Transport of Oxygen in Soil Pore-Water Systems: Implications for Modeling Emissions of Carbon Dioxide and Methane from Peatlands

Biogeochemistry DOI 10.1007/s10533-014-0012-0

Transport of oxygen in soil pore-water systems: implications for modeling emissions of carbon dioxide and methane from peatlands

Zhaosheng Fan • Jason C. Neff • Mark P. Waldrop • Ashley P. Ballantyne • Merritt R. Turetsky

Received: 4 February 2014 / Accepted: 8 July 2014 Ó US Government 2014

Abstract Peatlands store vast amounts of soil carbon rather than water content directly. Variations in O2 and are significant sources of greenhouse gases, including content above and below the WT can be large and thus carbon dioxide (CO2)andmethane(CH4) emissions. The may play an important role in partitioning of carbon traditional approach in biogeochemical model simula- fluxes between CO2 and CH4. In this paper, we propose tions of peatland emissions is to simply divide the soil an oxygen-based approach, which simulates the vertical domain into an aerobic zone above and an anaerobic zone and radial components of O2 movement and consumption below the water table (WT) and then calculate CO2 and through the soil aerobic and anaerobic environments. We CH4 emissions based on the assumed properties of these then use both our oxygen-based and the traditional WT- two discrete zones. However, there are major potential based approaches to simulate CO2 and CH4 emissions drawbacks associated with the traditional WT-based from an Alaskan fen peatland. The results of model approach, because aerobic or anaerobic environments are calibration and validation suggest that our physically ultimately determined by oxygen (O2) concentration realistic approach (i.e., oxygen-based approach) cause less biases on the simulated flux of CO2 and CH4.The results of model simulations also suggest that the Responsible Editor: Jack Brookshire traditional WT-based approach might substantially under-estimate CH emissions and over-estimate CO & 4 2 Z. Fan ( ) emissions from the fen due to the presence of anaerobic Biosciences Division, Argonne National Laboratory, Argonne, IL 60439, USA zones in unsaturated soil. Our oxygen-based approach e-mail: [email protected] can be easily incorporated into existing ecosystem or earth system models but will require additional validation J. C. Neff with more extensive field observations to be imple- Department of Geological Sciences, University of Colorado, Boulder, CO 80309, USA mented within biogeochemical models to improve simulations of soil C fluxes at regional or global scale. M. P. Waldrop USGS, Menlo Park, CA 94025, USA Keywords Water table Model Oxygen A. P. Ballantyne Microbial Habitat Warming Aerobic Anaerobic Department of Ecosystem and Conservation Sciences, University of Montana, Missoula, MT 59812, USA Introduction

M. R. Turetsky Department of Integrative Biology, University of Guelph, Peatlands cover approximately 4 % of world’s terres- Guelph, ON N1G 1G2, Canada trial surface area (Matthews and Fung 1987), but store 123 Biogeochemistry approximately 20 % of the world’s terrestrial carbon soil C undergoes aerobic or anaerobic decomposition (C) stocks (Batjes 1996; Tarnocai et al. 2009). (Boggie 1977; Estop-Aragones et al. 2012). For Peatlands are also more prevalent in high latitudes of example if a peatland has a deep WT and the surface the Northern Hemisphere where surface warming has of the peatland is not favorable to O2 movement (e.g., accelerated over the last 50 years (IPCC 2013). high bulk density, high tortuosity, or low pore Peatlands play a signiﬁcant role in regulating global connectivity), a signiﬁcant proportion of the soil C climate because they are important sources of methane located above the WT (e.g., deep soil C) might

(CH4) to the atmosphere, contributing approximately undergo anaerobic decomposition even though soil 15–20 % of world’s CH4 emission (Aselman and moisture conditions are unsaturated. In this case, the Crutzen 1989; Matthews and Fung 1987). Because the traditional WT-based approach would notably under- warming potential of CH4 is 24 times greater than that estimate the soil anaerobic fraction and thus over- of carbon dioxide (CO2) over a 100-year time scale predict CO2 emissions and under-predict CH4 emis- (Ramaswamy et al. 2001), evaluating the fraction of C sions (Bohn and Lettenmaier 2010). emitted as CO2 and CH4 from peatlands and the There are multiple examples of low O2 availability sensitivity of these emissions to climate change is in the zone above the WT from ﬁeld studies. For critical for understanding and predicting the northern example, work by Estop-Aragones et al. (2012, 2013) high latitude C balance (Bridgham et al. 2008; Nisbet illustrated that the concentration of dissolved O2 et al. 2014). within 20 cm of peat above the WT in a temperate fen Most existing ecosystem or earth system models frequently remained low (0–50 lmol L-1). From this have the capability of simulating CO2 production result, they concluded that WT was a weak predictor under aerobic and anaerobic conditions, CH4 produc- of aerobic and anaerobic zones, given that a signiﬁcant tion under anaerobic conditions, CH4 transport (e.g., fraction of soil above the WT was likely subject to ebullition and diffusion transport), and microbial anaerobic conditions. In Canadian peatlands, Silins oxidation of CH4 under aerobic conditions (e.g., and Rothwell (1999) showed that the anaerobic zones Frolking et al. 2002, 2010; Walter and Heimann above the WT were as thick as 40 cm (e.g., WT depth 2000; Wania et al. 2010; Zhuang et al. 2004). of * 80 cm and aerobic limit depth of * 40 cm) due

Generally, most representations of peatland structure to slow O2 diffusion. These patterns of O2 availability use a one-dimensional framework with two layers, undoubtedly are important for C emissions. For including an upper, variably saturated ‘acrotelm’ and a example, the highest CH4 concentrations were com- permanently saturated lower layer, the ‘catotelm’, monly observed above the WT (instead of below WT) which is commonly several meters thick (Ingram (e.g., Deppe et al. 2010; Knorr et al. 2008), suggesting

1978; Morris and Waddington 2011).This diplotelmic that significant CH4 might be produced in the unsat- model for simulating peatland C cycling processes is a urated soils above the water table. Moreover, many very common component of existing ecosystem or researchers(e.g., Sexstone et al. 1984; Tiedje et al. earth system models. 1984) have shown significant rates of denitrification in While the original diplotelmic model assumed that unsaturated soil (even in well-drained soil settings) many ecological and biogeochemical processes could due to both slow O2 diffusion to the center of water- be explained by a single discrete boundary (depth in filled pores and fast O2 consumption by microbes. relation to a drought water table), a common approach Together, there is strong evidence that the fraction of employed by many ecosystem models is to use current anaerobic zones in unsaturated soils might be fluctuations in depth of water table (WT) as a proxy of substantial. aerobic and anaerobic soil zones. While WT depth Soils are a porous media, where the arrangements certainly is a strong predictor of many variables of various soil particles create complex pore charac- including rates of decomposition, reliance on a simple teristics (e.g., pore connectivity and tortuosity), which threshold hinders the representation of both vertical results in heterogeneous distributions of water and air, and horizontal spatial heterogeneity in peatlands. In the two most important determinants of microbial terms of simulating CO2 and CH4 production and activities within the soil. These important soil char- transport in peatlands, oxygen (O2) availability is a acteristics are amenable to process based modeling more direct control on whether a certain proportion of and are also considered in this study. The goal of this 123 Biogeochemistry

Fig. 1 Model schematic that was used to simulate the vertical (Panel a) and radial movement (Panel b) of oxygen in the soil–water systems study was to develop a more physically realistic approach to separate peat soils into aerobic and anaerobic zones than the WT-based approach in order to more accurately simulate the emissions of greenhouse gases from peatlands. To reach this goal, we developed a simulation model based on soil pore characteristics to estimate the vertical and horizontal

(radial) transport of O2 in the unsaturated soil of peatlands. We then used the model to examine the importance of anaerobic zones in unsaturated peatland soils. There are limited field data available at present that can be used to test these physical representations Fig. 2 The observed profile of carbon bulk density in the of soil processes (e.g., O consumption and spatial Alaskan rich fen. The model denotes the equation that we used 2 to calculate the carbon bulk density at different soil depth distribution of O2 concentrations).Instead, we used a mechanistic model based on physical principles to examine the sensitivity of CO2 and CH4 fluxes in an toward WT; Fig. 1a) and 2 radial or horizontal Alaskan fen to the representation of aerobic and movement in soil pore water due to the O2 concen- anaerobic zones in the soil. tration gradient within a given air-filled pore (i.e., movement of dissolved O2 in the horizontal direction from the center of the pore toward soil particles; Model development Fig. 1b). Below are mathematical constructs describ- ing processes that affect the coupled O2 movement and The O2 concentration in soil is controlled by both O2 consumption in the soil pore-water system. consumption (a sink) due to microbial activities and

O2 movement (a sink or source) due to O2 concentra- Vertical transport of oxygen tion gradients. Oxygen movement is divided into 1) vertical movement in the gaseous phase due to the O2 The vertical transport of O2 due to a concentration concentration gradient within a given soil proﬁle (i.e., gradient in the unsaturated soil (Fig. 1a) can be

O2 movement in the vertical direction from surface simulated using Fick’s law:

123 Biogeochemistry oC o2C the Moldrup et al. (1997) model was the most robust a ¼ D a S ð1Þ ot a ox2 model to calculate sa with high moisture content and defined as: where Ca is the concentration of O2 in the gaseous -3 12b phase (mol m ), t is the time (s), D is the diffusion 3 a ha 2 -1 s ¼ 0:66h ð5Þ coefficient of O2 in the gaseous phase (m s ), x is the a a r soil depth (m), and S is the O2 consumption rate -3 -1 3 -3 (mol m s ) that is calculated as: where ha is the volumetric air content (cm cm ) and 8 b is an empirical parameter (unitless) that was set to > S ¼ Sref FmFT 3.0 following Pingintha et al. (2010). < hi 2 The upper boundary condition for Eq. (1) was F 2:43 h2 h h 2 > M ¼ o;sa sa o;sa ð Þ determined based on the field observed O concentra- :> 2 bTc FT ¼ ae tion at the soil surface (Elberling et al. 2011) and given as: where Sref is the reference consumption rate of O2 (at optimal saturation and 10 °C) and set to 3.0 9 10-5 CaðÞ¼x ¼ 0; t 300 lM ð6Þ mol m-3 s-1 based on the range reported for rooted A variable O2 flux condition was assumed to be the soils (oxygen consumed by both roots and microor- lower boundary condition and calculated based on the ganisms; Langeveld and Leffelaar 2002; Leffelaar following equation: 1979); FM and FT are the soil moisture and temper- o ature functions regulating the oxygen consumption Ca J ¼Da o ð7Þ rate, respectively; ho,sa is the optimal effective soil x saturation and set to 0.642 cm3 cm-3; h and T are -2 -1 sa c where J is the O2 flux density (mol m s ). the observed effective soil saturation (cm3 cm-3) and temperature (°C), respectively; a and b are empirical Radial transport of oxygen parameters set to 0.623 and 0.048 (Fan et al. 2008), respectively. The effective soil saturation (i.e., hsa)is The radial transport of dissolved O2 within soil pore defined as: water in the horizontal direction (Fig. 1b) can be mathematically described with the following equation hw hr hsa ¼ ð3Þ (Arah and Vinten 1995) r hr o2 o 3 -3 Cw 1 Cw where hw is volumetric moisture content (cm cm ), S ¼ Dw 2 þ ð8Þ 3 -3 or r or hr is the residual moisture content (cm cm ) that is water (such as thin water film surrounding soil where Dw is the diffusion coefficient of O2 in the liquid 2 -1 particles) held in a soil at high tension (e.g., phase (m s ), Cw is the concentration of O2 in the -10 kPa) (Caron and Nkongolo 2003), and r is liquid phase (mol m-3), and r is the radius from the porosity (cm3 cm-3). center of air-filled pore (m).

The diffusion coefficient, Da, is defined as: The diffusion coefficient, Dw, is calculated using the Stokes–Einstein equation:

Da ¼ Da;0sa ð4Þ 0:5 8 TkðÞ/H2OMH2O 4 Dw ¼ 7:4 10 sw 10 where Da,0 is the diffusion coefﬁcient of O2 in the free 0:6 lVO2 air that is set to 2 9 10-5 m2 s-1(Hillel 1998) and s a ð9Þ is the tortuosity in the gaseous phase (unitless). At high moisture content, the traditional Penman (1940) where Tk is the absolute soil temperature (K), /H2O is approach is known to over-estimate tortuosity and an empirical parameter for water and set to 2.26 the Millington and Quirk (1961) approach is known to following Reid et al. (1977), MH2O is the molecular under-estimate tortuosity. Pingintha et al. (2010) weight of water (18 g mol-1), l is the viscosity of compared six tortuosity models and concluded that water (centipoises), VO2 is the molar volume of O2 at

123 Biogeochemistry

3 -1 its normal boiling point (25.6 cm mol ), sw is the 0.1 m. The soil matrix potential, x, at a given moisture tortuosity in the liquid phase (cm3 cm-3), and 10-4 is content, is calculated using the Mualem-van Genuch- the unit conversion factor. ten model (Mualem 1976; van Genuchten 1980): The viscosity of water, l, is a function of soil hs hr temperature and calculated using the empirical equa- hw ¼ hr þ ð14Þ n 1:01 tion derived based on the observed viscosity at ½1 þ jjax n different temperatures (Kestin et al. 1978): where hr and hs are the residual and saturated water contents (cm3 cm-3), respectively, a is an empirical l ¼ 1:02 107T4 1:924 105T3 þ 1:46 c c parameter related to the air-entry pressure (m-1), and 3T2 : 2T : 10 c 6 27 10 c þ 1 802 ð10Þ n is an empirical parameter related to the soil pore connectivity (unitless). Parameters a and n, together, where Tc is the soil temperature (°C). constrain the SWRC shape. The four parameters in Eq. The tortuosity in the liquid phase, sw, is similar to (14), a, n, h , and h , were set to 2.0, 1.7, 0.15, and 0.88 the calculation of tortuosity in the gaseous phase (sa) r s and defined as (Moldrup et al. 1997): for organic soil (Letts et al. 2000).By integrating Eq. (8) with the boundary conditions defined in Eq. (12), 12b the analytical solution of Eq. (8) is (Arah and Vinten hw 3 sw ¼ 0:66hw ð11Þ 1995): r S ÂÃ where all of the parameters have been defined earlier. C ¼ r2 r2 ln r2 þ r2 ln r2 1 for r \r\r w 4D b b b a b The inner and outer boundary conditions for Eq. (8) w are defined as (Arah and Vinten 1995): ð15Þ 8 r r > hw At the outer boundary ( = a), Eq. (15) can be < C ¼ C s ; for r ¼ r w a w 1 r a rewritten based on Eq. (12) as: > o ð12Þ : Cw h S ÂÃ Cw ¼ 0 and ¼ 0; for r ¼ rb w 2 2 2 2 2 o Casw ¼ r rb ln r þ rb ln rb 1 r 1 r 4Dw 3 -3 where sw is the solubility of O2 in soil–water (m m ) r ¼ ra relative to solubility in free air and set to 0.03 ð16Þ following Schurgers et al. (2006), ra is the radius of typical air-filled pore that is empty (with no water) at a The above equation can be numerically solved to obtain the value of rb, the radius of the aerobic zone given moisture content (m), and rb is the radius of aerobic zone surrounding the air-filled pore (m).The surrounding the air-filled pore. radius of typical air-filled pore is calculated based on Once the radius (rb) of the aerobic zone surrounding the soil water retention curve (SWRC; the relationship the typical air-filled pore (ra) is determined, the between water content and water potential): fraction of anaerobic zones in the unsaturated soil (fan) can be calculated as: 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > ra ¼ rminrmax > 2 n <> 2e fan ¼ 1 pr ð17Þ r ¼ b min qgjjx ð13Þ > where n is the number of air-filled pores (with radius of > 2e : r ¼ r ) per unit area and calculated as: max qg 0:1 a r n ¼ ð18Þ where rmin and rmax are the smallest and largest radii of pr2 air-filled pores that are empty at a given matrix a potential (x), respectively, e is the surface tension of It should be noted that Eq. (17) assumes that there are water (N m-1), q is the density of water (kg m-3), and no over-lapping soil pores, which might over-estimate g is the acceleration due to gravity (9.8 m s-2). the fraction of anaerobic zones in the unsaturated soil Equation 13 indicates that the largest radius of air- (Langeveld and Leffelaar 2002). Also, the soil pores filled pore corresponds to the soil matrix potential of are assumed to be cylindrical in our model simulation

123 Biogeochemistry for the sake of simplicity; however, it also should be using PP-systems infrared gas analyzers (see Chivers noted that different pore shapes (regular or irregular) et al. 2009). might affect the model simulations. Soil bulk density was measured by excavating a known volume of soil, carefully separating each soil Model application and evaluation horizon, and oven drying them at 65 °C, and quanti- fying mass per unit volume for each soil horizon Site description and data collection interval. Soil C concentration of each soil horizon was measured using a Carlo Erba NA1500 elemental We applied our oxygen diffusion model to simulate analyzer (Carlo Erba Instrumentaziones, Milan, Italy) the fraction of anaerobic zones in an Alaskan rich fen (Manies and Harden 2011). Soil C bulk density and to assess the importance of anaerobic decompo- required for model implementation was then calcu- sition in the unsaturated soil of the peatland. The rich lated by multiplying the measured C concentration by fen is part of the Alaska Peatland Experiment (APEX; soil bulk density for each depth (Fig. 2). 64.82 8N, 147.87 8W) located near the Bonanza Creek Experimental Forest outside of Fairbanks, Alaska. Description of carbon model The thickness of peat (or thickness of organic C horizon) above the mineral soil is approximately We used a simple one-pool C model coupled with either 90 cm. Hourly soil temperature and water table our oxygen-based or the traditional WT-based position have been measured since 2006. During the approaches to simulate the soil CH4 and heterotrophic growing season, CH4 emission was measured approx- CO2 respiration, and then we compared the simulation imately twice a month using static chambers placed on results to examine the performance of both approaches. top of metal flux collars installed permanently in the The oxygen-based or WT-based approach was first used peat. A minimum of four headspace samples were to identify the soil aerobic and anaerobic zones, and the collected over a 30–40 min period, and were analyzed one-pool C model was then used to calculate the CO2 using gas chromatography (see Turetsky et al. and/or CH4 production (and oxidation) from each of the 2008).In conjunction with the methane flux measure- aerobic and anaerobic zones as described below. ments, rates of ecosystem respiration were collected The flux of CO2 and CH4 for the oxygen-based using the same chambers that were shrouded to approach is calculated based on soil temperature, soil exclude light. Concentrations of CO2 inside each moisture content, and soil C content with the follow- chamber were measured over a several minute period ing equation (Fig. 3)

8 X ÂÃ X ÂÃX ÂÃ > > CO2 ¼ kc;1 OCi 1 fan;i FT;i FM;i þ kc;2 OCi fan;i FT;i þ kc;3 OCi FT;i > > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffli i fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}i > > above WT below WT > > þ CO > 2;0oxd 1 <> BX X C > B ÂÃÂÃC > CH B k OC f F k OC F C 1 f > 4 ¼ @ m;1 i an;i T;i þ m;2 i T;i A ðÞ oxd > i i > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} > > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}above WT below WT > > CH4 P :> CO2;oxd ¼ CH4 P foxd ð19Þ

123 Biogeochemistry

Fig. 3 Schematic diagram of how to simulate CO2 and CH4 ﬂuxes with oxygen- based and water table (WT) based approaches. The shapes of the fraction of anaerobic zone do not represent the actual simulations, and the sizes of box do not represent the actual simulations of each component of CO2 and CH4 ﬂuxes

-1 where kC,1,kC,2, and kC,3 are the rates (year )ofC factors including redox potential, electron accep- decomposition to CO2 under aerobic conditions, tors, and soil pH; for this reason, we assumed that anaerobic conditions above WT, and anaerobic con- the decomposition rates of C to CO2 and CH4 ditions below WT, respectively; fan,i is the fraction of above WT were different from the ones below WT anaerobic zones in the unsaturated soil; km,1 and km,2 to reflect the different soil biogeochemical envi- are rates of the C decomposition to CH4 under ronment between above and below WT. It was anaerobic conditions above WT and anaerobic condi- assumed that all CO2 will be released to the tions below WT, respectively;OCi is the organic C atmosphere after it is produced (i.e., CO2 reduction content at the soil depth i; FT,i and FM,i are the soil is minimal); CH4 will be released to atmosphere temperature and moisture functions regulating the C after it is produced and if it is not oxidized. This decomposition at different soil depth i, which are assumption is reasonable because little evidence of defined in Eq. (2); CO2,oxd is the CO2 produced due bubble production or release was found at the rich to the oxidization of CH4; foxd is the fraction of fen (M. Turetsky, unpublished data). There are five produced CH4 that was oxidized. We assumed that unknown parameters (kC,1,kC,2,kC,3,km,1,andkm,2) half of the produced CH4 was oxidized before in the Eq. (19) that are estimated using observation releasing to atmosphere (Walter and Heimann data as discussed later.

2000). It should be noted that C decomposition For the WT-based approach, the ﬂuxes of CO2 and under anaerobic condition is controlled not only by CH4 are calculated with the following equation soil temperature and moisture but also by other (Fig. 3):

123 Biogeochemistry

8 X ÂÃX ÂÃ > CO2 ¼ kc;1 OCi FT;i FM;i þ kc;3 OCi FT;i þCO2;oxd > > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}i |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}i > > above WT below WT > 0 1 > <> BX ÂÃC B C ð20Þ > CH4 ¼ B km;2 OCi FT;i C ðÞ1 foxd > @ A > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}i > > below WT > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} > > CH4 P :> CO2;oxd ¼ CH4 P foxd

There are three unknown parameters in Eq. (20), kc,1, respiration (Schuur and Trumbore 2006); therefore, kc,3, and km,2, to be calibrated using observation data as it was assumed that 50 % of measured soil respiration discussed later. was contributed by soil heterotrophic respiration. However, we do acknowledge that the contribution of heterotrophic respiration might have seasonal and Model parameterization, calibration, annual variations, which were not considered in our and validation model simulations. For the WT-based approach, there are three

The soil temperature above 50 cm was linearly parameters, kc,1,kc,3, and km,2, to be calibrated (see interpolated based on the measured soil temperature Eq. 20). In addition to the three parameters, there are at 0, 2, 10, 25, and 50 cm depths. The soil temperature two more parameters (kc,2 and km,1) to be calibrated for below 50 cm was assumed to be equal to the measured the oxygen-based approach (see Eq. 19). We added soil temperature at 50 cm. This assumption is reason- one constraint to both oxygen-based and WT-based able because the soil temperature below 50 cm is approaches by assuming that the ratio between aerobic relatively stable. Soil moisture proﬁles with depth are and anaerobic CO2 ﬂux ranged from 0.31 to 1.26 based not measured at the APEX sites and were linearly on the laboratory incubation studies on the soil interpolated based on the measured WT by assuming samples collected from the same rich fen peatlands that soil moisture content at the surface is equal to the (Kane et al. 2013). We also added one more constraint residual water content (hr) and linearly increased with to the oxygen-based model by assuming that the ratio soil depth to reach saturation at the WT. The model between production rates of anaerobic CO2 (kc,2) and was run on a daily time step with a 1-cm soil depth anaerobic CH4 (km,1) above WT (and previous to any resolution. oxidation) was the same as the ratio between produc-

We used the observed environmental data (e.g., soil tion rates of anaerobic CO2 (kc,3) and anaerobic CH4 temperature, WT) collected in year 2011 to calibrate (km,2) below WT. the oxygen-based and WT-based one-pool C models. After the oxygen-based and WT-based models were This was done by tuning the C decomposition rates in calibrated, we used the environmental data collected in order to match the simulated seasonal CH4 and years 2006 and 2010 to validate model performance. heterotrophic CO2 respiration with the observed This was done by predicting the growing-season flux of values. Our modeling exercises were only focused CO2 and CH4 using the measured environmental data on the growing season (June, July, and August) and the calibrated decomposition rates, and then because the environmental data (e.g., WT) were comparing the predicted growing-season fluxes of continuously measured during this period. In boreal CO2 and CH4 with the observed fluxes in 2006 and black forest ecosystems, heterotrophic respiration 2010. The reason that we used these 3 years for model contributed to approximately 40–60 % of soil calibration and validation is because the other years for

123 Biogeochemistry which we have APEX data were inﬂuenced by unusual ﬂuxes simulated with WT-based approach (t-test:

flood conditions (Wyatt et al. 2012). df = 499, p \ 0.05). Similarly, the CH4 fluxes in 2006 and CO2 and CH4 fluxes in 2010, simulated with Statistical analysis oxygen-based approach, are also significantly different from those simulated with WT-based approach A global optimization strategy, stochastic ranking (t-test: df = 499, p \ 0.05). For oxygen-based evolutionary strategy (SRES), was used to estimate approach, the RMSEs for CO2 and CH4 fluxes are the unknown parameters (Runarsson and Yao 2000). 50.5 and 0.37 in 2006, respectively, and the RMSEs

Many studies (e.g., Moles et al. 2003)havedemon- for CO2 and CH4 are 5.02 and 0.09 in 2010, strated that SRES is more robust and computationally respectively. For WT-based approach, the RMSEs efficient than other global optimization strategies to for CO2 and CH4 fluxes are 57.0 and 0.41 in 2006, solve similar problems with high dimensionality. The respectively, and the RMSEs for CO2 and CH4 following steps were used to obtain the uncertainties and fluxesare 5.11 and 0.10 in 2010, respectively. There- statistical information on the predicted growing-season fore, the results of our model validation indicate that

fluxes of CO2 and CH4 in 2006 and 2010. First, 500 simulated fluxes of CO2 and CH4 from the oxygen- samples of CO2 fluxes were randomly drawn from a based approach were closer to the observed values -2 normal distribution with a mean of 127.0 g C–CO2 m than that from the WT-based approach, suggesting that -2 and a standard deviation (SD) of 5.7 g C–CO2 m the performance of the oxygen-based approach was during the growing season of 2011 (see Table 1). better than that of the WT-based approach. Because

Another 500 samples of CH4 ﬂuxes were also randomly the traditional WT-based approach would represent no drawn from a normal distribution with a mean of 0.28 g anaerobic environments in the unsaturated soil, the -2 -2 C–CH4 m and a SD of 0.08 g C–CH4 m during the traditional WT-based approach leads to a sudden growing season of year 2011 (see Table 1). As a result, change from zero to 100 % anaerobic environment at

500 pairs of CO2 and CH4 fluxes were generated based the interface of unsaturated and saturated soil zones on the observed mean and SD in year 2011. Second, (i.e., near the water table), while our improved oxygen parameters were estimated for each pair of CO2 and CH4 approach leads to more gradual shift from zero to fluxes using the SRES method described earlier, 100 % anaerobic environment from surface soil to the resulting in total of 500 sets of parameters. Third, each deep saturated zone (Fig. 4). parameter set was used to predict the CO2 and CH4 The mean WT position in 2006 was the deepest fluxes in years 2006 and 2010, resulting in 500 pairs of among the three study years (i.e., 2006, 2010, and predicted CO2 and CH4 fluxes for each of the 2 years 2011); however, the CH4 flux during the growing (i.e., 2006 and 2010) forming distributions from which season of 2006 was highest resulting in CH4 fluxes that statistics can be calculated. We also calculated the root- were more than double those observed in 2010 and mean-square errors (RMSEs) between observations and 2011). This pattern cannot be captured by the tradi- simulations for years 2006 and 2010. tional WT-based approach but was captured by our We used a two-sample t test with the assumption of oxygen-based approach (Table 1). equal variance to evaluate if the CO2 or CH4 fluxes The results show that oxygen-based and WT-based simulated with oxygen-based approach are different approaches likely provide similar simulations on CO2 from those simulated with WT-based approach. An and CH4 fluxesin the early summer (i.e., early June) a = 0.05 significance level was used to determine if (Fig. 5). As the water table depths increases, the the means of two datasets (e.g., the 500 CO2-fluxes differences between the simulations on CO2 and CH4 simulated with oxygen-based versus with WT-based fluxes with oxygen- and WT-based approaches likely for year 2006) were significantly different. become greater in the mid-summer (i.e., late July and early August). In the late summer, the simulations on

CO2 and CH4 ﬂuxes with oxygen- and WT-based Simulation results approaches tend to become similar again. Similarly, our results show that the simulated fraction of

In 2006, the CO2 ﬂuxes simulated with oxygen-based anaerobic zones in the unsaturated soils shows approach are signiﬁcantly different from the CO2 seasonal variations and increases from * 26 % 123 123

Table 1 The results of model calibration and validation

CO2 ﬂux (g C–CO2)CH4 ﬂux (g C–CH4)

Aerobic Anaerobic CO2 Anaerobic CO2 CO2 from the Total CO2 CH4 flux from CH4 flux from Total CH4 CO2 from Above WT from below WT oxidized CH4 flux above WT below WT flux

Model calibration Year 2011 Observation – – – 127 (±5.7)a ––0.28 (±0.08) WT-based model 66.8 (±3.9) – 60.4 (±3.5) 0.28 (±0.08) 127 (±5.7) – 0.28 (±0.08) 0.28 (±0.08) Oxygen-based model 44.6 (±7.5) 47.8 (±10.8) 34.3 (±10.4) 0.28 (±0.08) 127 (±5.7) 0.16 (±0.06) 0.12 (±0.05) 0.28 (±0.08) Model validation Year 2006 Observation – – – 185 (±48.7) – – 0.66 (±0.45) WT-based model 73.0 (±4.3) – 55.1 0.25 128 (±5.7) – 0.25 0.25 (±0.08) (±3.3) (±0.08) (±0.08) Oxygen-based model 47.1 (±7.9) 55.8 32.0 0.31 (±0.08) 135 (±6.5) 0.20 (±0.07) 0.11 (±0.04) 0.31 (±12.5) (±9.7) (±0.08) Year 2010 Observation – – – 113 (±17.0) – – 0.3 (±0.05) WT-based model 61.6 – 49.7 0.23 111 (±4.8) – 0.23 (±0.07) 0.23 (±0.07) (±3.6) (±2.9) (±0.07) Oxygen-based model 43.2 (±7.3) 41.2 28.2 0.25 (±0.07) 113 (±5.1) 0.14 (±0.05) 0.11 (±0.04) 0.25 (±0.07) (±9.3) (±8.5) a The values inside parentheses represent the standard deviations

The model calibration was done by tuning the decomposition rates to match the simulated and observed ﬂuxes of CO2 and CH4 in year 2011. The calibrated decomposition rates were then used to predict the ﬂuxes of CO2 and CH4 in year 2006 and 2010 Biogeochemistry Biogeochemistry

Fig. 4 The simulated fractions of anaerobic zones in the rich fen. The white lines denote the observed water table position

(mean value of three years) in early June to * 38 % anaerobic zones based on a linear function of O2 (mean value of 3 years) in late August as water table concentration. Yet, many studies (e.g., Leffelaar 1979; depth increases. The simulated fraction of anaerobic Smith 1980) indicated strong non-linear relationships zones in the unsaturated soils also shows annual between O2 concentration and fraction of anaerobic variations, from * 37 % (mean value of growing zones in unsaturated soils. Dimitrov et al. (2010)and season) in 2006 to * 32 % (mean value of growing Grant and Routlet (2002) simulated the fraction of season) in 2010 and 2011. anaerobic zones using the empirical Michaels-Menten

function of O2 concentration. Wu and Blodau (2013) simulated the fraction of anaerobic zones using a Discussion dichotomous approach where aerobic and anaerobic zones occur above and below a threshold concentration

Thereareanumberofrecentecosystemmodeling of O2.These empirical and/or linear approaches are easy studies that include O2 and link the dynamics of O2 to implement numerically; however, they are valid only concentrations with ecosystem processes (e.g., soil CO2 within the bounds of the soil conditions used to derive and CH4 respiration) using empirical and/or linear those empirical and/or linear functions. Therefore, it is relationships. Li et al. (2000) simulated the fraction of challenging to apply empirical approaches to a broad

123 Biogeochemistry

30–60 %) of boreal soil C is stored in peatland ecosystems (Gorham 1991; Hobbie et al. 2000; Lal 2005), and they are a dominant ecosystem in boreal regions where climate change is accelerating (IPCC 2013), and some important parameters or environmental data are available to initialize the model for these regions (Fan et al. 2008, 2011). However, this model may also be applicable for use in other ecosystems and soils (uplands or lowlands, boreal or tropical regions, organic or mineral soils) with appro- priate corresponding parameters. Model simulations suggest that the presence of anaerobic conditions in the unsaturated zone above the

WT could play an important role in overall soil CH4 and CO2 ﬂuxes. This is supported by numerous ﬁeld experimental studies (e.g., Deppe et al. 2010; Estop- Aragones et al. 2012, 2013; Silins and Rothwell 1999) that have measured anaerobic conditions above the WT. Silins and Rothwell (1999) showed that only half of the unsaturated soil above the WT in two drained Canadian peatlands was aerobic, which is similar to our simulated fraction (* 34 %) of anaerobic environments in the unsaturated soil. Despite the fact that our modeling approaches (the WT versus oxygen

Fig. 5 The simulated time series of CO2 and CH4 fluxes with approaches) simulated observed C flux data well oxygen-based and WT-based approaches during the growing (Table 1), our study highlights the importance of these season anaerobic zones to both CO2 and CH4 flux estimates. Our model calibration and validation suggests that the range of soil conditions. Mechanistic models that WT-based approach, which does not consider anaer- include the underlying physical and biological mecha- obic zones in the unsaturated soil zone, may lead to nisms can likely produce more reliable future predic- biased predictions of CO2 and CH4 fluxes relative to tions under a wider array of conditions. the oxygen-based approach. Similarly, at a larger Our oxygen-based approach not only provides scale, Bohn and Lettenmaier (2010) indicated that the better model validation than the traditional WT-based WT formulation (uniform or wet-dry formulations) approach, but provides a better physical representation used in the earth system models would cause signif- of the underlying mechanisms and processes (e.g., soil icant biases (±100 % or more) on the estimates of pore characteristics) that control the production of CH4 flux from wetlands in western Siberia. CO2 and CH4 in peatlands, which forms a solid It should be noted that our oxygen-based approach foundation for future model development and also is only a first step in identifying the importance of soil provides guidance on future experimental design and aerobic and anaerobic zones in thick organic soil data collection. Moreover, the information on soil pore profiles. After the aerobic and anaerobic zones are characteristics (e.g., pore size distribution) can be identified, how to accurately simulate fluxes of CO2 roughly obtained with SWRC. Therefore, combining and CH4 also will depend on how to mathematically SWRC with O2 dynamic and the subsequent soil CO2 represent the factors and processes that control C and CH4 respiration (or aerobic/anaerobic environ- decomposition and transport. In our model applica- ments) have the potential to link our oxygen-based tion, we assumed that C decomposition was dependent approach to a broad range of soil conditions. only on soil temperature, moisture, and oxygen The reason we chose to study boreal peatlands is conditions. Many other important factors and pro- because a significant proportion (approximately cesses including soil redox potential, pH, electron 123 Biogeochemistry acceptors, plant-mediated transport, and microbial variables. This could be achieved by first incorporat- dynamics (Davidson and Janssens 2006; Limpens ing the oxygen-based model into ecosystem or earth et al. 2008) are not considered in our modeling system models and then calibrating the incorporated exercises, which may be responsible for the large model with measured ecosystem variables and states discrepancies between the simulated and observed (e.g., CO2 and CH4 flux) to inversely estimate the fluxes of CO2 and CH4. Since the time series of CH4 oxygen-consumption rate. The last approach is similar and CO2 fluxes utilized in this study were temporally to the traditional model calibration and validation limited, there might be uncertainty in calculating the procedures that are used to estimate C decomposition growing-season fluxes with sub-daily environmental rates by ecosystem and earth system models (e.g., measurements, which might also help explain the Thornton and Rosenbloom 2005). In general, while discrepancies between observations and simulations measurement of O2 consumption rates are fairly of our oxygen-based approach. difficult, we argue that improved data would benefit The oxygen-based approach can be easily incorpo- not only predictions of C fluxes as outlined in this rated into existing ecosystem and earth system models study, but also other issues related to soil ecology, soil and the corresponding physical parameters of our microbiology, and soil biogeochemistry. model can also be easily measured and obtained from Field experiments that simultaneously measure the laboratory studies (e.g., measurements of SWRC). net flux and depth profiles of CO2,CH4, and O2 along Unfortunately, there are limited experimental data with vertical variation in soil temperature, moisture, available to calibrate and validate our model simula- redox potential, and possible microbial community tions. As a result, our model simulations might differ dynamics would assist in the calibration and validation from reality and different model parameters and of our oxygen-based approach, but also would likely factors (e.g., O2 consumption rate, SWRC, soil pore improve traditional WT-based ecosystem and earth size distribution, soil biogeochemistry, and ratios system models. For example, most ecosystem models among production of aerobic CO2, anaerobic CO2, use the measured flux of CO2 and CH4 from soil to and CH4) might cause different model simulation atmosphere to calibrate and validate the model results. Therefore, additional experimental and obser- performance. Some ecosystem models also compare vational data (e.g., O2 profile) are required to examine the simulated profiles of soil temperature and moisture and improve the performance of the oxygen-based with measured data. However, very few ecosystem model. models compare simulated profiles of CO2,CH4, and Future work should quantify O2 consumption rates O2 with depth to measured profiles, yet these com- and explore whether this is a key biological parameter parisons are needed to verify if the models are controlling the simulated fraction of anaerobic zones. correctly parameterized or structured, especially for There are three potential methods (experiments and/or microbial dynamics and C decomposition. Future modeling) that would directly or indirectly determine studies that collect such data in general will be helpful

O2 consumption rates. The ﬁrst potential method is to in gaining better insight into processes occurring in use controlled laboratory experiments to measure the subsurface soils, and connections to surface processes changes in dissolved and gaseous O2 concentration such as C emissions. with time under different environmental conditions Our oxygen-based model not only has the potential

(e.g., moisture, temperature, and O2 concentration). to replace the traditional WT-based approach, but also Another approach would be to use laboratory or field has other potential applications. For example, inter- experiments coupled with numerical modeling. This actions among soil microorganisms and effects on could be done by first measuring the micro-profiles of biogeochemistry remain one of the most important

O2 concentration (and other gases and chemicals) in missing components in earth system models (Allison soil pores with micro-sensors (e.g., Nielsen et al. 2010; et al. 2010; Lawrence et al. 2009; Treseder et al. 2012).

Sayama et al. 2005) and then calculating the O2 In order to incorporate soil microorganisms into earth consumption rates based on the measured micro- system models (as an additional C pool and/or a profiles with numerical modeling(e.g., Nielsen et al. driving factor of C decomposition), it becomes critical 2010). Finally, a useful approach might also be to to first reliably simulate soil habitat (e.g., soil water couple modeling to in situ measurements of ecosystem and aeration). These soil conditions then could be used 123 Biogeochemistry as a cornerstone to simulate microbial physiology (i.e., Deppe M, Knorr KH, McKnight DM, Blodau C (2010) Effects conditions leading to nutrient immobilization, growth, of short-term drying and irrigation on CO2 and CH4 production and emission from mesocosms of a northern bog respiration, etc.), population dynamics, and microbi- and an alpine fen. Biogeochemistry 100:89–103 ally-mediated processes (i.e., sulfate reduction, nitri- Dimitrov DD, Grant RF, Lafleur PM, Humphreys ER (2010) fication/denitrification) in the unsaturated and Modeling the effects of hydrology on ecosystem respira- saturated soil zones. Our oxygen-based approach tion at Mer Bleue bog. J Geophys Res. doi:10.1029/ 2010JG001312 might offer an initial platform for exploring microbial Elberling B, Askaer L, Jorgensen CJ, Joensen HP, Kuhl M, Glud interactions within the soil and their potential to alter RN, Lauritsen FR (2011) Linking soil O2,CO2, and CH4 biogeochemical cycles (Treseder et al. 2012). concentrations in a wetland soil: implications for CO2 and CH4 fluxes. Environ Sci Technol 45:3393–3399 Acknowledgments This work was supported by the U.S. Estop-Aragones C, Knorr KH, Blodau C (2012) Controls on Department of Energy, Office of Science, Office of Biological in situ oxygen and dissolved inorganic carbon dynamics in and Environmental Research, Climate and Environmental peats of a temperate fen. J Geophys Res. doi:10.1029/ Science Division under contract DE-AC02-06CH11357, by 2011JG001888 the National Science Foundation (NSF) for the APEX project Estop-Aragones C, Knorr KH, Blodau C (2013) Belowground (DEB-0425328, DEB-0724514, DEB-0830997), and by the in situ redox dynamics and methanogenesis recovery in a USGS Climate Research & Development Program. Additional degraded fen during dry-wet cycles and flooding. 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