011; Kumar et al., 2016). It is an objective method of producing meaningful, mutually exclusive groups based on similarities among entities (Balijepally et al., 2011). This approach is descriptive, a-theoretical, and non-inferential with sound mathematical support (Balijepally et al., 2011). Clustering outcomes are driven by large effect sizes or the accumulation of many smaller effects across features, and they are mostly unaffected by differences in covariance structure (Dalmaijer et al., 2020). Sufficient statistical power is achieved with relatively small samples (Dalmaijer et al., 2020), provided cluster separation is sufficient. Traditional notions about statistical power only partially apply to cluster analysis (Dalmaijer et al., 2020). Increasing the number of sample points above a sufficient sample size does not improve power, but effect size is important (Dalmaijer et al., 2020). Clustering is useful when large subgroup separation is expected and when MDS improves cluster separation (Dalmaijer et al., 2020).

We determined the optimal number of clusters using the library cluster and the function pam in R (Reynolds et al., 2006; Schubert and Rousseeuw, 2019, 2021). This approach uses the k-medoids algorithm, which partitions a data set into k groups or clusters and is a robust alternative to k-means clustering (Kaufman and Rousseeuw, 2009). The k-medoid algorithm is less sensitive to noise and outliers, compared to k-means, because it uses medoids as cluster centers. The k-medoids algorithm requires the user to specify k, the number of clusters to be generated. A useful approach to determine the optimal number of clusters is the silhouette method. We fit an increasing number of clusters from 2 to 50 to construct a silhouette plot and choose the number of clusters that maximized the average silhouette width (Fig. S2).

While useful, there are limitations to cluster analysis that can affect cluster patterns and the stability of clusters. The final cluster solution is dependent upon the clustering variables, the similarity/dissimilarity measure used, the clustering algorithm, and the data used to estimate clusters. Therefore, varying elements of clustering methods can lead to many alternative cluster solutions (Balijepally et al., 2011). Cluster solutions can also be produced in the absence of natural structure in the data, and there is no statistical basis to reject the null hypothesis that there are no natural groupings in the data (Balijepally et al., 2011). Cluster algorithms also cannot differentiate between relevant versus irrelevant variables. Therefore, only the variables expected to be influential should be used (Balijepally et al., 2011) and should emanate from past research or explicit theory and be consistent with the objectives of the study.

Due to the limitations of this approach, it is important to validate the cluster solution to ensure its meaningfulness and utility (Punj and Stewart, 1983; Balijepally et al., 2011). Consistency is established by checking the stability of cluster solutions obtained by using multiple algorithms (Punj and Stewart, 1983) or through splitting a sample, analyzing the cluster solutions for the two halves separately, and checking their consistency. After checking for reliability, the validity of a cluster solution is established through external validity and criterion-related validity. External validity ensures that clusters are representative of the actual population (Cook and Campbell, 1979) and can be verified by clustering on a hold-out sample using the same variables and assessing the similarity of the two solutions. This analysis was repeated five times to ensure that the 20 000 pixel subsample would produce similar results in the dimensions and clustering. For simplicity, we show the results of the first analysis, and a comparison of clustering methods and measures of stability are available in the Supplement.

To measure dissimilarity across the cluster once defined, each cluster was represented by one of the data points in the cluster named the cluster medoid. The medoid had the lowest average dissimilarity between it and all other objects in the cluster. The medoid can be considered a representative example of the members of that cluster. We calculated the dissimilarity between every location within the cluster to the medoid to create a measure of how different each location was from the medoid condition of each cluster. We utilized the pointDistance function in the raster package, which provided a unit-less relative measure of dissimilarity that was determined by measuring the difference between the first and second dimensions produced by the isoMDS of each point in a cluster to the dimensions of the medoid.

To extrapolate the cluster and dissimilarity layers across the entire US beyond the 20 000-pixel subsample and to show the predictive validity (Kerlinger, 1986), we employed the machine learning algorithm random forest (RF) with the package randomForest (Liaw and Wiener, 2002) to model the first and second dimensions using the land cover and climate layers as predictors. We then created a random forest model of the cluster layer using the first and second dimension as the explanatory variables. All models were then projected spatially to produce a spatially explicit cluster layer and a dissimilarity layer beyond the 20 000 sample points that were used in the MDS analysis. The RF algorithm was first introduced by Breiman (2001) and uses an ensemble of regression trees to predict target values. In RF, a series of bootstrapped data sets are used to generate independent regression trees; at each node, a random sample of predictor variables is selected for use. The RF prediction is the ensemble of multiple individual trees. We created 500 trees for each year and site, using 80 % of the data for model fitting and 20 % for model validation. The fit of each RF was evaluated with the out-of-bag mean square error (OOB MSE), and variable importance was computed as the amount of the prediction error increased when a particular predictor was permuted. Initially, 500 RF trees were generated. Overall model fit was evaluated with the average of the 500 OOB MSEs from the final model for each year and site, and variable importance was calculated as the average rank of each predictor variable for the 500 models. This approach allowed us to measure the importance of the original data on the first and second dimensions defined by the MDS and how the MDS leads to cluster and dissimilarity patterns. This step was essential to producing a spatially explicit cluster and dissimilarity layers for the entire US, since the MDS analysis limits the number of observations that can be analyzed. This is also important for evaluating the meaningfulness of the cluster by using the original variables used in the development of the distance matrix to predict clusters.

Representativeness studies discern when, where, and at what frequency networks are measuring ecological processes (Baldocchi et al., 2012; Jongman et al., 2017; Vaughan et al., 2001; Villarreal et al., 2018). To understand the representativeness of current CH4 infrastructure, we defined clusters (Sulkava et al., 2011) and measured the dissimilarity between each location in a cluster to the medoid. We extracted the cluster and dissimilarity for all active tower sites measuring CH4 that were distributed across the US and measured the tower cluster representativeness (TRcluster) as the percent overlap between the range of dissimilarity sampled by the infrastructure (rcluster) divided by the range of dissimilarity observed in the entire cluster (r; Eq. 1). 1TRcluster=rclusterr×100

We recognize that it is essential to capture the distribution of dissimilarity across an entire cluster to upscale ecosystem measurements. We also report the sampling intensity of the major ecosystem types within the cluster and report the ecosystem representativeness (TRIGBP) by the International Geosphere–Biosphere Programme (IGBP) vegetation types of the towers (Eq. 2). 2TRIGBP=rIGBPr×100

This approach allows the evaluation of representativeness that is not based on a specific research site, but on the dissimilarity of a location to other locations in the landscape, and we use the range to indicate a capacity to scale within a cluster which is based on both the effects of landscape dominant land cover, climate, and the specific ecosystems measured (IGBP).

Land cover, climate, and location were condensed down to two dissimilarity dimensions (Fig. 2a). Both climatic factors and location were the most important variables for determining dimensions and explained 99 % of the variance in dimensions (Fig. S1). Using the first and second dimensions, the US was divided into 10 clusters (Fig. S2) that were distributed across temperature and wetness gradients (Fig. 2; Table 2). The coldest zones were in Alaska and included clusters Na and Nb. Cool to temperate clusters in the midwestern and western US include NW, W, and NEa. Temperate clusters extend from the midwestern to the eastern US and include clusters NEb and Ea. Warm regions were distributed across clusters Eb, SW, and SE. Dry clusters (Na, SW, W, and Nb) were distributed across the western US and Alaska, and wet clusters (Ea, Eb, and SE) were in the south-eastern US and Hawaii. Individual clusters represented 7 %–16 % of the US each by area (Table 2) with cluster NW as the largest cluster in the Pacific Northwest, and the smallest cluster being cluster Nb in the northern half of Alaska.

Across all clusters, dissimilarity ranged from 0.01 to 0.33 (Fig. 3). The mean dissimilarity was 0.04, and most areas within a cluster were less than or equal to the mean. Southern Alaska (cluster Na), Hawaii (clusters SE and Eb), Florida (cluster SE), Puerto Rico (cluster SE), and the northeast (cluster NEa) had greater than average dissimilarity in their respective clusters.

Dominant landscape land cover types also varied across clusters, with forests, scrub, and herbaceous ecosystems dominating clusters (> 20 % coverage; Table 2). Although irrigated croplands did not have high coverage rates across any cluster, non-irrigated croplands had high coverage rates in NEb, Ea, and NEb. Wetlands did not have high coverage rates in any cluster.

There were 70 active EC towers measuring CH4 distributed across forest (3 towers), grasslands (4 towers), shrublands (1 tower), agriculture (19 towers), wetlands (37 towers), barren (2 towers), and aquatic (4 towers) IGBP vegetation classes. Less than half of the active towers (43 %) were providing data to the community through AmeriFlux, limiting the development of CH4-derived products. For this reason, we will first focus this analysis on the active towers providing data to AmeriFlux. Although CH4 EC tower infrastructure was not a part of a single organized network designed to be representative of the climate, landscape, and dominant IGBP vegetation classes that exist within the US, EC tower infrastructure that was providing data to AmeriFlux was distributed across 8 of the 10 clusters (Table 3), with clusters NW and SE without any active towers providing data to the community. Tower representativeness (TRcluster) of clusters ranged from 0 %–88 %. The greatest TRcluster was for Eb and NEa, and the lowest TRcluster was for NW and SE, which had no towers. TRcluster was low (< 50 %) for most clusters, and high coverage was not associated with a higher frequency of towers. A high TRcluster was found in clusters where towers were dispersed across IGBP vegetation classes and where towers in wetlands, forests, or the arctic tundra (barren) were distributed across the observed range in the dissimilarity of clusters. Most clusters were substantially under-sampled (Table 3, Fig. 4) due to an insufficient number of towers measuring CH4 and poor distribution across the cluster.

The representativeness of IGBP vegetation types within clusters was poor for all vegetation types, excluding forests in the NEa. TRIGBP ranged from 0 %–79 %, and wetlands were the only IGBP class to be sampled across eight clusters. Ideally, IGBP classes should be distributed both within and across clusters where the classes exist. There was not a single cluster with towers in all of the IGBP classes (forest, scrub, aquatic ecosystems, crops, wetlands, barren tundra, and grasslands) that are found within that cluster.

There were important gains in the TRcluster when considering all CH4 towers regardless of if they were providing data to AmeriFlux (Table 4 and Fig. 4). The clusters with substantial gains in representativeness (> 10 %) include Na, NEb, Ea, and the SE. The TRcluster of the NW, Ea, SW, W, and the SE would be further enhanced by more than 10 % with the addition of CH4 instrumentation at NEON tower sites.