Corresponding author: J. Loisel, Department of Earth and Environmental Sciences, Lehigh University, 1 West Packer Avenue, Bethlehem, PA 18015, USA. (firstname.lastname@example.org)
 Northern peatlands contain vast amounts of organic carbon. Large-scale datasets have documented spatial patterns of peatland initiation as well as vertical peat accumulation rates. However, the rate, pattern, and timing of lateral expansion across the northern landscape remain largely unknown. As peatland lateral extent is a key boundary condition constraining the dynamics of peatland systems, understanding this process is essential. Here we use ground penetrating radar (GPR) and peat core analysis to study the effect of local slope and topography on peatland development at a site in south-central Alaska. The study site is unique in that a thick tephra (volcanic ash) layer, visible in the GPR data, interrupted the peatland development for about one thousand years during the mid Holocene. In our analysis, this tephra layer serves as a re-initiation point for peatland development. By comparing the initial mineral basin vs. the post-tephra surfaces, the influence of topography and slope on peatland expansion rate and peat-carbon sequestration was analyzed. Our results show that (1) peatland surface slope becomes progressively shallower over the Holocene, (2) slope affects peatland lateral expansion nonlinearly, (3) the relationship between lateral expansion rate and slope follows a power-law behavior, and (4) peatland expansion becomes slope-limited above a threshold (0.5°). Furthermore, we propose a conceptual model linking slope to peatland lateral expansion where slope gradient and basin topography exert deterministic controls on peatland lateral expansion directly or through hydrology and vertical accumulation rates.
 Northern peatlands have been affecting the global carbon (C) cycle as well as the climate system by acting as carbon dioxide (CO2) sinks and methane (CH4) sources to the atmosphere since the last deglaciation, about 15,000 years ago [e.g., MacDonald et al., 2006; Yu, 2011]. The timing of peatland initiation across the circum-arctic region of the globe is relatively well established and is based on large-scale compilations of radiocarbon-dated basal peat samples [MacDonald et al., 2006; Gorham et al., 2007; Korhola et al., 2010; Yu et al., 2013]. However, the spatial and temporal patterns of peatland lateral development and expansion across the northern landscape since the last deglaciation are still poorly constrained. As peatland spatial extent is a key dimensional parameter that is included in peatland carbon flux calculations [Korhola et al., 2010; Yu et al., 2010], large-scale estimates of peatland area change over time are in critical need of refinement. A process-based understanding of lateral expansion dynamics paired with regional-scale reconstructions of peatland spreading rates would provide new means to evaluate this important control on peat C-flux terms.
 Comprehensive datasets of basal peat ages indicate that new peatland formation peaked between 10,000 and 8000 years ago in the northern hemisphere as a result of (1) land availability following deglaciation, and (2) orbitally induced warm summer temperatures [MacDonald et al., 2006; Gorham et al., 2007; Yu et al., 2010]. In large-scale estimates of Holocene peat-C fluxes, this period of “explosive” peatland initiation is assumed to have led to rapid and expansive peatland spreading over the landscape, although lateral expansion rates have neither been explicitly estimated nor calculated at large scale. Therefore, in large-scale peat-C pool reconstructions, frequencies of basal initiation dates are often used as a proxy for peatland area change over time, and peatland area is thus assumed to increase linearly over time after the peatland initiation [MacDonald et al., 2006; Frolking and Roulet, 2007; Gorham et al., 2007; Yu et al., 2010]. Given the documented control exerted by landscape morphology on peatland development [e.g., Korhola, 1994; 1996; Borren et al., 2004], this assumption significantly limits our ability to reconstruct realistic past large-scale peat-C pools and associated C flux histories [Yu, 2011].
 Most northern peatlands formed by paludification, that is, by peat inception over mineral soils [Heinselman, 1970; Sjörs, 1983]. Peat formation typically begins in waterlogged topographic depressions [Anderson et al., 2003; Ireland and Booth, 2010]. Subsequent lateral expansion is mostly driven by local- and regional-scale hydrological processes that are closely linked to landscape morphology (Figure 1). For example, topography, slope, and parent material (substrate) exert fundamental constraints on peatland development by controlling water storage as well as flow direction [Graniero and Price, 1999]. Over multidecadal to millennial timescales, peatland bodies probably contribute to their own expansion pattern by locally impeding drainage due to low peat hydraulic conductivity, which saturates the surrounding mineral soils and allows further expansion [Korhola et al., 2010; Morris et al., 2011]. Although very few studies have examined peatland lateral expansion processes, internal peatland mechanisms such as water retention due to low hydraulic conductivity, decreasing soil permeability because of acidic compound leaching, and vertical accumulation of organic matter that raises the local water table have also been proposed as important autogenic drivers for lateral expansion patterns [Belyea, 2009]. Finally, climatic conditions likely play an important, though likely secondary, role in lateral expansion by influencing peatland hydrology and moisture, which in turn control vegetation dynamics and biological processes such as plant growth and peat decay [Belyea and Malmer, 2004]. Vertical peat accumulation rates are also sensitive to temperature [Yu et al., 2011]. Overall, it is generally assumed that local factors such as basin slope and topography constrain the rate of lateral peatland expansion across the high latitudes [Figure 1; Bauer et al., 2003; Mäkilä and Moisanen, 2007], though general rules or threshold values describing these relationships remain elusive.
 Peatland lateral expansion rates have been the object of empirical studies based on radiocarbon (14C) dates of several basal peat samples collected along transects at individual sites [e.g., Ugolini and Mann, 1979; Damman, 1979; Foster and King, 1984; Foster et al., 1988; Foster and Wright, 1990; Korhola, 1994, 1995; 1996; Mäkilä, 1997; Crawford, 2000; Anderson et al., 2003; Bauer et al., 2003; Asselin and Payette, 2006; Mäkilä and Moisanen, 2007; Tipping, 2008; Peregon et al., 2009; van Bellen et al., 2011]. These studies have shown that lateral expansion does not take place in an even manner; while steadily decreasing rates of lateral expansion have been reconstructed at several peatland sites [e.g., van Bellen et al., 2011], distinctly faster and slower phases seem to characterize other peatland systems [e.g., Korhola, 1996]. These different temporal patterns suggest the existence of several modes of peatland development that relate to topographic constraints (Figure 1) or to relationships between rates of vertical growth and lateral expansion [Belyea and Baird, 2006; Figure 1]. In an idealized concentric raised bog, for example, the ecosystem size and shape is internally controlled by geophysical constraints such that height growth leads to concentric lateral expansion, as long as there are no topographic barriers [Ingram, 1982; Foster and Wright, 1990; Morris et al., 2011]. In reality, however, this developmental model would reach a growth limit if effective precipitation remained stable: as the bog spreads concentrically across a flat plain, it increases in height which increases the hydraulic head and leads to drying conditions. Therefore, effective precipitation must play an important role in the development of raised bogs, as they are independent from the regional aquifer. Conversely, nonraised peatland development across the high-latitude regions is probably more closely linked to the initial mineral basin topography and slope than to climatic conditions, as the surrounding catchment areas may mediate the amount of water run-on to peatlands (Figure 1).
 Here we combine geophysical (ground penetrating radar; GPR) and paleoecological approaches to study the effect of slope and topography on peatland development at a site in south-central Alaska. We argue that GPR provides high-density spatial data that are essential for these analyses because it allows for the calculation of stratigraphic slopes in the immediate vicinity of each peat core. Relying on slopes calculated from solely interpolating depth differences between cores would introduce an unacceptable amount of uncertainty, given the relatively large spacing between bore holes and the relatively low slope. In addition, it was suggested that GPR produces accurate estimates of peat thickness, typically with much less than 10% discrepancy from core data [Rosa et al., 2009]. Another study has similarly found that GPR provides a more accurate measure of peat thickness than manual probing when the peat-to-mineral interface consists of lake sediments or clay [Jol and Smith, 1995]. Overall, our study demonstrates that slope gradient and basin topography exert deterministic controls on peatland lateral expansion.
2 Materials and Methods
2.1 Study Site
 Petersville peatland (62°25′N, 150°41′W, 450 m above mean sea level) is located in the Susitna River basin, in the Cook Inlet region of south-central Alaska (Figure 2a). The regional climate is cool continental, with 30-year (1971–2000) monthly mean temperatures of -11.7°C in January and 14.9°C in July (as recorded in Talkeetna, 40 km to the south-east of Petersville site). Mean annual temperature is 1.0°C, and mean annual precipitation is 715 mm, of which 352 mm falls as snow [Alaska Climate Research Center, 2009].
 Petersville site is a sloping patterned peatland (~1 km2) that has developed over glacial clay and has a general northeast-southwest slope, with an elevation difference of about 10 m between the highest (NE) and lowest (SW) portions. This peatland represents a mosaic of minerotrophic and oligotrophic peatland types, with pH values ranging from 3.9 to 4.5. The minerotrophic assemblages are found in the wetter center of the basin, while the ombrotrophic communities are located toward the drier peatland margins. The ground layer is dominated by Sphagnum (peat moss), although several Amblystegiaceae (brown mosses) including Drepanocladus spp. inhabit wet depressions, and sparse Pleurozium schreberi (feather moss) colonize the drier peatland margins. The vascular plant assemblage is dominated by ericaceous shrubs and by herbaceous species including Scheuchzeria palustris and Carex pauciflora. Surrounding upland vegetation is dominated by Alnus spp. and Picea glauca (white spruce). Peat inception occurred at 14 ka (1 ka = 1000 calibrated years before present).
 A 15- to 25-cm-thick tephra layer was identified along the peat cores and corresponds to the mid-Holocene Mount Hayes eruptions [3490-4330 cal. BP; de Fontaine et al., 2007]. Mount Hayes is located about 100 km to the south-west of the study site (Figure 2a). The ash layer provenance within our peat samples was confirmed on the basis of glass shard mineralogy (K. Wallace, pers. comm., 2008). The absence of plant remains and the low organic matter content (<25%) of the tephra layer suggest that most of the peatland plants were buried and killed by this catastrophic perturbation [Kent et al., 2001; Hotes et al., 2004; 2006; Gómez-Romero et al., 2006].
2.2 General Approach and Study Design
 To determine the effect of topography and slope on peatland development, we reconstructed peatland lateral expansion rates along a 500-m-long transect by combining peat-core analysis with GPR and total station surveys (Figure 2b). The transect runs across two different subsurface slope settings (shallow vs. steep). In addition, the thick ash layer, visible in the GPR data due to its very low water content [Figure 3; Topp et al., 1980; Huisman et al., 2003], was used as a stratigraphic marker to compare the initial lateral expansion rate over the mineral basin (14 ka and onward) to the post-tephra (3.4 ka and onward) expansion rate across the transect. This combined approach allows us to survey a large area of the peatland using GPR and to obtain detailed stratigraphic information using peat core analysis.
2.3 Field Survey and Sampling
 The mineral basin topography and the relative position of the tephra layer within the peat matrix were determined using GPR in March 2010 along a 500-m-long transect established across the deepest portion of the basin as well as two upland edges (Figure 2b). The survey was performed along the transect using a Malå RAMAC/GPR CUII system (Malå, Sweden) equipped with 200 MHz antennas. The antenna separation was 60 cm, and step size was 10 cm. This frequency provided a high vertical measurement resolution while maintaining adequate penetration depth along the profile [Kettridge et al., 2008]. GPR data were processed using the MATGPR [Tzanis, 2006] and ReflexW [Sandmeier, 2008] software. Processing steps include correction of time zero, dewow (low frequency noise reduction), and a linear/exponential gain function to compensate for attenuation and signal spreading. Depth conversion was done by calibrating the GPR data to the known depth to the tephra and mineral basin reflector based on measurements from the peat cores (calculated velocity = 0.0367 ± 0.0016 m ns-1). Migration was performed on the transect using the calculated velocity; however due to the shallow slopes observed throughout the peatland, no variation was observed between the nonmigrated profile outside the uncertainty range. Unmigrated GPR data are presented to retain clarity. Reflection events associated with the tephra and basin outline were digitized from the radargram and output for slope analysis. Variable surface topography was accounted for after depth data were extracted from the radargrams.
 In the summer of 2010, peatland surface elevation along the transect was obtained using a total station (DeWalt automatic level, Baltimore, USA). The step size was 100 cm, and the vertical accuracy was 0.32 cm. Nine peat cores were also collected along the transect in summers of 2009 and 2010 using a Russian-type peat corer (Figure 2b).
2.4 Peat Core Analysis
 Plant macrofossils were identified within the basal peat samples as well as above the Hayes tephra layer to determine the type of peatland formation processes (terrestrialization vs. paludification). Peat subsamples (2 cm3) were gently boiled in a 5% KOH solution and rinsed with distilled water through a 150-µm sieve [Mauquoy et al., 2010]. For each sample, Sphagnaceae (peat mosses), Amblystegiaceae (brown mosses), herbaceous, ligneous and unidentifiable organic matter (UOM) material were quantified as a percentage of the total sample by volume. To determine water content, bulk density, and organic matter content, peat subsamples (1 cm3) were dried overnight at 105 °C, weighed, and burned at 550 °C for 2 hours [Dean, 1974].
 Peat inception age along the transect was established using AMS radiocarbon (14C) dating. For each core, the basal peat sample was identified as the deepest layer with a minimum organic matter content of 50% based on loss-on-ignition at 550°C. Dating material was composed of nonaquatic plant taxa (e.g., Scorpidium stems and leaves), which were handpicked and cleaned with distilled water. In horizons that lacked good dating material, root-free bulk peat samples (size fraction: 63–125 µm) were analyzed (Table 1). The 14C samples were submitted to Keck AMS Carbon Cycle Lab at University of California, Irvine, and results were calibrated using the program CALIB 6.0 based on the INTCAL09 calibration data set [Reimer et al., 2009; Stuiver and Reimer, 2010].
Table 1. AMS Radiocarbon (14C) Dating Results From Peat Cores at Petersville Peatland, South-Central Alaska
* Keck AMS Carbon Cycle Lab at University of California, Irvine
root-free bulk peat
2855 ± 30
2970 ± 100
root-free bulk peat
3020 ± 15
3240 ± 80
root-free bulk peat
3685 ± 20
4010 ± 80
root-free bulk peat
3405 ± 35
3690 ± 130
root-free bulk peat
6370 ± 200
7200 ± 410
root-free bulk peat
5910 ± 60
6730 ± 160
root-free bulk peat
7830 ± 30
8620 ± 80
11,360 ± 50
13,230 ± 110
root-free bulk peat
10,200 ± 150
11,860 ± 550
2.5 Tephra Analysis
 A 10-cm-long tephra sample from the mid-Holocene Hayes ash layer was analyzed for particle texture. The analysis of these tephra samples was completed using a LS 13 320 laser diffraction particle size analyzer [Zobeck, 2004]. A subsample from each 2 cm interval of the tephra was taken, air-dried and passed through a 0.2 cm sieve. Samples were homogenized, and an average sample weight of about 0.3 g was used for analysis. Two subsamples were run for each interval (Table 2).
Table 2. Textural Fractions of the Mid-Holocene Hayes Tephra Samples at Petersville Peatland (core PE08-A35)
Sample Depth (cm)
2.6 Water Table Depth Monitoring
 Three water level probes (Odyssey Dataflow loggers, Christchurch, New Zealand) were installed in 1 m-long PVC monitoring wells in August 2009. While one of the wells was set up at the peatland-upland interface, the other two were installed at 40 and 90 m toward the peatland center, along the transect (Figure 2b). Water table depth variability between and within each of these sites was recorded every 60 minutes from 15 August 2009 to 31 August 2011. The water level data for each well was bootstrapped, and a 84% confidence interval was used to compare all three datasets [e.g., Payton et al., 2003].
3.1 Identifying the Tephra Layer Using Ground Penetrating Radar
 The mid-Holocene tephra layer was clearly visible along the entire length of the GPR survey and represented by a clear reflection (Figures 3 and 4a). The relative thinness of the tephra layer combined with its low clay content (Table 2) probably explains the good signal penetration below this layer. The identification of this “tephra reflection” was confirmed through measurements of low water and organic matter content along peat profiles (Figure 3).
3.2 Changes in Topography, Slope, and Lateral Expansion Rates
 The mineral-to-peat interface was sharp and easily identifiable along the GPR profile, enabling accurate determination of the peatland basin morphology along the transect (Figure 4a). Peat thickness was highly variable, from 3.29 ± 0.25 m in the center of the peatland to 0.30 ± 0.04 m along the peatland margins. In addition to the mineral basin and tephra layers, other reflections were recorded along the profile, likely corresponding to changes in peat stratigraphy and moisture content within the peat [Slater and Reeve, 2002; Comas et al., 2005; Figure 3; 4a].
 Slope steepness of the mineral basin (mineral-to-peat interface), the post-tephra (tephra-to-peat interface), and the modern surfaces were calculated using peat thickness values (GPR data) combined with peatland surface elevation (data from total station). Slope values ranged between 0 and 4.9 ± 0.11° (Figure 4c). Uncertainties for the slope of the tephra (±0.09°) and for the mineral basin (±0.11°) were determined using the velocity range (0.034–0.039 m ns−1) that was calculated for the study site. The initial mineral basin topography was characterized by a moderate gradient (mean slope = 2°) along the first portion of the transect (0–150 m), followed by a flat (mean slope < 0.4°) central portion (150–290 m), and finally by a shallow gradient (mean slope = 0.9°) along the third part of the transect (290–500 m; Figure 4c). Post-tephra topography had a similar pattern but was characterized by more gentle slope gradients, with mean values of 1.5° and 0.5° for the first and third portions of the transect, respectively (Figure 4e). Likewise, the modern surface topography was shallower than the post-tephra surface, with mean slope values of 0.9° and 0.1° for the first and third portions of the transect, respectively (Figure 4e).
 Initial mineral basin and post-tephra lateral expansion rates were calculated on the basis of peat sample ages (Table 1) and distance from the center. Expansion rates varied from 0.01 m yr−1 for the steepest slope (2°) to 0.47 m yr−1 for the shallowest slope (0.5°). Intermediate rates (0.06 and 0.08 m yr−1) were found for intermediate slope gradients (1.5° and 0.9°, respectively). Overall, faster rates were associated with shallower slopes (Figure 4d).
3.3 Changes in Peat Stratigraphy, Thickness, and Bulk Density
 Basal peat deposits accumulated on glacial clay and were composed of herbaceous peat (Cyperaceae (sedge) fragments) with large fractions of unidentifiable organic matter (UOM; Figure 5c). Post-tephra peat deposits were similarly composed of Cyperaceae fragments, herbaceous rootlets, and high proportions of unidentifiable organic matter.
 Both initial and post-tephra peat deposits were dense at the peatland margins and becoming less dense toward the central portion of the transect (Figures 5a and 5b). Similarly, peat thickness and distance from the central portion of the transect were strongly correlated (minimum R2 = 0.92, p = 0.003) under both initial and post-tephra geomorphic conditions, with the thickest peat deposits found within the central portion of the transect (Figure 5d). These post-tephra results emphasize that age alone does not explain peat thickness and bulk density differences between the central vs. marginal portions of the peat basin so that the oldest deposits are not necessarily the deepest ones.
3.4 Water Table Depth and Variability Along the Transect
 Continuous water table depth fluctuations are presented in Figure 6. Throughout the nonfrozen periods, the well closest to the peatland margin has experienced the driest and most variable conditions (mean = 17.8 cm below the land surface, 1 standard deviation (σ) = 14.6 cm), as well as the driest recorded value (34.3 cm). Conversely, the well closest to the peatland center (at 90 m) was characterized by the wettest and least variable mean conditions (mean = 11.5 cm, 1 σ = 3.6 cm). Water table depth values for the well at 40 m along the transect were wetter and less variable than at the peatland margin but also drier and slightly more variable than at the center (mean = 15.9 cm, 1 σ = 3.9 cm). Statistically significant differences between these observations was confirmed on the basis of a bootstrapping analysis (84% confidence interval), which indicated statistical differences between the 40 m (15.5–16.4 cm) and 90 m (11.1–11.8 cm) times series, as well as between the upland (13.2–16.2 cm) and 90 m data sets. The upland and 40 m time series were not statistically different.
4.1 Peatland Basin Development and Lateral Expansion Process
 Cross-sectional views of the transect at Petersville confirm a simple concave basin structure with the greatest peat thickness in the central portion of the basin and becoming shallower toward the margins (Figures 4b and 5d). We propose that slope and topography have exerted fundamental controls on the peatland development and associated lateral expansion rate through the following direct and indirect mechanisms.
 (1) Prior to peat inception, the mineral basin across the central (and concave) portion of the transect was characterized by a flat surface (slope < 0.5°) that was surrounded by higher ground. Water flowed toward the center of the basin following gravity, which resulted in wet conditions or even water ponding [Ireland and Booth, 2010; Figure 1]. Under these wet and resultant anoxic conditions, peat started accumulating throughout the flat portion of the concave basin, presumably at a low rate [Belyea and Clymo, 2001], around 13,000 years ago due to limited plant and peat decomposition, further increasing water retention locally through a first positive feedback mechanism: vertical peat accumulation → reduced hydraulic conductivity → increased water storage and stability → vertical peat accumulation [see Ingram, 1982; Anderson et al., 2003; Figure 1].
 (2) Over time, vertical peat accumulation in the center of the basin raised the water table locally, which increased the hydraulic head gradient between the peatland center and the margins [Morris et al., 2011]. Subsurface water flowed toward the margins, allowing peat to spread laterally through “swamping” of adjacent mineral soils. The resulting effect was an increase in the total peatland area, which further decreased water table depth variability at the peatland center through a second positive feedback mechanism: lateral expansion → increased peatland area → peatland center is farther away from the margins → reduced water level variability and increased water storage at the center → peat buildup at the center → lateral expansion [Morris et al., 2011; Figure 1].
 (3) At any point during peatland development, peatland margins probably experienced larger water table fluctuations than the peatland center [Hendon et al., 2001; Loisel and Garneau, 2010]. Our observations from monitoring wells along the transect at Petersville provide support to this hypothesis, as we have recorded drier and more variable water table depths at the peatland margin vs. wetter and less variable values toward the peatland center (Figure 6). Similarly, lithological data showed that peat density increased as peat thickness decreased, such that peat deposits became thinner and denser toward the peatland margins (Figure 5a). Bauer et al.  have also reported high bulk density values for peat samples taken at the peatland-upland interface at sites in northern Canada. Similarly, Lapen et al. , Baird et al. , and Lewis et al.  found that peat hydraulic conductivity at the margins of their study peat bogs was generally lower than that in central areas. Altogether, these results point toward the possibility that dense peat at the margins might be important in maintaining wet conditions in other parts of the peatland by limiting subsurface water seepage. Therefore, we propose that these highly decomposed, thin and dense peat deposits at the peatland margins further impeded water flow through a third positive feedback mechanism: peat decay at the margins → increased bulk density at the margins → reduced lateral subsurface water losses → reduced water level variability at the peatland center → peat buildup at the center → lateral expansion → peat decay at the “new” margins (Figure 1).
4.2 Surface Slope Shallowing and Slope Threshold for Lateral Expansion
 By comparing the mineral basin, post-tephra, and modern surface slope steepness across the three portions of the transect, we observed a progressive “slope shallowing” over time (Figures 4b and 5d). Indeed, the calculated mineral basin slopes were steeper than the corresponding post-tephra slopes, which were steeper than the modern surface values (Figures 4c and 4d). We speculate that slope shallowing has occurred as a direct consequence of peat “basin infilling,” where the formation and accumulation of thick deposits in the central portion of the peatland vs. thin and dense deposits toward the margins has progressively been leveling out the peatland surface (positive feedback loop 4 in Figure 1). From an ecosystem dynamics standpoint, slope shallowing can thus be viewed as a positive feedback that reduces water flow and increases water storage over a large area, further promoting peat formation [Foster et al., 1983; Figure 1]. In other words, by smoothing out basin irregularities and generating a gentler slope for itself, the net effect is a more stable water table level, which should limit peat decay and facilitate peat accumulation [Foster et al., 1983]. Our results on lateral expansion lend support to this idea (Figure 4d), as shallow slopes were associated with rapid expansion.
 It is important to mention that it is assumed in our analysis that all three studied surfaces (basin, tephra layer, and modern surface) have not changed since their formation. However, we recognize that post-tephra slope values might have progressively steepened over the past 4000 years due to difference in peat formation rates above and below the ash layer along the transect (likely more compaction has occurred in the center than at the margins). As a result, the post-tephra slopes calculated for this study represent maximum and thus conservative, values. Indeed, assuming a peat compressibility of 26% [Price et al., 2005], the initial tephra slope might have been, on average, 1.5 times shallower than the results presented here. These “corrected” results provide a strong support to the “slope shallowing” hypothesis because they indicate a stronger shallowing than our initial measurements. However, as peat compressibility is difficult to assess [Price et al., 2005], the maximum slope values that were directly calculated along the transect were preferred.
 In terms of expansion rate, our analysis does not take into consideration the fact that the original clay basin and the tephra layer might have created different conditions for peatland development. This assumption was necessary to study the effect of slope on lateral expansion rate. Given that our transect was divided into three sections with three distinct slopes (i.e., three case studies), we argue that this assumption is reasonable. To further quantify the relationship between slope and lateral expansion, we also combined our datasets with a data synthesis from published studies [Figure 7; Foster and King, 1984; Korhola, 1994; Mäkilä, 1997; Asselin and Payette, 2006; Tipping, 2008; Peregon et al., 2009]. For the data synthesis, slope was directly obtained from the published figures (peatland cross-sectional views where elevation and distance along a transect are available) using Data Thief III [Tummers, 2006]. Lateral expansion rates were calculated by dividing the horizontal distance between two peat cores of known ages (14C-dated basal peat). If not already calibrated, the published 14C age estimates were calibrated using the program CALIB 6.0 based on the INTCAL09 calibration data set [Reimer et al., 2009; Stuiver and Reimer, 2010]. Age uncertainties associated with 14C dating were included in our lateral expansion rate calculations (error bars in Figure 7). However, we were unable to estimate topographic uncertainties. A summary of peatland site information is presented in Table 3. Lateral expansion rates were negatively correlated with slope and followed a power-law relationship (R2 = 0.59, p < 0.0001; Figure 7b). The existence of a “slope threshold” (approximate 0.5°) below which peat can rapidly spread laterally was also found (Figure 7a). We speculate that basins with slopes greater than ~ 0.5° fall into the “slope-limited regime” where the expansion is controlled by the slope, whereas basins having slopes less than ~ 0.5° fall into the “growth-limited regime” where expansion is limited by factors determining how fast bryophytes can colonize, survive, and grow (i.e., substratum, species and climate dependent). The widespread of lateral expansion rates that characterize the growth-limited regime peatland domain (Figure 7a) lends support to our hypothesis. This finding implies that vast and flat peatland-rich areas such as the Hudson Bay Lowlands in northern Canada, which have an averaged regional slope of 0.5–0.7 m km−1 (0.03–0.04°), probably experienced very rapid expansion following deglaciation and peat inception due to their shallow slope but also a favorable climate [Glaser et al., 2004; Gorham et al., 2007; Yu et al., 2009; Jones and Yu, 2010]. Therefore, current estimates of peatland CO2 sequestration and CH4 emission for the early Holocene, which are based on the implicit or explicit assumption that individual peatlands expanded linearly in their area since inception [MacDonald et al., 2006; Yu et al., 2010; 2011; Yu, 2011] might be minimum values as they probably underestimate rates of lateral expansion in flat, peatland-rich regions including the Yukon Flats (Canada and Alaska), the Hudson Bay Lowlands, and West Siberia. By extension, peat-C fluxes in the mid- and late-Holocene might currently be overestimated.
Table 3. Summary of Peatland Sites Used in the Data Synthesis (See Figure 7)
Expansion rate (m yr-1)
0.03 ± 0.0046
Foster and King, 1984
0.01 ± 0.0010
0.91 ± 0.4482
0.15 ± 0.0294
0.11 ± 0.0056
0.15 ± 0.0120
0.44 ± 0.0741
2.05 ± 0.7399
0.01 ± 0.0001
Asselin and Payette, 2006
0.02 ± 0.0228
0.02 ± 0.0006
0.03 ± 0.0013
2.36 ± 0.5240
Peregon et al., 2009
0.11 ± 0.0052
Great Vasyugan Mire
0.11 ± 0.0055
0.12 ± 0.0127
1.67 ± 0.2500
0.01 ± 0.0030
0.06 ± 0.0050
0.47 ± 0.0250
0.08 ± 0.0500
 Our proposed conceptual model can be used to develop simple process-based models to simulate peatland lateral expansion and predict future peat growth potential. GPR and stratigraphic studies could be used to further explore the subsurface slopes of peat-filled basins and test these models. Digital elevation models (DEMs) and light detection and ranging (LiDAR) could be used to estimate peatland basin shape and predict future rates [see the study by Buffam et al.  for an example], assuming that basin edge slope (at the peatland/upland interface) is representative of the peatland basin shape. However, as seen at Petersville site, the margins were steeper than the central portion of the peatland, limiting the use of DEMs or LiDAR to estimate slope. More conventional methods such as interpolating peat depth using peat cores can also provide adequate results, though GPR is a more efficient technique for providing accurate, high-resolution data.
 At Petersville site, early peatland development was characterized by high lateral expansion rates as peat was rapidly spreading across the central and flat portion of the transect and presumably the basin. By 8000 cal. BP, 86% of the transect was colonized by peat. Following this early stage, rates of lateral expansion slowed down as basin steepness increased toward the modern margins. Early rapid development patterns were similarly found by Mäkilä  and Mäkilä and Moisanen  in Finnish mires, as well as by van Bellen et al.  in northern Québec. On the other hand, on the basis of a large dataset (n = 954) of multiple basal peat ages from individual peatlands that presumably accounts for horizontal growth of northern peatlands, Korhola et al.  proposed that extensive lateral expansion of high-latitude peatlands occurred between 5000 and 3000 cal. BP (i.e., many thousands of years after peat inception) due to the Neoglacial climate cooling and wet conditions [Korhola et al., 2010]. Though climatic conditions might play a role in peat lateral expansion by modifying moisture inputs to peat basins and affecting net peat accumulation (Figure 1), we argue that landscape morphology provides fundamental constraints on lateral expansion rates that can be aided or hindered by climatic conditions, especially under the “growth-limited” regime (slope less than 0.5°).
 The importance of mineral basin slope and water flow in controlling lateral expansion processes has important implications for the interaction between vertical accumulation and lateral expansion. Based on the premise that peat growth occurs under more variable conditions at the margins than at the peatland center, long-term rates of vertical peat accumulation are expected to be higher toward the peatland center than at its margins. In other words, peat accumulation rates as reconstructed from peat cores are probably sensitive to coring location. For example, if early-stage peat accumulation occurred close to the “paleo” margin but that the peatland kept spreading laterally over time, increasing vertical peat accumulation rates should be expected for that particular coring site simply because of changing distance from the expanding peatland margin.
5 Conclusions and Implication
 Peatland lateral extent is a key boundary condition constraining the carbon dynamics of peatland systems. By combining peat-core analysis with surface and subsurface landscape morphological surveys along a 500-m-long transect at Petersville peatland, we have demonstrated that slope gradient and basin topography exert deterministic controls on peatland development (Figure 1). We have found that, over their developmental history, peatlands have the tendency and ability to smooth out basin irregularities and generate a gentler slope for themselves. This slope shallowing and stabilizing mechanism reduces water flow and increases water storage, further promoting peat formation through a positive feedback loop [Foster et al., 1983]. On the basis of our new data and data synthesis, we also demonstrated that (i) shallow slopes are associated with rapid expansion, (ii) lateral expansion rate and slope follow a power-law relationship, and (iii) there exists a slope threshold (approximate 0.5°). Overall, the power-law distribution allows for prediction of lateral expansion rates over a wide range of scales, and the slope threshold implies that lateral expansion in basins with slopes greater than ~ 0.5° is slope limited, whereas lateral expansion in basins with less than ~ 0.5° are peat growth limited. Therefore, flat peatland-rich areas probably experienced rapid expansion rates following deglaciation and peat inception, and current estimates of peatlands carbon sequestration and methane emissions for the early Holocene are probably erroneous, as they have probably underestimated the rate of lateral expansion across these regions.
 We thank Eric Klein, Robert Booth, Miriam Jones, Chris Bochicchio, Nathan Stansell, Bryan Mark, and Kristi Wallace for field and laboratory assistance; Alex Ireland and Frank Pazzaglia for discussions; Lisa Belyea, Nigel Roulet, Robert Booth, and an anonymous reviewer for providing comments on an earlier version of the manuscript; and Craig Seibert from Gate Creek Cabins in trapper Creek, Alaska, for hospitality and field assistance. The research was funded by US NSF grants (ATM no. 0628455 and EAR no. 0819717) and an NSERC Canada Postgraduate Scholarship (BESC-D3-362645-2008).