Restored wetlands are a complex mosaic of open water and new and old emergent vegetation patches, where multiple environmental and biological drivers contribute to the measured heterogeneity in methane (CH4) flux. In this analysis, we replicated the measurements of CH4 flux using the eddy covariance technique at three tower locations within the same wetland site to parse the spatiotemporal variability in CH4 flux contributed by large-scale seasonal variations in climate and phenology and short-term variations in flux footprint movement over a mosaic of vegetation and open water. Using a hierarchical statistical model accounting for site-level environmental effects, tower-level footprint and biological effects, and temporal autocorrelation, we partitioned the key drivers of the daily CH4 flux variability among the three replicated towers. The daily mean air temperature and mean friction velocity, a measure of momentum transfer, explained a significant variability in CH4 flux across the three towers, and the abundance and spatial aggregation of vegetation in the flux footprint along with the daily gross primary productivity explained much of the tower-level variability. This statistical model captured 67% of the total variance in the daily integrated growing season CH4 fluxes at this site, which bridged an order of magnitude from 80 to 480 mg C m−2 d−1 during the measurement period from 10 May 2012 to 24 October 2012.
Measured CH4 fluxes from peatland and wetland ecosystems have notoriously large spatial and temporal variability that can span orders of magnitude within a single landscape [Baldocchi et al., 2012; Teh et al., 2011]. Analyzing the contribution of spatial and temporal heterogeneity to measured CH4 flux is essential for understanding the mechanistic drivers of wetland ecosystem carbon cycling. Previous studies using the eddy covariance technique in northern peatlands and wetlands have demonstrated that accounting for spatial heterogeneity as a mechanistic driver of CO2 and CH4 flux is critical for attributing measured flux variability to spatially variable soil moisture, vegetation cover, landscape morphology, and land use [Herbst et al., 2011; Parmentier et al., 2012; Sturtevant and Oechel, 2013]. Combining eddy covariance measurements with chamber measurements or other small-scale techniques can also help assess the drivers of spatial heterogeneity in ecosystem flux [Hendriks et al., 2010; Schrier-Uijl et al., 2010; Teh et al., 2011]. In heterogeneous agricultural peatlands, accounting for the relative percentage of the landscape composed of drainage ditches and uplands was critical for calculating a landscape-scale flux, since the CH4 fluxes within these two land features can differ by up to 3 orders of magnitude [Schrier-Uijl et al., 2010; Teh et al., 2011]. Recent work also demonstrated that oversimplification in the representation of spatial and temporal water table variability at periodically inundated peatlands can result in large biases in modeled CH4 flux [Bohn and Lettenmaier, 2010]. This previous work clearly demonstrates that accurately representing spatial heterogeneity is essential for interpreting and predicting CH4 flux within most ecosystems.
In temperate wetlands, unique mechanisms control CH4 flux from vegetated and open water surfaces, creating a complex and heterogeneous biogeochemical landscape. Areas covered by plants have high rates of CO2 uptake and also produce the highest rates of CH4 efflux, since porous aerenchyma tissue used to transport oxygen from the atmosphere to roots is also a key conduit for CH4 flux from the soil to the atmosphere [Chanton et al., 1992b; Schimel, 1995]. Plants also impact the net CH4 released to the atmosphere by promoting redox cycling of alternative electron acceptors in the rhizosphere, which influence the rates of CH4 production and consumption [Hatala et al., 2012; Laanbroek, 2009; Neubauer et al., 2005]. Fluxes of CH4 from open water surfaces are regulated by diffusion and ebullition (bubbling), where the rates of diffusive CH4 efflux are correlated with friction velocity (u*; m/s) from open water surfaces [Cole et al., 2010; Herbst et al., 2011; Sebacher et al., 1983]. CH4 flux from both plants and open water surfaces are also controlled by temperature (TA; °C), because higher temperatures increase both the rate of CH4 production by methanogens [Zeikus and Winfrey, 1976] and the rate of transport from the soil or water to the atmosphere [Frolking and Crill, 1994]. In wetlands, these myriad driving variables contribute to the measured process variability in CH4 flux that can be conceptually separated into two categories that cooccur at the spatial scale of a flux tower: (1) drivers that are spatially continuous but shift in time and provoke a response in CH4 flux, for example, TA or u* fluctuations, and (2) underlying spatial variability in the drivers that produce and release CH4, for example, a dynamic mosaic of open water and vegetation. Using three eddy flux towers within a recently restored temperate wetland, we measured large variability in half-hourly and daily CH4 fluxes among the three tower sites. Using this replicated design, we examined the controls on landscape-scale variability in measured CH4 flux from both large-scale temporally dynamic drivers and drivers that varied both temporally and spatially.
The CH4 flux measured by the eddy covariance technique is the net result of fluxes from the complex mosaic of open water and plant patches operating simultaneously within the flux tower footprint. We detangled the variability within the flux measurements at the three towers by analyzing the spatial dynamics within each flux footprint, which describes the spatial area of the landscape from which the measured fluxes originated. Flux footprint models have been used to interpret how spatial heterogeneity contributes to the variability in CO2 fluxes measured by eddy covariance in eastern forests [Chasmer et al., 2011] and to validate the quality of eddy covariance measurements with respect to their representativeness of particular land use types [Goeckede et al., 2008, 2004]. A multiple-tower approach combined with flux footprint analysis was used to examine the impact of the spatial transition between distinct desert and irrigated ecosystems on eddy covariance measurements [Baldocchi and Rao, 1995]. A multiple-tower approach was also used within the same landscape to estimate the measurement error in the eddy covariance CO2 fluxes at the Howland Forest site, where differences in the measured fluxes between the two towers were interpreted as measurement error [Hollinger and Richardson, 2005]. An important distinction between the objectives of Hollinger and Richardson  and our analysis is that our study was conducted within a single nonsteady-state restored ecosystem, where large differences in the measured CH4 fluxes between the three towers comprise both the process error (underlying variability in the CH4 fluxes) and the measurement error inherent within the eddy covariance technique. In this work, we used a two-dimensional analytical flux footprint model at the three eddy flux towers to calculate the spatial extent represented by each half-hour CH4 flux measurement [Detto et al., 2006; Hsieh et al., 2000]. We then mapped this flux footprint onto imagery from the WorldView-2 satellite to characterize the changing abundance and structure of vegetation and open water within the flux footprints over the course of the summer growing season.
The use of periodic remote sensing images in combination with flux footprint models can be especially useful for identifying the variability in the measured eddy covariance fluxes due to ecosystem dynamics in nonsteady-state landscape conditions, such as ecosystems that have been disturbed or restored. We explored the idea that dynamic changes in both vegetation abundance and structure within the flux footprint might explain the variability in the measured CH4 flux within the flux tower footprint. For example, in two flux footprints with the same abundance of vegetation, the rates of CH4 production might change depending on whether the plants are thinly and evenly distributed across the landscape, or clustered tightly together, possibly creating a biogeochemical hot spot. We used fractal analysis, which has a rich history in ecological pattern analysis [Mandelbrot, 1983], to classify the area-perimeter relationships of plant patches across the flux footprints. Fractal analysis has previously been used to analyze complex spatial patterns at the landscape scale for many environmental applications, including the measurement of spatial aggregation [Milne, 1992], the determination of spatial scales of anthropogenic deforestation [Krummel et al., 1987], and the assessment of landscape connectivity for population distributions [With et al., 1997]. In this analysis, examining both vegetation abundance and spatial fractal structure in tandem yielded nuanced insights into the spatial drivers of CH4 flux within dynamic flux footprints.
We investigated the spatiotemporal drivers of the measured CH4 flux variability over the course of the summer growing season with the three replicate wetland flux towers by deconstructing the impact of large-scale environmental drivers of CH4 flux that were consistent across all the three sites from the drivers of CH4 flux that acted locally at the scale of individual flux tower footprints. The questions driving this analysis were the following:
How variable are measured CH4 fluxes across the three flux towers operating within the same wetland site, and how much of the measured variability can be explained by the environmental and biological drivers of wetland CH4 flux?
How variable are emergent vegetation abundance and spatial fractal structure within the measured flux footprints at the three towers over the course of the growing season?
Are relationships between the site-level drivers TA and u* and CH4 flux consistent among all the three flux towers?
Does the variability in emergent vegetation abundance and spatial structure within individual flux towers explain a significant variability in the measured CH4 flux?
To parse the site- and tower-level variability in CH4 flux, we constructed a hierarchical statistical model that accounted for site-level effects, tower-level effects, and temporal autocorrelation. We used this model to examine the relative contribution of spatially uniform site-level drivers such as air temperature and u* and tower-level spatially heterogeneous drivers such as gross primary productivity (GPP) and flux footprint composition. Within this multi-tower analysis, we used the variability both within and among the measured tower fluxes to parse the variability that was captured by biological and environmental drivers. Understanding the relative contribution of these drivers advances our understanding of ecosystem-atmosphere carbon fluxes in restored wetlands, which have been identified as having major potential for ecosystem carbon sequestration in the future [Miller et al., 2008]. As investigators seek to measure the eddy fluxes of more spatially complex trace gases like CH4 and N2O in heterogeneous landscapes, integrating multiple measurements with flux footprint analysis and remote sensing provides a method for assessing the impacts of heterogeneity from environmental and biological drivers at multiple spatial scales.
2.1 Site Description
The site within this analysis is a restored freshwater wetland (latitude: 38.05°N, longitude: 121.77°W, elevation: 3 m below sea level) that was converted from a drained degraded peatland pasture by flooding in October 2010 (Figure 1a). Before the field was flooded, a heterogeneous bathymetry was excavated within five checks surrounded by built-up levees to preserve small patches of extant wetland vegetation and create areas of shallow water and contiguous areas of deep water. As a result, the water depth at the site ranges from a few centimeters to about 2 m. Maintaining spatial heterogeneity of shallow and deepwater areas was identified as a management goal in this restoration project, because spatially heterogeneous wetlands might act as “keystone structures” that encourage biodiversity [Tews et al., 2004]. The water level across the wetland was maintained at a constant height for the duration of this study.
Vegetation dynamics at the site are controlled by in-filling of vegetation as the vegetation within the site continues to expand following flooding in 2010; by the end of the study in October 2012, plants covered 63% of the site. Vegetation patches within the wetland are composed of Schoenoplectus acutus (common names: tule and hardstem bulrush) and Typha latifolia (common names: cattail and bulrush). Typha latifolia is a cosmopolitan plant that reproduces primarily through clonal ramet growth, with a dense advancing front of sprouts that outcompete other plants, aptly described as a “phalanx strategy” of population growth [Dickerman and Wetzel, 1985]. Schoenoplectus acutus is a native wetland species specific to North America that also reproduces clonally [Farrer and Goldberg, 2009; Miller and Fujii, 2010]. At the scale of broad wetland plant functional types (for example, submerged versus emergent macrophytes), plant species differences play an important role in controlling the resulting CH4 flux to the atmosphere [Bubier, 1995; Laanbroek, 2010]. Species may also impact the resulting CH4 flux within narrower functional groups (for example, sedges) by differential contributions to soil carbon substrate supply [Ström et al., 2005; Ström et al., 2012]. However, for the purposes of our analysis, we grouped Typha and Schoenoplectus into a single-vegetation class due to the similarity in their CH4 transport mechanisms and due to an absence of evidence supporting differences in their rate of soil substrate supply.
The data used in this analysis were collected from 10 May to 25 October in 2012, when temperature and incoming solar radiation were high and precipitation was absent due to the regional Mediterranean climate. This study is part of a long-term local network of Ameriflux sites that are measuring biogeochemical fluxes over multiple years to determine the effect of ecological dynamics and land use change on greenhouse gas fluxes. Winds during the study period were large in magnitude and consistent in direction, with a mean daytime wind speed of 5.3 m/s and a mean nighttime wind speed of 4.6 m/s (Figure 2).
2.2 Eddy Covariance Flux Measurements
We measured the fluxes of CO2, H2O, CH4, and energy from 10 May 2012 until 25 October 2012 (170 days) with two eddy covariance systems at the wetland: one stationary tower in the center of the wetland (hereafter referred to as “Permanent Tower”) and a second tower built in the bed of a pickup truck that was moved every week between one location south of the Permanent Tower (“South Tower”) and a second location north of the Permanent Tower (“North Tower”) (Figure 1b). Eddy covariance instrumentation at the Permanent Tower was situated 4.08 m above the wetland water surface, and the portable tower eddy covariance instrumentation was located 4.26 m above the water surface at the North Tower and South Tower sites. Each tower contained an identical set of eddy covariance instrumentation; we measured the wind velocity in the three vector directions and the speed of sound (u, v, w, and sos; m/s) with a sonic anemometer (Gill WindMaster WM-1590; Gill Instruments Ltd, Lymington, Hampshire, England), CO2 and H2O densities (ρCO2 and ρH2O; mmol/m3) with an open-path infrared gas analyzer (LI-7500A; LI-COR Biogeosciences, Lincoln NE, USA), and CH4 density (ρCH4; mmol/m3) with an open-path infrared gas analyzer (LI-7700; LI-COR Biogeosciences, Lincoln NE, USA). We used a digital data logger system (LI-7550A; LI-COR Biogeosciences, Lincoln NE, USA) to record raw turbulence data at 10 Hz. At the Permanent Tower, we measured the air temperature (Tair; °C) and humidity with an aspirated and shielded thermistor and capacitance sensor (HMP45C; Vaisala, Vantaa, Finland), logged at 10 Hz and analyzed as 30 min averages in post-processing.
Using standard analysis techniques, we processed the 10 Hz turbulence data to half-hourly eddy covariance fluxes with in-house software written in MATLAB. This software removed artificial data spikes in the 10 Hz data (values greater than 6 standard deviations from the mean in a 1 min window) and values of 10 Hz ρCO2, ρH2O, and ρCH4 corresponding to diagnostic values that indicated a fouled laser path. We then rotated the x axis of the 10 Hz sonic anemometer data to the mean wind direction in each half-hour window by applying a coordinate rotation to align the mean vertical and lateral velocities to 0. We calculated the fluctuations in sonic temperature from fluctuations in speed of sound after accounting for crosswind and humidity effects and calculated friction velocity (u*; m/s) after these corrections [Kaimal and Gaynor, 1991; Schotanus et al., 1983]. For each half-hour window of turbulence data, we applied the Webb-Pearman-Leuning correction to account for the effects of air density fluctuations [Detto and Katul, 2007; Webb et al., 1980], and we applied the relevant additional spectroscopic corrections for ρCH4 fluctuations measured with the LI-7700 instrument [McDermitt et al., 2010]. We explored the possibility of including additional corrections for spectral loss between the LI-7700 and sonic anemometer by comparing the cospectrum of sensible heat flux to the spectrum of CH4 flux measured with the LI-7700 [Aubinet et al., 1999]. However, the spectral correction factor was less than 5% for measurements during our study period, which is well within the accuracy of an individual flux measurement, so we did not apply further spectral loss corrections. After these corrections, we computed the covariances to calculate the fluxes of CO2 (µmol m−2 s−1), CH4 (nmol m−2 s−1), and evaporation (mmol m−2 s−1), where positive values represent fluxes from the ecosystem into the atmosphere and negative fluxes represent uptake by the ecosystem from the atmosphere. We filtered out the values with anomalously low-turbulence conditions (|uw| < 0.02) to constrain our analysis to periods where the air near the sensors was well mixed, where only 6% of half-hourly flux data were removed by this criterion [Detto et al., 2011]. Other periods of missing values in this analysis are due to bad sensor signal conditions and brief sensor malfunction (8% additional data), which we did not include in the subsequent statistical analysis.
We partitioned the net CO2 fluxes into gross primary productivity (GPP; µmol m−2 s−1) and ecosystem respiration through standard FLUXNET methodology by partitioning nighttime CO2 flux as respiration and extrapolating to daytime respiration with a 2 week running temperature response function [Reichstein et al., 2005]. While we acknowledge that this simple partitioning method may not be ideally suited for complex landscapes, we think that it is sufficient to capture basic patterns in GPP. Furthermore, we did not want to introduce artifacts into the statistical analysis by using additional covariates to constrain the GPP partitioning. Because both the daily pattern in CH4 fluxes and GPP fluxes follow a regular diel cycle (Figure 3), we calculated the daily integrals of CH4 flux (mg C m−2 d−1) and GPP (g C m−2 d−1) only for days that had greater than 85% of possible half-hourly values (136 complete daily integrals for the Permanent Tower, 52 for the South Tower, and 46 for the North Tower). By this methodology, we linearly interpolated small gaps (less than 1 h) rather than gap-filling fluxes with methods dependent on environmental drivers in order to avoid introducing statistical artifacts from gap-filling methods into our subsequent statistical analyses. The minimum flux detection limit for the LI-7700 sensor in the delta meteorological conditions with this processing software is 3.78 nmol m−2 s−1, and the random flux uncertainty is 7.1 nmol m−2 s−1, values orders of magnitude lower than any CH4 flux measured during this study [Detto et al., 2011]. Within this analysis, the average fluxes are presented as the mean ± the standard deviation.
2.3 Satellite Imagery Classification
For this analysis, we used images collected from the WorldView-2 satellite (DigitalGlobe, Boulder, CO), which contain eight spectral bands ranging from 400 to 1040 nm with a pixel resolution of 1.8–2.1 m. Images used in this analysis were collected on 19 May 2012, 12 July 2012, 9 August 2012, and 2 September 2012 (hereafter referred to as “May,” “July,” “August,” and “September”). Before the classification analysis, the imagery was processed for atmospheric corrections using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes module based on the MODTRAN4 radiative transfer code in ENVI 4.8 (Exelis, Boulder, CO). All the images were then clipped to the spatial extent of the wetland. Although the images were already georectified, we georegistered all the images to the 19 May 2012 image using 25 control points per image located on immobile features like levees and roads to maximize the image-to-image spatial precision for comparative analysis. Prior to image classification, we masked all the levees and roads using a shapefile created with high-precision GPS with an additional two-pixel buffer mask around each levee or road feature to prevent erroneous classification of levee vegetation as wetland vegetation.
To classify the wetland vegetation, we used the spectral angle mapper (SAM) routine in ENVI. The SAM technique determines the spectral similarity between a reference spectrum and a pixel spectrum by calculating the angle between the two spectra, treating the spectra as vectors in a space with dimensionality equal to the number of bands (in this case, eight). We chose this method since it is relatively insensitive to illumination and albedo effects and uses the most significant identifying information from all the eight spectral bands to separate the image into classes. Within the SAM routine, we defined four reflectance classes: water, senescent vegetation, floating aquatic vegetation, and photosynthetic vegetation. We classified both Schoenoplectus and Typha emergent vegetations into a single class because of their similarity in both function and spectral reflectance, since Schoenoplectus acutus and Typha latifolia share the same growing season and both convectively transport CH4 from the soil to the atmosphere [Yavitt and Knapp, 1995]. We identified the reference spectra for classification by mapping three patches (3–5 m in diameter) of each classification type near the permanent eddy covariance tower with a high precision (0.5 m spatial resolution) GPS (Trimble XT; Trimble Navigation Limited, Sunnyvale, CA) on 13 May 2012. We used the same GPS-located shapefiles as reference spectra for all the images, and weekly visits to the field site confirmed that the patches did not change class over the duration of this study. The reference spectra for each of the classes followed typical patterns (Figure S1 in the supporting information). Within the SAM routine, we defined the maximum distance between the classification pixels and the reflectance spectra as 1 rad.
We evaluated the accuracy of this classification routine by comparing the classified results to the ground-truth plots established with high-accuracy GPS on 13 May 2012. Five plots of 3–5 m in diameter for each class (separate from the set used as reference spectra) were mapped on 13 May 2012 and were tracked every other week to account for class transitions. The accuracy of our classification was robust, where user's accuracy ranged from 89 to 98% and producer's accuracy from 87 to 98% for the four classes defined in this analysis (Table S1 in the supporting information). For subsequent statistical analysis, we only used the percent of the flux footprint covered by emergent vegetation, since the proportions within the four classes at each time step are all highly correlated through methodology.
2.4 Eddy Flux Footprint Model
To model the spatial origin of the flux measurements made with the eddy covariance towers, we used an analytical two-dimensional footprint model [Detto et al., 2006; Hsieh et al., 2000]. The flux tower footprint describes the spatial portion of the landscape represented by each half-hourly eddy covariance flux measurement and is a function of land surface roughness and atmospheric turbulence and stability [Schmid, 2002]. We chose this model because it has algorithms that extend and contract the dimensions of the footprint with changing atmospheric stability. This footprint model estimates footprint extent and lateral dispersion by a parameterization for different atmospheric stability conditions and uses friction velocity (u*; m/s), the Obukhov atmospheric stability length (L; m), variance in lateral wind (σv; m/s), momentum roughness length (z0; m), and measurement height (zm; m) as driving variables. We calculated z0 iteratively using the relationships between roughness length, u*, and canopy height [Sonnentag et al., 2011]. This model has been tested against several data sets, and in general, it succeeds at reproducing the source region for flux measurements at eddy covariance towers in spatially heterogeneous ecosystems [Baldocchi and Rao, 1995; Detto et al., 2006]. We used the 85% analytical footprint for this analysis (i.e., the areal extent from which 85% of the measured eddy flux originated), because as the analytical footprint approaches 100%, the areal extent rapidly expands, although there is in fact a very small contribution to the measured flux from this extensive area. To analyze the impact of footprint variability on the daily CH4 fluxes, we calculated the half-hourly 85% flux footprint at each tower. We overlaid this half-hourly flux footprint on the classified satellite image to calculate the spatially weighted fraction of vegetation and fractal dimension within the footprint, and then aggregated the vegetation characteristics to a daily mean. Thus, this analysis accounts for variability due to changes in turbulence and wind direction that modify the footprint extent and changes in vegetation abundance within the tower footprint that occur over a longer, monthly time scale.
2.5 Spatial Fractal Analysis
We used fractal analysis to characterize the spatial patterns of emergent vegetation within the tower footprints at the three sites. Fractal analysis yields insight into the relationship between the perimeter and area of emergent vegetation patterns and provides a quantitative metric for the structure of vegetation patterns within the flux footprints. In this analysis, we used the perimeter-area fractal dimension to calculate the fractal pattern among emergent vegetation patches within the flux footprint to evaluate spatial complexity. The fractal dimension (D) characterizes the degree of complexity of a two-dimensional polygon by relating the perimeter of a patch (P) to its area (A) by log(P) = ½ D log(A). For simple Euclidean shapes like circles and rectangles, D will tend to 1 but for more complex shapes where the perimeter becomes increasingly plane filling, D will approach 2. Thus, D can well describe the expansion of emergent vegetation through space; if D is near 1, then there is a smaller patch edge with respect to area; whereas if D is closer to 2, there is a larger patch edge with respect to area. We applied this metric to the emergent vegetation patches within each half-hour flux footprint and calculated D by conducting a linear logistic regression of P on A and calculating the slope for footprints with greater than 5 emergent vegetation patches to obtain robust regression statistics. For this analysis, we only used the values of D, where the R2 statistics were greater than 0.95 and the P value of the regression was below 10−5. For this analysis, we calculated the mean fractal dimension of the tower footprint at a daily interval to match the daily integral flux measurements.
2.6 Statistical Methods
We used hierarchical mixed effects modeling with a temporal autocorrelation structure to examine the drivers of the daily CH4 flux between and within the sites. In a simple linear model, we fit all the daily integrals of CH4 flux, m, as
where ε ~ N(0, σ2) and X is the matrix of regression variables, β is the vector of regression coefficients, and ε is the vector of errors, which are normally distributed with variance σ2 around 0. However, implementing this type of normal linear model on the CH4 flux data collected within our study violates many statistical assumptions about independence of observations due to the inherent correlation structure between the measurements both within the towers and through time. Instead, we implement a hierarchical model that accounts for the effects on m at each tower t by
where Xt is the model matrix of regression variables at tower t and as before and β is the vector of regression coefficients. However, in this model, we have added Zt as the model matrix for random effects at tower t and bt as the vector of random effect coefficients for tower t. Parameter bt follows a normal distribution, where ψ is the covariance matrix for the random effects at tower t. The final term in the hierarchical linear regression is the error term ε, which follows a normal distribution with a mean of 0, where σ2Λt is the covariance matrix for the regression errors within tower t. We included the daily mean air temperature (TA), daily mean friction velocity (u*), daily integrated gross primary productivity (GPP), daily mean footprint vegetation (% Veg), and daily mean footprint fractal dimension (Frac dim). Within this data set, we did not find statistical evidence for a nonlinear relationship between CH4 flux and temperature, likely due to the relatively narrow range of the daily mean temperatures experienced at our site. However, we caution that applying this approach in colder ecosystems will require careful consideration of the appropriate temperature response model for CH4 flux, because the temperature dependence of respiration is generally more sensitive in cold ecosystems [Lloyd and Taylor, 1994].
In this analysis, we assumed that the regression variables all followed a normal distribution, which we determined after examining the distributions of our data. We imposed a within-tower temporal autocorrelation structure as an autoregressive order 1 (AR-1) process on ψ, which captured the residual correlation pattern in the hierarchical model (Figure S2 in the supporting information). The hierarchical mixed model was fitted using the nonlinear mixed-effects package in R [Pinheiro et al., 2013]. In our model comparison, we used the recently developed approximations of R2 for hierarchical mixed models to calculate the proportion of variance in m captured by the model through R2marginal as the proportion of variance captured by the fixed regression parameters β and R2conditional as the proportion of variance captured by the full mixed model with both the regression parameters and the random tower effects [Nakagawa and Schielzeth, 2013].
3.1 CH4 and CO2 Fluxes Across the Three Towers
The measured daily fluxes of CH4 across the three flux towers demonstrated large day-to-day variability both within and between the towers (Figure 3a). The seasonal daily-integrated CH4 flux at the Permanent Tower was 245 ± 98 mg C m−2 d−1, demonstrating that the fluxes at the Permanent Tower were larger than those from the North and South Towers, where the integrated fluxes were 209 ± 48 mg C m−2 d−1 and 193 ± 41 mg C m−2 d−1, respectively. All the three sites had a seasonal trend in CH4 flux, where the peak occurred in late June to early July. The distributions of the difference in half-hourly CH4 fluxes between the Permanent Tower and the North and South Towers also showed consistently larger CH4 fluxes from the Permanent Tower than the North and South Towers (Figures 3c and 3d). The median of the distribution of the half-hourly CH4 flux differences between the towers indicated fluxes were 83 ± 125 nmol m−2 s−1 larger at the Permanent Tower than the North Tower and 62 ± 104 nmol m−2 s−1 larger at the Permanent Tower than the South Tower during the growing season. These differences highlight the importance of gaining perspective from multiple locations within a spatially heterogeneous and complex landscape, since the drivers of this variability may not initially be apparent.
Patterns in the daily GPP across all the three sites mirrored that of CH4 flux (Figure 3b). There was a relatively large variability in GPP across all the three sites, albeit less variability than in the daily CH4 fluxes. The GPP fluxes at the Permanent Tower are consistently lower than those from the North and South Towers, indicating higher rates of ecosystem photosynthesis. The average daily integrated GPP during the growing season at the Permanent Tower was −10.5 ± 2.3 g C m−2 d−1, at the North Tower average growing season GPP was −5.9 ± 0.8 g C m−2 d−1, and at the South Tower average growing season GPP was −8.0 ± 2.0 g C m−2 d−1. The seasonal trend in GPP slightly lagged that of the seasonal CH4 flux, where peak uptake occurred in middle to late July. Similar to the patterns in CH4 flux, the half-hourly fluxes of GPP at the Permanent Tower were also consistently larger than those from the North and South Towers. The median of the half-hourly GPP flux difference indicated that the GPP fluxes were on average 7.1 ± 5.4 µmol m−2 s−1 larger at the Permanent Tower than the North Tower and 4.3 ± 4.2 µmol m−2 s−1 larger (more negative) at the Permanent Tower than the South Tower (Figure 3d).
Although there appears to be large variability in the daily CH4 and GPP fluxes across the three towers, all the towers had consistent diel trends in CO2 and CH4 flux (Figure 4). The largest daytime CO2 uptake and the largest nighttime CO2 efflux occur at the Permanent Tower (Figure 4b), with mean maximum daily uptake at −17.4 ± 7.6 µmol m−2 s−1 and mean nighttime respiration at 5.1 ± 4.8 µmol m−2 s−1. The North Tower had lower rates of net daytime CO2 uptake than the Permanent Tower, with growing season maximum uptake at −10.1 ± 2.7 µmol m−2 s−1, and the North Tower also had lower rates of nighttime CO2 respiration at 2.8 ± 2.7 µmol m−2 s−1 (Figure 4a). The maximum daytime net CO2 uptake at the South Tower nearly matched that of the Permanent Tower at −17.0 ± 5.3 µmol m−2 s−1, although the nighttime CO2 respiration flux was significantly lower at 2.1 ± 2.3 µmol m−2 s−1 (Figure 4c).
The diel patterns in the CH4 flux had much larger variability than those for net the CO2 flux; however, the seasonal CH4 fluxes at the time of the daily maximum incoming PAR (about noontime) and nighttime CH4 fluxes (daily CH4 flux average, where PAR < 5 µmol m−2 s−1) were significantly different for each tower (z test, p < 10−5). The daily maxima in CH4 flux across all the three sites occurred midday, since the two dominant wetland plant species at the site, Typha and Schoenoplectus, both convectively transport CH4 from the soil to the atmosphere while their stomata are open (Figures 4d–4f). The Permanent Tower had the largest mean daily maximum CH4 flux at 294 ± 211 nmol m−2 s−1 and a mean nighttime minimum flux at 210 ± 179 nmol m−2 s−1 and also had the largest range of variability over the course of the growing season of all the three towers (Figure 4e). The North and South Towers had similar rates of mean daily maximum CH4 flux at 244 ± 78.0 nmol m−2 s−1 and 245 ± 57.2 nmol m−2 s−1, respectively (Figures 4d and 4f). However, the North Tower had higher rates of mean nighttime CH4 flux at 199 ± 93.9 nmol m−2 s−1 compared with those from the South Tower at 157 ± 51.2 nmol m−2 s−1.
3.2 Trends in Flux Footprints Over the Study Period
A corresponding flux footprint was modeled for each half hour when an eddy flux measurement was collected at each tower, the half-hourly values of the fraction vegetation and fractal dimension were extracted for each footprint and then the fraction vegetation and fractal dimension were aggregated to a daily average to match the time scale of the daily integrated CH4 flux. Over the entire course of this study period, the climatological flux footprints were stable in direction with little diel variability due to the strong and reliable winds through the California Delta during the summertime (Figure 2). The mean extent of the climatological daytime 85% flux footprints across all the three locations was 135 m, and the mean extent of the climatological nighttime 85% flux footprints across all the three sites was 152 m. While the flux footprints at other eddy flux sites around the world are much more variable in time and space [Goeckede et al., 2008], the turbulence during the study period at this site was both regular and strong.
At all the three tower locations, the mean fraction of vegetation within the flux footprint increased throughout the study period, paralleling the summer growing season (Figures 5a–5c). In May, the flux footprints at all the three sites contained 20–30% emergent photosynthetic vegetation, which more than doubled at all the sites by the end of the study period in September. The fraction of vegetation within the flux footprints at the North Tower increased the least, and by September, the flux footprints at the site contained an emergent vegetation fraction of 0.57 ± 0.05, compared with 0.30 ± 0.06 in May. The vegetation fraction within the Permanent Tower footprint expanded the largest amount over the study period, from 0.22 ± 0.03 in May to 0.62 ± 0.02 in September. The vegetation fraction within the flux footprints at the South Tower expanded at a moderate amount over the study period, from 0.28 ± 0.04 in May to 0.63 ± 0.05 in September.
There was a significant decrease in the mean fractal dimension of the emergent vegetation patches within the Permanent and South Tower flux footprints over the study period, whereas the North Tower footprints remained stably fractal from July onward (Figures 5d–5f). In May, the pattern of emergent vegetation within all the three sites had a highly fractal structure, where the fractal dimension was near 1.75 across all the towers (a fractal dimension of 2 is a perfect complex fractal). As the study period progressed, the fractal dimension at all the sites decreased, forming less complex and more geometric shapes, although the footprints still remained overall fractal in composition by the end of the growing season. The Permanent Tower had a moderate decline in fractal dimension over the study period, from 1.76 ± 0.02 in May to 1.60 ± 0.02 in September, and the South Tower had a large decline in fractal dimension from 1.74 ± 0.01 in May to 1.54 ± 0.02 in September. At the North Tower site, the vegetation within the flux footprint remained stably fractal from July onward throughout the remainder of the growing season with the smallest seasonal decline in fractal dimension, from 1.76 ± 0.01 in May to 1.64 ± 0.01 in September.
3.3 Statistical Modeling of CH4 Flux
We fit the statistical model described in section 2.6 to the daily CH4 flux data across the three sites with a hierarchical structure to capture site-level effects, tower-level effects, and temporal autocorrelation over the course of the study period. We only used linear regression in this analysis, since there was no support for a more complex model structure through examining the patterns in both our data and the modeled residuals. The best fit statistical model included the significant covariates (p < 0.01) mean daily air temperature (TA; °C) and mean daily friction velocity (u*; m/s), which were constant across all the three towers, and the tower-level covariates mean daily vegetation fraction in the tower footprint (% Veg, nondimensional 0–1), GPP, and mean daily fractal dimension of vegetation within the flux footprint (Frac dim, nondimensional 1–2). The site-level drivers TA and u* explained 39% of the variance in the daily integrated CH4 flux across all the three towers, while the tower level drivers vegetation fraction (% Veg), GPP, and vegetation fractal dimension (Frac dim) explained an additional 27% of the variance in the measured daily CH4 flux (Figure 6b). Overall, the hierarchical regression model captured 67% of the variance within the measured daily CH4 flux across the three towers.
The estimated intercept of the statistical model was negative, so all of the fitted regression parameters had a positive relationship with the daily CH4 flux, with the flux footprint variables % Veg and Frac dim having the largest estimated magnitude of effect on the estimated regression fit (Figure 6a). All the regression parameters significantly explained a substantial amount of variance within the daily CH4 flux data set across the three towers (Figure 6b). The estimated random tower effects describe changes in the modeled intercept of each regression line that capture tower-level variability that was unexplained by other covariates within the model. The estimated North Tower effect was negative, with a mean (and 95% confidence interval) of −62 (−112–17) mg C m−2 d−1; the Permanent Tower effect was near 0, with a mean of 17 (−33–96) mg C m−2 d−1; and the South Tower effect was positive, with a mean of 46 (−4–110) mg C m−2 d−1 (Figure 6c). This indicated that the North Tower measured consistently lower daily CH4 fluxes than the other two towers after accounting for the regression variables alone, the modeled Permanent Tower fluxes from the regression variables alone were well fit to the data, and the modeled South Tower fluxes were consistently higher than the fluxes from the other two towers. Overall, the statistical model captures most of the variability in the measured CH4 fluxes; however, the model is unable to capture the patterns in the magnitude of the largest measured fluxes, particularly those that are above 300 mg C m−2 d−1 (Figure 6d). This possibly indicates that the statistical model in this analysis is not capturing a process that is driving the magnitude of the CH4 fluxes at this particularly high range, perhaps ebullition events, which can be infrequent but large.
4.1 Patterns in CH4 Flux Across the Three Towers
The magnitude of the daily CH4 flux was variable over the study period, but all the three towers demonstrated significant seasonal trends, where seasonal CH4 flux peaked in early summer and then declined over the course of the growing season, paralleling the pattern in seasonal GPP (Figure 3). GPP is linked to CH4 flux on hourly to daily time scales, because methanogenic microbes living near the plant rhizosphere can use root exudates as a primary substrate [Aulakh et al., 2001; Hatala et al., 2012; Holzapfel-Pschorn et al., 1986], and GPP and CH4 flux are linked on daily time scales across a wide climatic range of ecosystems [Whiting and Chanton, 1993]. While GPP was a significant predictor of CH4 flux in our study, surprisingly, the peak in the seasonal pattern of daily integrated CH4 flux preceded that for GPP, indicating a more complex relationship between GPP and CH4 flux on daily time scales across the growing season. Multiple potential hypotheses exist for this complex pattern that we were unable to test in this study, including (1) the period of peak root exudation and microbial carbon substrate supply precedes the peak in GPP flux within wetland plants and (2) an increase in O2 transport to the rhizosphere during the peak GPP flux promotes CH4 oxidation, dampening the magnitude of the net CH4 flux that escapes to the atmosphere. Future research that examines net production and consumption of CH4 within the ecosystem before it is released to the atmosphere could help to detangle these processes.
Although the diel pattern in the CH4 flux was more variable than that for the GPP, there were consistent diel cycles in the CH4 flux at all three towers (Figure 3). Diel cycles in both the net CO2 and CH4 fluxes are controlled by wetland plant physiology and nighttime transport processes, including convective mixing as the water surface cools [Godwin et al., 2013; Poindexter and Variano, 2013]. The diel trend in the CO2 uptake is controlled by photosynthetic activity. The trend for the CH4 flux is also linked through stomata, because both Typha and Schoenoplectus convectively transport CH4 from the soil to the atmosphere as a by-product of their aerenchyma vascular structure designed to transport O2 to their roots for respiration [Dacey and Klug, 1979; Raimbault et al., 1977]. The mean daily maximum rate of the CH4 flux was similar among the towers ranging from 244 to 294 nmol m−2 s−1 and was an order of magnitude larger than the maximum daily rate of CH4 flux from a nearby rice paddy site, which also demonstrated a diel cycle in CH4 flux with a maximum near 30 nmol m−2 s−1 during the growing season [Hatala et al., 2012]. There was more variability in the daily maxima of CH4 flux at the Permanent Tower than the North and South Towers, likely driven by the more variable flux footprint composition at the Permanent Tower, when compared with the North and South Towers (Figure 5). While the North and Permanent Towers had similar rates of nighttime CH4 flux, the South Tower site had much lower rates of nighttime CH4 flux. At nighttime, the processes of ebullition, convection, and diffusion dominate the transport of CH4 between the soil, water, and atmosphere because plant stomata are closed. The lower rates of nighttime CH4 flux at the South Tower could be the result of multiple processes, for example: (1) a lower partial pressure of CH4 within the soil matrix due to peat structural differences and/or (2) differences in plant sheltering or bathymetry causing differences in the convection of nighttime mixing.
4.2 Spatial Changes in Flux Footprints
Analyzing the concurrent spatial changes in both the amount and structure of emergent vegetation of the flux tower footprints yields insight into differences among landscape-scale vegetation dynamics within the three different sites. At the South Tower, the vegetation within the flux footprint increased moderately during the study period, while the fractal dimension significantly decreased (Figure 5). This indicates that the emergent vegetation growth within the South Portable tower footprint during the study period occurred in a way that geometrically expanded and filled in vegetation patches on the landscape, creating shapes with lower perimeter to area ratios. Conceptually, this can be interpreted as complex patches merging together to form more regular shapes or a complex shape growing to a larger, more rotund shape. Vegetation expansion patterns at the Permanent Tower followed a similar pattern, although with a larger expansion of vegetation that maintained a higher level of spatial complexity when compared with the South Tower. At the North Tower, the increase in vegetation abundance and stable fractal dimension described a process of patch growth into more complex shapes and the formation of new complex patches.
The changes in both vegetation abundance and complexity within the three sites in this study could reflect adaptations to landscape-scale resource patterns or water depth limitations. The spatial complexity of wetland vegetation is considered a valuable keystone structure for restoration that can enhance habitat diversity, and as a result, biodiversity [Tews et al., 2004]. It is worth noting that this analysis only examines changes in the aboveground components of emergent wetland vegetation, and a significant portion of wetland plant biomass occurs belowground, which is not captured by satellite imagery. Research has demonstrated that restored wetlands impacted by anthropogenic influence have less complex spatial patterns at all scales, so spatial complexity, measured in this study through the fractal dimension, might also help to promote wetland biogeochemical cycling [King et al., 2004]. The fractal dimension of vegetation within the tower footprint was a significant driver of daily CH4 fluxes, indicating that in this study, vegetation structure in addition to vegetation abundance is an ecologically significant driver of variation in the daily CH4 flux (Figure 6b).
4.3 Temporal and Spatial Drivers of Daily CH4 Flux
Hierarchical statistical modeling revealed strong explanatory variables for the observed variability in the daily CH4 fluxes across all the towers. Across all the sites, TA (mean daily air temperature) and u* (mean daily friction velocity) significantly explained 39% of the variance in the daily CH4 flux (Figure 6b). Temperature controls both the rates of CH4 transport and CH4 production, because warmer temperatures encourage the diffusion of CH4 from the water to the atmosphere and also promote methanogenic microbial activity that produces CH4 [Parashar et al., 1993]. The u* controls the CH4 flux from the ecosystem to the atmosphere through a purely transport mechanism; a higher u* increases the turbulent mixing depth of the water surface and stimulates a higher rate of CH4 flux from water surfaces to the atmosphere [Cole et al., 2010; MacIntyre et al., 1995]. The high degree of explanatory power contributed by TA and u* within the statistical model indicated that much of the growing season CH4 flux in this wetland is transport limited, meaning that CH4 is abundant within the soil and the water column, and controls on transport are a key driver of the daily CH4 flux.
Within the sites, GPP and flux footprint vegetation abundance and fractal dimension contributed significantly to explaining the variance in the daily CH4 flux measurements. GPP has long been recognized as a driver of CH4 flux, because GPP controls the flow of substrates for methanogens [Whiting and Chanton, 1993]. In this study, although GPP was a statistically significant driver of the daily CH4 flux, we were surprised that it did not explain a larger portion of variability in the measured CH4 flux (Figure 6b). We think that the lower fraction of variance explained by GPP could be due to the fact that the algorithm for partitioning net CO2 fluxes into GPP and ecosystem respiration is not well suited for heterogeneous landscapes, such as the complex wetland within this study. We emphasize that the development of more sophisticated net CO2 flux partitioning methods should be investigated within heterogeneous landscapes, where accounting for complex spatial structures can be important for detangling the net and gross CO2 fluxes.
Vegetation abundance is expected to have a clear positive relationship with CH4 flux, because plants not only contribute substrate to methanogenic communities but also are the primary conduits for CH4 from the soil to the atmosphere in vegetated wetlands [Chanton et al., 1992a; Joabsson et al., 1999; Schimel, 1995]. While GPP captured a statistically significant portion of the variability in CH4 flux, including covariates that directly described the spatial abundance and structure within the flux footprints explained a larger amount of variance within the daily CH4 flux. Including the vegetation fraction in our model increased the explained variance in the data by 17%, and including the fractal dimension increased the explained variance by another 10% (Figure 6b). Furthermore, these structural land cover variables can be obtained from remotely sensed imagery and might significantly improve the performance of CH4 modeling efforts at large spatial scales.
Structural landscape patterns of vegetation could impact the resulting measured net CH4 fluxes through CH4 production and/or transport. A more complex vegetation fractal structure has a high edge to area ratio, increasing the light-harvesting potential of the photosynthetic canopy and potentially supplying the rhizosphere with additional carbon substrates through root exudates. A more complex fractal structure could also increase the efficiency of roots at scavenging soil CH4 and transporting it to the atmosphere through vegetation aerenchyma. Although this analysis demonstrated that fractal dimension is a significant driver of CH4 for this temperate wetland, further research is required to determine the mechanistic link between fractal dimension and CH4 flux. In reality, many processes likely cooccur.
The statistically significant random tower effects demonstrated that there is an additional variability not currently captured by the regression covariates within our current model formulation, although there remained a significant overlap among the 95% confidence intervals for the modeled random effects (Figure 6c). This indicated that although the daily CH4 fluxes at individual towers followed the same mean behavior over the course of the growing season with respect to the other two towers, there remained a significant variability between the towers that was unexplained by the model. There are many possible hypotheses for the lingering unexplained variance, which could potentially be caused by differences in the nutrient distribution between the tower footprints or other smaller scale variations in ecosystem processes. Residual unexplained variance within the complete model could reflect an additional missing process contributing to CH4 flux across all the tower sites or could accurately reflect inherent variability in CH4 fluxes. While the statistical model well represented the measured data, there remained unexplained variance in the data particularly at the high rates of CH4 flux above about 350 nmol m−2 d−1 that was not well captured by the current model formulation. These fluxes at the very high end of the spectrum could be the result of rare ebullition events releasing much larger pulses of CH4 from the water to the atmosphere. Characterizing the controls on ebullition, such as changes in hydrostatic pressure [Varadharajan et al., 2010], might help to understand the variability in the measured CH4 fluxes of particularly large magnitude.
This analysis used a unique sampling design of the three replicated eddy covariance towers within the same wetland site to measure the ecosystem-atmosphere CH4 flux. Statistical analysis parsed the environmental drivers across the three sets of tower-measured CH4 fluxes and the environmental and biological drivers within the individual tower-measured CH4 fluxes. We found that across the towers, TA (mean daily air temperature) and u* (mean daily friction velocity) were significant drivers of the daily CH4 fluxes across all three towers and that within the towers, GPP (gross primary productivity), flux footprint vegetation abundance, and fractal dimension were equally important for explaining the variability in the daily CH4 flux. The relationships both among and within the towers at the same wetland site yield important insights for flux tower siting in order to capture the variability that can adequately represent an entire ecosystem. This approach is unique in that it uses three towers within the same ecosystem to deduce large-scale and local-scale drivers of CH4 flux, but in reality logistical budget constraints typically render this methodology impractical. Nevertheless, this analysis demonstrated that the local impacts on CH4 fluxes such as the changes in flux footprints need to be accounted for in order to more comprehensively characterize the mechanistic drivers of variability in the measured CH4 fluxes.
At this restored wetland site, the interactions among the drivers of the measured CH4 fluxes yield important considerations for the management of these landscapes as long-term ecological carbon sinks. Many have identified the potential for restored freshwater wetlands in this region to sequester carbon on a long time scale [Miller et al., 2008]; however, the mechanisms that lead to maximum CO2 uptake and minimum CH4 release remain uncertain. Furthermore, there may be limited possibilities for the role of management actions in minimizing the rate of CH4 flux, since much of the variability in CH4 flux at this site was driven by changes in TA and u*, which are essentially uncontrollable. While further study is required in other ecosystems and other climates to determine whether these controls on CH4 flux are consistent, the statistical relationships within this analysis provide promising potential scaling mechanisms for understanding large-scale fluxes of CH4 from wetland ecosystems.
The authors extend many thanks to Bryan Brock and the California Department of Water Resources for funding through DWR grant 006550. J.H.M. acknowledges support from the NSF Graduate Research Fellowship Program grant DGE-1106400. The authors thank Kristin Byrd and the U.S. Geologic Survey Commercial Imagery-Derived Requirements Database for the access to the WorldView 2 and Jessica O'Connell for her assistance in preprocessing the imagery. Data from the Mayberry wetland will be submitted to the Ameriflux database (http://ameriflux.lbl.gov/).