Given its central role in global carbon cycling (Raich and Potter, 1995), the flux of CO2 from soil to the atmosphere – collectively referred to as soil respiration (SR) – is heavily studied across a broad range of systems and spatiotemporal scales using methods ranging from small footprint flux chambers to large footprint flux towers (Bond-Lamberty and Thomson, 2010; Wolf et al., 2016). Our understanding of SR patterns is inherently linked to the scales at which measurements are made and we often lack knowledge of how the variation in SR changes as we move across scales. To rigorously and mechanistically link SR measurements across scales, it is essential to understand spatial heterogeneity in SR, how spatial heterogeneity changes across scales, and the environmental features that drive those SR patterns.

Knowledge of SR spatial heterogeneity – and underlying drivers of that heterogeneity – in permafrost associated ecosystems is particularly important given the large carbon stocks in permafrost (Tarnocai et al., 2009) and ongoing permafrost thaw (Grosse et al., 2011; Schuur et al., 2013, 2015). Numerous studies have investigated temporal dynamics of SR and most find strong influences of temperature and moisture (e.g., Davidson et al., 1998; Hanson et al., 1993), but much less is known about spatial variation in SR, where temperature and moisture appear to have weaker influences (Yim et al., 2003; Dore et al., 2014; Ohashi et al., 2015; Song et al., 2013).

Studies that examine spatial variation in SR often find rates to be associated with tree-stand variables such as basal area, species composition, and distance from SR measurement to tree stems (Ohashi et al., 2015; Katayama et al., 2009; Soe and Buchmann, 2005; Khomik et al., 2006), though such relationships are not ubiquitous (Song et al., 2013; Saiz et al., 2006; Sotta et al., 2004). Relatively little work on spatially resolved SR has occurred in permafrost-associated systems, though higher SR in permafrost-free domains has been observed (Vogel et al., 2005). Importantly, no study has provided spatially resolved SR estimates moving continuously across a permafrost transition, where the depth of soil that is above permafrost (referred to as active layer depth, ALD) increases along a spatial gradient to the point that permafrost is lost. It is critical that we fill this knowledge gap due to a combination of ongoing permafrost thaw (Grosse et al., 2011; Schuur et al., 2013, 2015), vast carbon stocks currently locked away in permafrost (Tarnocai et al., 2009), and the heavy contribution of SR to ecosystem carbon cycling (Raich and Potter, 1995; Longdoz et al., 2000).

Here we explore how the spatial structure and environmental correlates of SR change as we move across spatial and temporal scales. To do so, we generated spatially resolved SR rates – and associated below/above ground data – across a 75×75m spatial domain within boreal Alaska. This domain was selected to capture a spatially abrupt transition from a permafrost-associated system to a permafrost-free system, and at ∼6 Landsat pixels, a scale relevant to potential future work using remote sensing.

Previous work in forests has revealed that SR spatial autocorrelation occurs across a broad range of length scales (referred to as the “range” in variogram models), from less than 1 m to greater than 40 m (Foti et al., 2014; Russell and Voroney, 1998; Song et al., 2013; Singh et al., 2008; Rayment and Jarvis, 2000), but none of these estimates come from boreal forests. In addition, among-study variation in the length scale of spatial autocorrelation may be partially due to differences in the spatial scale of sampling. It is therefore difficult to generate quantitative a priori expectations for the parameters of SR variograms (functions that describe spatial continuity or variability) in our study system. Instead, we test the following qualitative hypotheses: (i) given previous work showing that spatial variability in SR is only weakly related to temperature and soil moisture (e.g., Song et al., 2013; Yim et al., 2003), we hypothesize that SR will be predominantly influenced by carbon inputs such that variability in SR throughout the spatial domain will be best explained by tree-stand variables (e.g., basal area); (ii) within the drier, permafrost-free domain we hypothesize that SR will again be best explained by tree-stand variables, but within the wetter permafrost-associated domain SR will be decoupled from carbon inputs and will therefore be poorly explained by tree-stand variables; and (iii) cold temperatures will fundamentally constrain SR such that we hypothesize a smaller coefficient of variation and less well defined spatial gradients (i.e., weaker spatial structure) in SR under colder temperatures.

Evaluation of the above-summarized hypotheses helps elucidate how a mixture of control processes leads to aggregate SR rates. Such knowledge is important for improving model predictions using multi-scale approaches.

The field site was within the Caribou-Poker Creeks Research Watershed (CPCRW), which comprises a relatively pristine, ∼100 km2 watershed ∼45 km north of Fairbanks, Alaska (Fig. 1a). The CPCRW is part of the Bonanza Creek Long-Term Ecological Research site. In July 2014, six parallel transects – each running east to west – were established (Fig. 1b); each was 72 m long and covered a permafrost-associated domain (eastern half of the sampling region), a permafrost-free domain (western half of the sampling region), and a transitional zone between these conditions (thin strip in the center of the sampling region, running south to north) (Fig. 2). In broad terms, the permafrost-associated domain was characterized by black spruce (Picea mariana) and understory mosses, while the permafrost-free domain was characterized by paper birch (Betula papyrifera) and leaf litter (see Fig. 1c for overview of vegetation transition).

To enable SR measurements, 10 cm diameter PVC soil collars were installed to ∼5 cm depth along each transect in two phases. First, 12 collars were installed on each transect following a cyclic sampling design aimed at efficient spatial sampling (Burrows et al., 2002): spatial positions were 0, 4, 12, 20, 24, 32, 40, 44, 52, 60, 64, and 72 m from the eastern terminus. This arrangement deviates from regular spacing of sampling locations to enable variogram analysis by providing good sampling across all spatial lags (i.e., the distance between sampling points). The design was determined by simulating a broad range of cyclic sampling designs to find a configuration that provided a relatively uniform distribution of sample numbers across all spatial lags. Repeating this sampling design across the 6 transects resulted in 72 soil collars. SR rate measurements were taken from each collar using an EGM-4 (PP Systems, http://ppsystems.com/) with a soil respiration chamber that is designed to provide a well-mixed headspace within the chamber. These initial measurements were used to identify a transition zone across which SR increased rapidly moving from east to west. This transition zone also coincided with the transition from permafrost to permafrost-free conditions. Higher density spatial sampling was performed across this transition zone whereby collars were installed every 1 m from positions 15 to 60 m (moving east to west) on each transect. The full design resulted in 51 collars per transect and a total of 306 collars across the field site (Fig. 1d).

The full set of 306 soil collars was sampled twice from 3 to 13 August 2014 between ∼09:30 LT (local time) and 22:00 LT; this sampling period is referred to here as “Summer” because that time of year is usually associated with some of the warmest temperatures of the year. The minimum time between soil collar installation and SR measurement was 2 days. The strong correlation between SR measurements taken from the same soil collars in Summer and Fall (Fig. S1) indicates that the length of time between installation and measurement did not fundamentally change observed SR patterns. Co-located air and soil (5 and 15 cm depths) temperatures were collected at the time of each measurement. For temperature measurements we used an analog thermometer at the time of sampling for each soil collar. For air temperature, we shaded the thermometer to avoid elevating the temperature due to solar inputs. For soil temperature, we placed the thermometer's stem into the ground to the specified depth. Two operators each used a separate EGM-4 and respiration chamber assembly; each operator measured each soil collar once and the order of sampling was randomized. Following the SR measurements a subset of collars were removed to enable soil coring for other purposes: positions 25–33 m (moving east to west) along the second transect (from south), 31–39 m along the third transect, 37–45 m along the fourth transect, and 21–29 m along the sixth transect were removed (Fig. 1d). No collars were removed from the first and fifth transects. SR was measured twice again from 10 to 24 September 2014 between ∼08:30 LT and 17:30 LT in the remaining collars, along with air and soil temperatures; this sampling period is referred to here as “Fall” because that time of year is usually associated with rapidly declining temperatures and leaf-drop from deciduous trees. Indeed, air temperatures measured during the Fall sampling period were significantly lower than those measured during the Summer sampling period.

It is important to note that analyses that directly compare results between Summer and Fall were repeated on the SR data using only locations that were sampled in both seasons. The purpose of repeating the analyses was to evaluate whether observed seasonal differences were due to differences (between seasons) in the sampling scheme; this showed that seasonal differences in SR patterns were not due to differences in the sampling scheme (see Results section).

For all SR measurements with the EGM-4 and respiration chamber assembly, the maximum change in CO2 concentration was set to 100 ppm and the maximum time of data collection was 2 min. The manufacturer (PP Systems) set the measurement interval, which was every 4.8 s. Raw CO2 concentration and timestamp data were collected and analyzed using custom R scripts. Plotting CO2 concentration against time commonly showed a small degree of non-linearity. The most pronounced non-linearity was usually between the first and second data points such that removing the first data point provided linear fits in nearly all cases. Other data excursions were noted, such as an abrupt increase in CO2 concentration with linear trajectories on either side. To generalize the data analyses we (1) dropped the first data point from each sample, (2) fit both a linear regression and a segmented regression to the remaining data to estimate the SR rate. Segmented regressions were estimated automatically using the function “segmented” in R package “segmented” (version 0.5–1.4; Muggeo, 2003, 2008). For each measurement, the rate was taken as either the slope of the linear regression or the slope of the first segment in the segmented regression, whichever had a higher R2. The only exception was when the first segment contained fewer than 4 data points; in those cases the slope from the full linear regression was used whereby all regressions contained at least 4 data points and had a maximum of 24 data points. The slope from the first segment was used instead of the second segment due to noticeable decreases in the SR rate with increasing sampling time, which was likely due to increasing CO2 concentrations in the recirculating system. This approach significantly improved model fits, relative to using rates recorded directly from the EGM-4 instrument. For each collar in each season the duplicate SR estimates were averaged.

To facilitate comparisons to other studies investigating spatial structure in SR, we quantified the coefficient of variation (CV) within the whole spatial domain, within the permafrost-associated domain, and within the permafrost-free domain; the CV was estimated in these spatial domains within each season. As a complementary approach, we estimated the slope of the power function – on log axes – relating variance in SR to mean SR. This is analogous to the classic “Taylor power law” that relates variance in population density – of a given biological species – to mean population density (Taylor, 1961; Taylor and Taylor, 1977; Eisler et al., 2008). Within each season, the 6 soil collars at a given east/west position were used to calculate a mean and variance. In the Fall some positions did not have 6 soil collars due to soil coring (Fig. 1d); Fall-time SR from these east/west positions were not used. To cover a broad range of mean SR conditions, the two seasons were examined together. Spatial and temporal structures were therefore examined simultaneously.

To examine how SR spatial variation might respond to the spatial advance of permafrost thaw, we iteratively quantified SR variance across spatial domains that had an increasing contribution of permafrost-free soils. Within each season, we began by quantifying SR variance using all soil collars within the eastern-most 20 m of the spatial domain, which represented 54 soil collars (Fig. 1d). Preliminary analyses indicated that the number of soil collars was sufficient for a reliable variance estimate. After quantifying SR variance within the eastern-most 20 m, we added the next most western set of soil collars and recalculated SR variance. This procedure was repeated until reaching the far western edge of the field domain. At each step we also estimated mean ALD at the soil collars found at the western edge of the domain used for variance estimation. This allowed us to connect changes in SR spatial variation to changes in ALD.

In addition to SR, we collected data on the following aboveground variables that may influence SR. A 150 cm soil probe was used to estimate active layer depth (ALD) to the nearest cm in September 2014; ALD was measured every 2.5 m along all 6 transects. A clinometer was used to estimate % slope at sampling locations (0, 4, 12, 20, 24, 32, 40, 44, 52, 60, 64, and 72 m from the eastern terminus) along each transect. Percent cover of feather moss was visually estimated at each soil collar within a 30×30cm quadrat, with the collar at the center. Tree plots of 5 m radius were established every 10 m along each transect, starting with a plot centered at 0 m at the eastern terminus of each transect. The tree plots were hemispherical with sampling occurring to the south of each transect. This was done to minimize disturbance to soil collars, which were placed on the north side of each transect. Within each tree plot, all woody stems with diameter at breast height (DBH) greater than 1 cm were identified and their DBHs were measured. The tree plot data were used to estimate the basal area and stem density.

Relating the variance of SR to its mean suggested clustering of SR in space and/or time (see Results section). In turn, we conducted formal spatial analyses using the “AutoKrige” function in R package “automap” (version 1.1–14) (Hiemstra et al., 2009), which uses model selection to automatically fit a variogram model (Matheron, 1963) and, in turn, generates a spatial interpolation. This package has been found to be robust via extensive use across scientific and engineering disciplines, currently with greater than 60 citations in the peer reviewed literature. To enable quantitative comparisons among SR variogram models, we used AutoKrige to fit Matern models (Pardo-Iguzquiza and Chica-Olmo, 2008) and, in turn, generate interpolations. We selected the Matern function because it has been shown to be a robust and flexible model, in general and for soil systems specifically (Stein, 1999; Minasny and McBratney, 2005). For ALD, slope, feather moss cover, tree-stem density, tree basal area, and Summer and Fall soil temperatures the AutoKrige function was used to select the best model among Matern, Gaussian, exponential and spherical structures. We allowed different model structures for these additional variables because we used the fitted variograms only to visualize the spatial structure of these variables (Fig. 2), as opposed to making quantitative comparisons of variogram parameter estimates. We also examined parameter values of the models fit to the SR variograms. These parameters included the nugget, range, and sill. The variogram nugget represents processes that occur at spatial scales smaller than the minimum distance between samples as well as sampling error. The variogram range is an estimate of the maximum spatial distance across which there is spatial autocorrelation. The variogram sill is the variance at which the variogram model levels off (Western et al., 1998). The Matern model is a special case and also includes the kappa parameter, which describes the smoothness of the fitted variogram (Minasny and McBratney, 2005).

We further aimed to explain variation in SR using the other measured variables. Given significant spatial autocorrelation in all data types, we used generalized least squares (GLS) regression and compared models – using residual standard errors – with Gaussian, exponential, or spherical spatial structure. Variogram and GLS analyses were used to study SR data across the entire spatial domain, within the permafrost-associated domain, and within the permafrost-free domain. The SR analyses were repeated separately within the Summer (August) and Fall (September). The SR data from both seasons were also pooled and a GLS regression was used without spatial structure to find the variable that best explained this spatiotemporal set of SR rates; spatial structure could not be used on the pooled set because measurements were made in both seasons at the same spatial locations.

Running GLS analyses required an estimate of each explanatory variable at the spatial location of each soil collar. Some data types – ALD, slope, stem density, and tree basal area – were collected at a coarser spatial grain than the soil collars. These variables were therefore linearly interpolated to provide an estimate of each at each soil collar; we did not use kriging due to some variables having poorly constrained variograms. Prior to GLS analysis the data were log-transformed to improve normality; feather moss percent coverage ranged from 0 to 100 such that a value of 1 was added prior to log-transformation. To allow direct comparisons of regression coefficients across explanatory variables, log-transformed data were further normalized to have a mean of 0 and variance of 1. Initial analyses indicated that a spherical spatial structure generally lead to lower root square errors in fitted models, relative to Gaussian and exponential spatial structures. GLS models were thus fit using spherical spatial structure and models with different explanatory variables were competed against each other by comparing their root square errors. All analyses were performed with R version 3.2.1 (R Development Core Team, 2016).

SR measured in a soil collar in Summer was strongly correlated to SR measured in the same soil collar in the Fall (Fig. S1). There was, however, a clear decline in both the mean and variance of SR from Summer to Fall (Table 1; Fig. S1). Across the full domain the two seasons had similar CVs (∼47–50 %), but across the two seasons the permafrost-associated domain CV was ∼10–18 % higher than the permafrost-free domain (Table 1). These results were maintained when Summer data were analyzed using the same sampling scheme used in the Fall (Table S1). The slope of the power function relating SR variance to mean SR was 1.57, with an R2 of 0.51 (Fig. 3).

We plotted SR variance within a given spatial domain against the position of the western boundary of that sampled domain (see Methods section). Doing so revealed a strong threshold at spatial positions near ∼40–45 m (moving east to west). At positions beyond this threshold SR variance increased rapidly and then stabilized at ∼55–60 m (Fig. 4a and b). ALD at the western boundary of the sampled domain also showed threshold behavior, increasing rapidly at spatial positions near ∼30–35 m and then reached its limit (150 cm) at about 50 m (Fig. 4a and b). These patterns in SR variation and ALD were found in both seasons even though the SR variance was much lower in the Fall (cf. Fig. 4a and b; Table 1). Also in both seasons, SR variance increased rapidly beyond an ALD threshold of ∼140 cm (Fig. 4c and d).

The variogram fits to SR revealed consistently larger nuggets in the Summer relative to the Fall and modest differences in the nuggets between permafrost-associated and permafrost-free domains (Table 1, Table S1). The range and sill were both larger in the Summer, with an especially large range (133 m) and sill (0.94) in the permafrost-free domain during Summer (Table 1). Using the fitted variograms to visualize the SR spatial structure showed elevated SR in the Summer in the permafrost-free domain, and a similar – but less pronounced – pattern in the Fall (Fig. 5). Visualization of the SR spatial structure within the permafrost-associated and permafrost-free domains – using variogram fits within those domains (Table 1) – confirmed a peak in SR near the center of the permafrost-free domain, an increase in SR from south to north in the permafrost-associated domain, and weak spatial structure across both domains in the Fall (Fig. 5). These patterns were maintained when analyzing Summer data using the reduced sampling scheme used for the Fall (Fig. S2).

GLS regression revealed that Summer SR was significantly related only to basal area when considering the full domain (Table 2). In the permafrost-free and permafrost-associated domains, multiple variables were significantly related to SR, with feather moss percent cover and basal area having the strongest relationships, respectively (Table 2). Similar patterns were observed when analyzing Summer data using the reduced sampling scheme used for the Fall (Table S1). Fall SR was also significantly related only to basal area when considering the full domain, and was again best explained by basal area in the permafrost-associated domain (Table 3). In contrast to the Summer, Fall SR in the permafrost-free domain was best explained by active layer depth (Table 3). When considering both seasons together, SR in the full, permafrost-associated, and permafrost-free spatial domains were best explained by soil temperature, but multiple variables had significant relationships with SR for all three domains (Table 4).

Through intensive field sampling and geospatial analyses we have revealed the spatial structure of SR across a boreal forest permafrost transition, shifts in that spatial structure between seasons and spatial scales, and the environmental variables that potentially drive spatial variation in SR within and across permafrost conditions. To the best of our knowledge this is the first direct characterization of SR spatial structure across a permafrost transition. A number of studies have characterized SR spatial structure in other ecosystems, however, and patterns revealed here show some commonality with previous work in terms of the level of variation and environmental correlates of SR.

Characterizing the spatial structure of SR – not just spatial variation – provides a number of unique opportunities to improve our basic understanding of processes that control the carbon balance in ecosystems and to reveal key thresholds in ecosystem function that are likely to arise in response to environmental change. While such efforts are relatively rare due (presumably) to logistic challenges, they provide insights that other approaches cannot. Here, for example, we revealed thresholding behavior both in terms of average SR rates (i.e., spatial discontinuities shown in Fig. 5) and spatial variation in SR (i.e., the steep increases shown in Fig. 4). These patterns provide powerful constraints on simulation models that attempt to predict carbon cycling fluxes across spatial environmental gradients and/or through time as environmental conditions change. A future challenge is therefore to couple highly resolved spatially explicit SR measurements – like those shown here – with dynamic ecosystem models. Doing so has significant potential to reveal important model limitations that, if overcome, may facilitate improved predictions of ecosystem function under environmental change.