Biogeochemistry

, Volume 121, Issue 3, pp 455–470

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

Authors

    • Biosciences DivisionArgonne National Laboratory
  • Jason C. Neff
    • Department of Geological SciencesUniversity of Colorado
  • Mark P. Waldrop
    • USGS
  • Ashley P. Ballantyne
    • Department of Ecosystem and Conservation SciencesUniversity of Montana
  • Merritt R. Turetsky
    • Department of Integrative BiologyUniversity of Guelph
Article

DOI: 10.1007/s10533-014-0012-0

Cite this article as:
Fan, Z., Neff, J.C., Waldrop, M.P. et al. Biogeochemistry (2014) 121: 455. doi:10.1007/s10533-014-0012-0

Abstract

Peatlands store vast amounts of soil carbon and are significant sources of greenhouse gases, including carbon dioxide (CO2) and methane (CH4) emissions. The traditional approach in biogeochemical model simulations of peatland emissions is to simply divide the soil domain into an aerobic zone above and an anaerobic zone below the water table (WT) and then calculate CO2 and CH4 emissions based on the assumed properties of these two discrete zones. However, there are major potential drawbacks associated with the traditional WT-based approach, because aerobic or anaerobic environments are ultimately determined by oxygen (O2) concentration rather than water content directly. Variations in O2 content above and below the WT can be large and thus may play an important role in partitioning of carbon fluxes between CO2 and CH4. In this paper, we propose an oxygen-based approach, which simulates the vertical and radial components of O2 movement and consumption through the soil aerobic and anaerobic environments. We then use both our oxygen-based and the traditional WT-based approaches to simulate CO2 and CH4 emissions from an Alaskan fen peatland. The results of model calibration and validation suggest that our physically 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 traditional WT-based approach might substantially under-estimate CH4 emissions and over-estimate CO2 emissions from the fen due to the presence of anaerobic zones in unsaturated soil. Our oxygen-based approach can be easily incorporated into existing ecosystem or earth system models but will require additional validation with more extensive field observations to be implemented within biogeochemical models to improve simulations of soil C fluxes at regional or global scale.

Keywords

Water tableModelOxygenMicrobialHabitatWarmingAerobicAnaerobic

Introduction

Peatlands cover approximately 4 % of world’s terrestrial surface area (Matthews and Fung 1987), but store approximately 20 % of the world’s terrestrial carbon (C) stocks (Batjes 1996; Tarnocai et al. 2009). Peatlands are also more prevalent in high latitudes of the Northern Hemisphere where surface warming has accelerated over the last 50 years (IPCC 2013). Peatlands play a significant role in regulating global climate because they are important sources of methane (CH4) to the atmosphere, contributing approximately 15–20 % of world’s CH4 emission (Aselman and Crutzen 1989; Matthews and Fung 1987). Because the warming potential of CH4 is 24 times greater than that of carbon dioxide (CO2) over a 100-year time scale (Ramaswamy et al. 2001), evaluating the fraction of C emitted as CO2 and CH4 from peatlands and the sensitivity of these emissions to climate change is critical for understanding and predicting the northern high latitude C balance (Bridgham et al. 2008; Nisbet et al. 2014).

Most existing ecosystem or earth system models have the capability of simulating CO2 production under aerobic and anaerobic conditions, CH4 production under anaerobic conditions, CH4 transport (e.g., ebullition and diffusion transport), and microbial oxidation of CH4 under aerobic conditions (e.g., Frolking et al. 2002, 2010; Walter and Heimann 2000; Wania et al. 2010; Zhuang et al. 2004). Generally, most representations of peatland structure use a one-dimensional framework with two layers, including an upper, variably saturated ‘acrotelm’ and a permanently saturated lower layer, the ‘catotelm’, which is commonly several meters thick (Ingram 1978; Morris and Waddington 2011).This diplotelmic model for simulating peatland C cycling processes is a very common component of existing ecosystem or earth system models.

While the original diplotelmic model assumed that many ecological and biogeochemical processes could be explained by a single discrete boundary (depth in relation to a drought water table), a common approach employed by many ecosystem models is to use current fluctuations in depth of water table (WT) as a proxy of aerobic and anaerobic soil zones. While WT depth certainly is a strong predictor of many variables including rates of decomposition, reliance on a simple threshold hinders the representation of both vertical and horizontal spatial heterogeneity in peatlands. In terms of simulating CO2 and CH4 production and transport in peatlands, oxygen (O2) availability is a more direct control on whether a certain proportion of soil C undergoes aerobic or anaerobic decomposition (Boggie 1977; Estop-Aragones et al. 2012). For example if a peatland has a deep WT and the surface of the peatland is not favorable to O2 movement (e.g., high bulk density, high tortuosity, or low pore connectivity), a significant proportion of the soil C located above the WT (e.g., deep soil C) might undergo anaerobic decomposition even though soil moisture conditions are unsaturated. In this case, the traditional WT-based approach would notably under-estimate the soil anaerobic fraction and thus over-predict CO2 emissions and under-predict CH4 emissions (Bohn and Lettenmaier 2010).

There are multiple examples of low O2 availability in the zone above the WT from field studies. For example, work by Estop-Aragones et al. (2012, 2013) illustrated that the concentration of dissolved O2 within 20 cm of peat above the WT in a temperate fen frequently remained low (0–50 μmol L−1). From this result, they concluded that WT was a weak predictor of aerobic and anaerobic zones, given that a significant fraction of soil above the WT was likely subject to anaerobic conditions. In Canadian peatlands, Silins and Rothwell (1999) showed that the anaerobic zones above the WT were as thick as 40 cm (e.g., WT depth of ~ 80 cm and aerobic limit depth of ~ 40 cm) due to slow O2 diffusion. These patterns of O2 availability undoubtedly are important for C emissions. For example, the highest CH4 concentrations were commonly observed above the WT (instead of below WT) (e.g., Deppe et al. 2010; Knorr et al. 2008), suggesting that significant CH4 might be produced in the unsaturated soils above the water table. Moreover, many researchers(e.g., Sexstone et al. 1984; Tiedje et al. 1984) have shown significant rates of denitrification in unsaturated soil (even in well-drained soil settings) due to both slow O2 diffusion to the center of water-filled pores and fast O2 consumption by microbes. Together, there is strong evidence that the fraction of anaerobic zones in unsaturated soils might be substantial.

Soils are a porous media, where the arrangements of various soil particles create complex pore characteristics (e.g., pore connectivity and tortuosity), which results in heterogeneous distributions of water and air, the two most important determinants of microbial activities within the soil. These important soil characteristics are amenable to process based modeling and are also considered in this study. The goal of this 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 of soil processes (e.g., O2 consumption and spatial 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 Alaskan fen to the representation of aerobic and anaerobic zones in the soil.

Model development

The O2 concentration in soil is controlled by both O2 consumption (a sink) due to microbial activities and O2 movement (a sink or source) due to O2 concentration gradients. Oxygen movement is divided into 1) vertical movement in the gaseous phase due to the O2 concentration gradient within a given soil profile (i.e., O2 movement in the vertical direction from surface toward WT; Fig. 1a) and 2 radial or horizontal movement in soil pore water due to the O2 concentration 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; Fig. 1b). Below are mathematical constructs describing processes that affect the coupled O2 movement and consumption in the soil pore-water system.
https://static-content.springer.com/image/art%3A10.1007%2Fs10533-014-0012-0/MediaObjects/10533_2014_12_Fig1_HTML.gif
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

https://static-content.springer.com/image/art%3A10.1007%2Fs10533-014-0012-0/MediaObjects/10533_2014_12_Fig2_HTML.gif
Fig. 2

The observed profile of carbon bulk density in the Alaskan rich fen. The model denotes the equation that we used to calculate the carbon bulk density at different soil depth

Vertical transport of oxygen

The vertical transport of O2 due to a concentration gradient in the unsaturated soil (Fig. 1a) can be simulated using Fick’s law:
$$ \frac{{\partial C_{a} }}{\partial t} = D_{a} \frac{{\partial^{2} C_{a} }}{{\partial x^{2} }} - S $$
(1)
where Ca is the concentration of O2 in the gaseous phase (mol m−3), t is the time (s), Da is the diffusion coefficient of O2 in the gaseous phase (m2 s−1), x is the soil depth (m), and S is the O2 consumption rate (mol m−3 s−1) that is calculated as:
$$ \left\{ \begin{aligned} S &= S_{ref} F_{m} F_{T} \hfill \\ F_{M} &= 2.43 \times \left[ {\theta_{o,sa}^{2} - \left( {\theta_{sa} - \theta_{o,sa} } \right)^{2} } \right] \hfill \\ F_{T} &= ae^{{bT_{c} }} \hfill \\ \end{aligned} \right. $$
(2)
where Sref is the reference consumption rate of O2 (at optimal saturation and 10 °C) and set to 3.0 × 10−5 mol m−3 s−1 based on the range reported for rooted soils (oxygen consumed by both roots and microorganisms; Langeveld and Leffelaar 2002; Leffelaar 1979); FM and FT are the soil moisture and temperature functions regulating the oxygen consumption rate, respectively; θo,sa is the optimal effective soil saturation and set to 0.642 cm3 cm−3; θsa and Tc are the observed effective soil saturation (cm3 cm−3) and temperature (°C), respectively; a and b are empirical parameters set to 0.623 and 0.048 (Fan et al. 2008), respectively. The effective soil saturation (i.e., θsa) is defined as:
$$ \theta_{sa} = \frac{{\theta_{w} - \theta_{r} }}{{\sigma - \theta_{r} }} $$
(3)
where θw is volumetric moisture content (cm3 cm−3), θr is the residual moisture content (cm3 cm−3) that is water (such as thin water film surrounding soil particles) held in a soil at high tension (e.g., −10 kPa) (Caron and Nkongolo 2003), and σ is porosity (cm3 cm−3).
The diffusion coefficient, Da, is defined as:
$$ D_{a} = D_{a,0} \tau_{a} $$
(4)
where Da,0 is the diffusion coefficient of O2 in the free air that is set to 2 × 10−5 m2 s−1(Hillel 1998) and τa is the tortuosity in the gaseous phase (unitless). At high moisture content, the traditional Penman (1940) approach is known to over-estimate tortuosity and the Millington and Quirk (1961) approach is known to under-estimate tortuosity. Pingintha et al. (2010) compared six tortuosity models and concluded that the Moldrup et al. (1997) model was the most robust model to calculate τa with high moisture content and defined as:
$$ \tau_{a} = 0.66\theta_{a} \left( {\frac{{\theta_{a} }}{\sigma }} \right)^{{\frac{12 - \beta }{3}}} $$
(5)
where θa is the volumetric air content (cm3 cm−3) and β is an empirical parameter (unitless) that was set to 3.0 following Pingintha et al. (2010).
The upper boundary condition for Eq. (1) was determined based on the field observed O2 concentration at the soil surface (Elberling et al. 2011) and given as:
$$ C_{a} \left( {x = 0,t} \right) = 300 \, \mu M $$
(6)
A variable O2 flux condition was assumed to be the lower boundary condition and calculated based on the following equation:
$$ J = - D_{a} \frac{{\partial C_{a} }}{\partial x} $$
(7)
where J is the O2 flux density (mol m−2 s−1).

Radial transport of oxygen

The radial transport of dissolved O2 within soil pore water in the horizontal direction (Fig. 1b) can be mathematically described with the following equation (Arah and Vinten 1995)
$$ S = D_{w} \left( {\frac{{\partial^{2} C_{w} }}{{\partial r^{2} }} + \frac{1}{r}\frac{{\partial C_{w} }}{\partial r}} \right) $$
(8)
where Dw is the diffusion coefficient of O2 in the liquid phase (m2 s−1), Cw is the concentration of O2 in the liquid phase (mol m−3), and r is the radius from the center of air-filled pore (m).
The diffusion coefficient, Dw, is calculated using the Stokes–Einstein equation:
$$ D_{w} = 7.4 \times 10^{ - 8} \frac{{T_{k} \left( {\phi_{H2O} M_{H2O} } \right)^{0.5} }}{{\mu V_{O2}^{0.6} }} \times \tau_{w} \times 10^{ - 4} $$
(9)
where Tk is the absolute soil temperature (K), ϕH2O is an empirical parameter for water and set to 2.26 following Reid et al. (1977), MH2O is the molecular weight of water (18 g mol−1), μ is the viscosity of water (centipoises), VO2 is the molar volume of O2 at its normal boiling point (25.6 cm3 mol−1), τw is the tortuosity in the liquid phase (cm3 cm−3), and 10−4 is the unit conversion factor.
The viscosity of water, μ, is a function of soil temperature and calculated using the empirical equation derived based on the observed viscosity at different temperatures (Kestin et al. 1978):
$$ \mu = 1.02 \times 10^{ - 7} T_{c}^{4} - 1.924 \times 10^{ - 5} T_{c}^{3} + 1.46 \times 10^{ - 3} T_{c}^{2} - 6.27 \times 10^{ - 2} T_{c} + 1.802 $$
(10)
where Tc is the soil temperature (°C).
The tortuosity in the liquid phase, τw, is similar to the calculation of tortuosity in the gaseous phase (τa) and defined as (Moldrup et al. 1997):
$$ \tau_{w} = 0.66\theta_{w} \left( {\frac{{\theta_{w} }}{\sigma }} \right)^{{\frac{12 - \beta }{3}}} $$
(11)
where all of the parameters have been defined earlier.
The inner and outer boundary conditions for Eq. (8) are defined as (Arah and Vinten 1995):
$$ \left\{ \begin{aligned} C_{w}& = C_{a} s_{w} \frac{{\theta_{w} }}{1 - \sigma }, \quad\quad\quad for \; r = r_{a} \hfill \\ C_{w} &= 0 \; and \; \frac{{\partial C_{w} }}{\partial r} = 0, \quad for \; r = r_{b} \hfill \\ \end{aligned} \right. $$
(12)
where sw is the solubility of O2 in soil–water (m3 m−3) relative to solubility in free air and set to 0.03 following Schurgers et al. (2006), ra is the radius of typical air-filled pore that is empty (with no water) at a given moisture content (m), and rb is the radius of aerobic zone surrounding the air-filled pore (m).The radius of typical air-filled pore is calculated based on the soil water retention curve (SWRC; the relationship between water content and water potential):
$$ \left\{\begin{array}{l}r_{a} = \sqrt {r_{\hbox{min} } r_{\hbox{max} } } \hfill \\ r_{\hbox{min} } = \frac{2\varepsilon }{\rho g\left| \omega \right|} \hfill \\ r_{\hbox{max} } = \frac{2\varepsilon }{\rho g \times 0.1} \end{array} \right. $$
(13)
where rmin and rmax are the smallest and largest radii of air-filled pores that are empty at a given matrix potential (ω), respectively, ε is the surface tension of water (N m−1), ρ is the density of water (kg m−3), and g is the acceleration due to gravity (9.8 m s−2). Equation 13 indicates that the largest radius of air-filled pore corresponds to the soil matrix potential of 0.1 m. The soil matrix potential, ω, at a given moisture content, is calculated using the Mualem-van Genuchten model (Mualem 1976; van Genuchten 1980):
$$ \theta_{w} = \theta_{r} + \frac{{\theta_{s} - \theta_{r} }}{{\left[ {1 + \left| {\alpha \omega } \right|^{n} } \right]^{{1.0 - \frac{1}{n}}} }} $$
(14)
where θr and θs are the residual and saturated water contents (cm3 cm−3), respectively, α is an empirical parameter related to the air-entry pressure (m−1), and n is an empirical parameter related to the soil pore connectivity (unitless). Parameters α and n, together, constrain the SWRC shape. The four parameters in Eq. (14), α, n, θr, and θs, were set to 2.0, 1.7, 0.15, and 0.88 for organic soil (Letts et al. 2000).By integrating Eq. (8) with the boundary conditions defined in Eq. (12), the analytical solution of Eq. (8) is (Arah and Vinten 1995):
$$ C_{w} = \frac{S}{{4D_{w} }}\left[ {r^{2} - r_{b}^{2} \ln \left( {r^{2} } \right) + r_{b}^{2} \ln \left( {r_{b}^{2} - 1} \right)} \right] \; for \; r_{a} < r < r_{b} $$
(15)
At the outer boundary (r = ra), Eq. (15) can be rewritten based on Eq. (12) as:
$$ C_{a} s_{w} \frac{{\theta_{w} }}{1 - \sigma } = \frac{S}{{4D_{w} }}\left[ {r^{2} - r_{b}^{2} \ln \left( {r^{2} } \right) + r_{b}^{2} \ln \left( {r_{b}^{2} - 1} \right)} \right] \; for \; r = r_{a} $$
(16)
The above equation can be numerically solved to obtain the value of rb, the radius of the aerobic zone surrounding the air-filled pore.
Once the radius (rb) of the aerobic zone surrounding the typical air-filled pore (ra) is determined, the fraction of anaerobic zones in the unsaturated soil (fan) can be calculated as:
$$ f_{an} = \left( {1 - \pi r_{b}^{2} } \right)^{\xi } $$
(17)
where ξ is the number of air-filled pores (with radius of ra) per unit area and calculated as:
$$ \xi = \frac{\sigma }{{\pi r_{a}^{2} }} $$
(18)
It should be noted that Eq. (17) assumes that there are no over-lapping soil pores, which might over-estimate the fraction of anaerobic zones in the unsaturated soil (Langeveld and Leffelaar 2002). Also, the soil pores are assumed to be cylindrical in our model simulation for the sake of simplicity; however, it also should be noted that different pore shapes (regular or irregular) might affect the model simulations.

Model application and evaluation

Site description and data collection

We applied our oxygen diffusion model to simulate the fraction of anaerobic zones in an Alaskan rich fen and to assess the importance of anaerobic decomposition in the unsaturated soil of the peatland. The rich fen is part of the Alaska Peatland Experiment (APEX; 64.82 ºN, 147.87 ºW) located near the Bonanza Creek Experimental Forest outside of Fairbanks, Alaska. The thickness of peat (or thickness of organic C horizon) above the mineral soil is approximately 90 cm. Hourly soil temperature and water table position have been measured since 2006. During the growing season, CH4 emission was measured approximately twice a month using static chambers placed on top of metal flux collars installed permanently in the peat. A minimum of four headspace samples were collected over a 30–40 min period, and were analyzed using gas chromatography (see Turetsky et al. 2008).In conjunction with the methane flux measurements, rates of ecosystem respiration were collected using the same chambers that were shrouded to exclude light. Concentrations of CO2 inside each chamber were measured over a several minute period using PP-systems infrared gas analyzers (see Chivers et al. 2009).

Soil bulk density was measured by excavating a known volume of soil, carefully separating each soil horizon, and oven drying them at 65 °C, and quantifying mass per unit volume for each soil horizon interval. Soil C concentration of each soil horizon was measured using a Carlo Erba NA1500 elemental analyzer (Carlo Erba Instrumentaziones, Milan, Italy) (Manies and Harden 2011). Soil C bulk density required for model implementation was then calculated by multiplying the measured C concentration by soil bulk density for each depth (Fig. 2).

Description of carbon model

We used a simple one-pool C model coupled with either our oxygen-based or the traditional WT-based approaches to simulate the soil CH4 and heterotrophic CO2 respiration, and then we compared the simulation results to examine the performance of both approaches. The oxygen-based or WT-based approach was first used to identify the soil aerobic and anaerobic zones, and the one-pool C model was then used to calculate the CO2 and/or CH4 production (and oxidation) from each of the aerobic and anaerobic zones as described below.

The flux of CO2 and CH4 for the oxygen-based approach is calculated based on soil temperature, soil moisture content, and soil C content with the following equation (Fig. 3)
$$ \left\{ \begin{aligned} &{\text{CO}}_{ 2} = \underbrace {{\sum\limits_{i} {\left[ {k_{c,1} \times {\text{OC}}_{i} \times \left( {1 - f_{an,i} } \right) \times F_{T,i} \times F_{M,i} } \right]} + \sum\limits_{i} {\left[ {k_{c,2} \times {\text{OC}}_{i} \times f_{an,i} \times F_{T,i} } \right]} }}_{above \, WT} + \underbrace {{\sum\limits_{i} {\left[ {k_{c,3} \times {\text{OC}}_{i} \times F_{T,i} } \right]} }}_{below \, WT} + {\text{CO}}_{2,oxd} \hfill \\ &{\text{CH}}_{ 4} = \underbrace {{\left( {\underbrace {{\sum\limits_{i} {\left[ {k_{m,1} \times {\text{OC}}_{i} \times f_{an,i} \times F_{T,i} } \right]} }}_{above \, WT} + \underbrace {{\sum\limits_{i} {\left[ {k_{m,2} \times {\text{OC}}_{i} \times F_{T,i} } \right]} }}_{below \, WT}} \right)}}_{{CH_{4\_P} }} \times \left( {1 - f_{oxd} } \right)\\ &{\text{CO}}_{2,oxd} = {\text{CH}}_{4\_P} \times f_{oxd} \hfill \\ \end{aligned} \right. $$
(19)
where kC,1, kC,2, and kC,3 are the rates (year−1) of C decomposition to CO2 under aerobic conditions, anaerobic conditions above WT, and anaerobic conditions below WT, respectively; fan,i is the fraction of anaerobic zones in the unsaturated soil; km,1 and km,2 are rates of the C decomposition to CH4 under anaerobic conditions above WT and anaerobic conditions below WT, respectively;OCi is the organic C content at the soil depth i; FT,i and FM,i are the soil temperature and moisture functions regulating the C decomposition at different soil depth i, which are defined in Eq. (2); CO2,oxd is the CO2 produced due to the oxidization of CH4; foxd is the fraction of produced CH4 that was oxidized. We assumed that half of the produced CH4 was oxidized before releasing to atmosphere (Walter and Heimann 2000). It should be noted that C decomposition under anaerobic condition is controlled not only by soil temperature and moisture but also by other factors including redox potential, electron acceptors, and soil pH; for this reason, we assumed that the decomposition rates of C to CO2 and CH4 above WT were different from the ones below WT to reflect the different soil biogeochemical environment between above and below WT. It was assumed that all CO2 will be released to the atmosphere after it is produced (i.e., CO2 reduction is minimal); CH4 will be released to atmosphere after it is produced and if it is not oxidized. This assumption is reasonable because little evidence of bubble production or release was found at the rich fen (M. Turetsky, unpublished data). There are five unknown parameters (kC,1, kC,2,kC,3, km,1, and km,2) in the Eq. (19) that are estimated using observation data as discussed later.
https://static-content.springer.com/image/art%3A10.1007%2Fs10533-014-0012-0/MediaObjects/10533_2014_12_Fig3_HTML.gif
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

For the WT-based approach, the fluxes of CO2 and CH4 are calculated with the following equation (Fig. 3):
$$ \left\{ \begin{aligned} &{\text{CO}}_{2} = \underbrace {{\sum\limits_{i} {\left[ {k_{c,1} \times {\text{OC}}_{i} \times F_{T,i} \times F_{M,i} } \right]} }}_{above \, WT} + \underbrace {{\sum\limits_{i} {\left[ {k_{c,3} \times {\text{OC}}_{i} \times F_{T,i} } \right]} }}_{below \, WT} + {\text{CO}}_{2,oxd} \hfill \\ &{\text{CH}}_{4} = \underbrace {{\left( {\underbrace {{\sum\limits_{i} {\left[ {k_{m,2} \times {\text{OC}}_{i} \times F_{T,i} } \right]} }}_{below \, WT}} \right)}}_{{CH_{4\_P} }} \times \left( {1 - f_{oxd} } \right) \hfill \\ &{\text{CO}}_{2,oxd} = {\text{CH}}_{4\_P} \times f_{oxd} \hfill \\ \end{aligned} \right. $$
(20)
There are three unknown parameters in Eq. (20), kc,1, kc,3, and km,2, to be calibrated using observation data as discussed later.

Model parameterization, calibration, and validation

The soil temperature above 50 cm was linearly interpolated based on the measured soil temperature at 0, 2, 10, 25, and 50 cm depths. The soil temperature below 50 cm was assumed to be equal to the measured soil temperature at 50 cm. This assumption is reasonable because the soil temperature below 50 cm is relatively stable. Soil moisture profiles with depth are not measured at the APEX sites and were linearly interpolated based on the measured WT by assuming that soil moisture content at the surface is equal to the residual water content (θr) and linearly increased with soil depth to reach saturation at the WT. The model was run on a daily time step with a 1-cm soil depth resolution.

We used the observed environmental data (e.g., soil temperature, WT) collected in year 2011 to calibrate the oxygen-based and WT-based one-pool C models. This was done by tuning the C decomposition rates in order to match the simulated seasonal CH4 and heterotrophic CO2 respiration with the observed values. Our modeling exercises were only focused on the growing season (June, July, and August) because the environmental data (e.g., WT) were continuously measured during this period. In boreal black forest ecosystems, heterotrophic respiration contributed to approximately 40–60 % of soil respiration (Schuur and Trumbore 2006); therefore, it was assumed that 50 % of measured soil respiration was contributed by soil heterotrophic respiration. However, we do acknowledge that the contribution of heterotrophic respiration might have seasonal and annual variations, which were not considered in our model simulations.

For the WT-based approach, there are three parameters, kc,1, kc,3, and km,2, to be calibrated (see Eq. 20). In addition to the three parameters, there are two more parameters (kc,2 and km,1) to be calibrated for the oxygen-based approach (see Eq. 19). We added one constraint to both oxygen-based and WT-based approaches by assuming that the ratio between aerobic and anaerobic CO2 flux ranged from 0.31 to 1.26 based on the laboratory incubation studies on the soil samples collected from the same rich fen peatlands (Kane et al. 2013). We also added one more constraint to the oxygen-based model by assuming that the ratio between production rates of anaerobic CO2 (kc,2) and anaerobic CH4 (km,1) above WT (and previous to any oxidation) was the same as the ratio between production rates of anaerobic CO2 (kc,3) and anaerobic CH4 (km,2) below WT.

After the oxygen-based and WT-based models were calibrated, we used the environmental data collected in years 2006 and 2010 to validate model performance. This was done by predicting the growing-season flux of CO2 and CH4 using the measured environmental data and the calibrated decomposition rates, and then comparing the predicted growing-season fluxes of CO2 and CH4 with the observed fluxes in 2006 and 2010. The reason that we used these 3 years for model calibration and validation is because the other years for which we have APEX data were influenced by unusual flood conditions (Wyatt et al. 2012).

Statistical analysis

A global optimization strategy, stochastic ranking evolutionary strategy (SRES), was used to estimate the unknown parameters (Runarsson and Yao 2000). Many studies (e.g., Moles et al. 2003) have demonstrated that SRES is more robust and computationally efficient than other global optimization strategies to solve similar problems with high dimensionality. The following steps were used to obtain the uncertainties and statistical information on the predicted growing-season fluxes of CO2 and CH4 in 2006 and 2010. First, 500 samples of CO2 fluxes were randomly drawn from a normal distribution with a mean of 127.0 g C–CO2 m−2 and a standard deviation (SD) of 5.7 g C–CO2 m−2 during the growing season of 2011 (see Table 1). Another 500 samples of CH4 fluxes were also randomly drawn from a normal distribution with a mean of 0.28 g C–CH4 m−2 and a SD of 0.08 g C–CH4 m−2 during the growing season of year 2011 (see Table 1). As a result, 500 pairs of CO2 and CH4 fluxes were generated based on the observed mean and SD in year 2011. Second, parameters were estimated for each pair of CO2 and CH4 fluxes using the SRES method described earlier, resulting in total of 500 sets of parameters. Third, each parameter set was used to predict the CO2 and CH4 fluxes in years 2006 and 2010, resulting in 500 pairs of predicted CO2 and CH4 fluxes for each of the 2 years (i.e., 2006 and 2010) forming distributions from which statistics can be calculated. We also calculated the root-mean-square errors (RMSEs) between observations and simulations for years 2006 and 2010.
Table 1

The results of model calibration and validation

 

CO2 flux (g C–CO2)

CH4 flux (g C–CH4)

Aerobic CO2

Anaerobic CO2 from Above WT

Anaerobic CO2 from below WT

CO2 from the oxidized CH4

Total CO2 flux

CH4 flux from above WT

CH4 flux from below WT

Total CH4 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

(±3.3)

0.25

(±0.08)

128 (±5.7)

0.25

(±0.08)

0.25 (±0.08)

Oxygen-based model

47.1 (±7.9)

55.8

(±12.5)

32.0

(±9.7)

0.31 (±0.08)

135 (±6.5)

0.20 (±0.07)

0.11 (±0.04)

0.31

(±0.08)

 Year 2010

Observation

 

113 (±17.0)

0.3 (±0.05)

WT-based model

61.6

(±3.6)

49.7

(±2.9)

0.23

(±0.07)

111 (±4.8)

0.23 (±0.07)

0.23 (±0.07)

Oxygen-based model

43.2 (±7.3)

41.2

(±9.3)

28.2

(±8.5)

0.25 (±0.07)

113 (±5.1)

0.14 (±0.05)

0.11 (±0.04)

0.25 (±0.07)

aThe 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

We used a two-sample t test with the assumption of equal variance to evaluate if the CO2 or CH4 fluxes simulated with oxygen-based approach are different from those simulated with WT-based approach. An α = 0.05 significance level was used to determine if the means of two datasets (e.g., the 500 CO2-fluxes simulated with oxygen-based versus with WT-based for year 2006) were significantly different.

Simulation results

In 2006, the CO2 fluxes simulated with oxygen-based approach are significantly different from the CO2 fluxes simulated with WT-based approach (t-test: df = 499, p < 0.05). Similarly, the CH4 fluxes in 2006 and CO2 and CH4 fluxes in 2010, simulated with oxygen-based approach, are also significantly different from those simulated with WT-based approach (t-test: df = 499, p < 0.05). For oxygen-based approach, the RMSEs for CO2 and CH4 fluxes are 50.5 and 0.37 in 2006, respectively, and the RMSEs for CO2 and CH4 are 5.02 and 0.09 in 2010, respectively. For WT-based approach, the RMSEs for CO2 and CH4 fluxes are 57.0 and 0.41 in 2006, respectively, and the RMSEs for CO2 and CH4 fluxesare 5.11 and 0.10 in 2010, respectively. Therefore, the results of our model validation indicate that simulated fluxes of CO2 and CH4 from the oxygen-based approach were closer to the observed values than that from the WT-based approach, suggesting that the performance of the oxygen-based approach was better than that of the WT-based approach. Because the traditional WT-based approach would represent no anaerobic environments in the unsaturated soil, the traditional WT-based approach leads to a sudden change from zero to 100 % anaerobic environment at the interface of unsaturated and saturated soil zones (i.e., near the water table), while our improved oxygen approach leads to more gradual shift from zero to 100 % anaerobic environment from surface soil to the deep saturated zone (Fig. 4).
https://static-content.springer.com/image/art%3A10.1007%2Fs10533-014-0012-0/MediaObjects/10533_2014_12_Fig4_HTML.gif
Fig. 4

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

The mean WT position in 2006 was the deepest among the three study years (i.e., 2006, 2010, and 2011); however, the CH4 flux during the growing season of 2006 was highest resulting in CH4 fluxes that were more than double those observed in 2010 and 2011). This pattern cannot be captured by the traditional WT-based approach but was captured by our oxygen-based approach (Table 1).

The results show that oxygen-based and WT-based approaches likely provide similar simulations on CO2 and CH4 fluxesin the early summer (i.e., early June) (Fig. 5). As the water table depths increases, the differences between the simulations on CO2 and CH4 fluxes with oxygen- and WT-based approaches likely 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 approaches tend to become similar again. Similarly, our results show that the simulated fraction of anaerobic zones in the unsaturated soils shows seasonal variations and increases from ~ 26 % (mean value of three years) in early June to ~ 38 % (mean value of 3 years) in late August as water table depth increases. The simulated fraction of anaerobic zones in the unsaturated soils also shows annual variations, from ~ 37 % (mean value of growing season) in 2006 to ~ 32 % (mean value of growing season) in 2010 and 2011.
https://static-content.springer.com/image/art%3A10.1007%2Fs10533-014-0012-0/MediaObjects/10533_2014_12_Fig5_HTML.gif
Fig. 5

The simulated time series of CO2 and CH4 fluxes with oxygen-based and WT-based approaches during the growing season

Discussion

There are a number of recent ecosystem modeling studies that include O2 and link the dynamics of O2 concentrations with ecosystem processes (e.g., soil CO2 and CH4 respiration) using empirical and/or linear relationships. Li et al. (2000) simulated the fraction of anaerobic zones based on a linear function of O2 concentration. Yet, many studies (e.g., Leffelaar 1979; Smith 1980) indicated strong non-linear relationships between O2 concentration and fraction of anaerobic zones in unsaturated soils. Dimitrov et al. (2010) and Grant and Routlet (2002) simulated the fraction of anaerobic zones using the empirical Michaels-Menten function of O2 concentration. Wu and Blodau (2013) simulated the fraction of anaerobic zones using a dichotomous approach where aerobic and anaerobic zones occur above and below a threshold concentration of O2.These empirical and/or linear approaches are easy to implement numerically; however, they are valid only within the bounds of the soil conditions used to derive those empirical and/or linear functions. Therefore, it is challenging to apply empirical approaches to a broad range of soil conditions. Mechanistic models that include the underlying physical and biological mechanisms can likely produce more reliable future predictions under a wider array of conditions.

Our oxygen-based approach not only provides better model validation than the traditional WT-based approach, but provides a better physical representation of the underlying mechanisms and processes (e.g., soil pore characteristics) that control the production of CO2 and CH4 in peatlands, which forms a solid foundation for future model development and also provides guidance on future experimental design and data collection. Moreover, the information on soil pore characteristics (e.g., pore size distribution) can be roughly obtained with SWRC. Therefore, combining SWRC with O2 dynamic and the subsequent soil CO2 and CH4 respiration (or aerobic/anaerobic environments) have the potential to link our oxygen-based approach to a broad range of soil conditions.

The reason we chose to study boreal peatlands is because a significant proportion (approximately 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 appropriate 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 approaches) simulated observed C flux data well (Table 1), our study highlights the importance of these anaerobic zones to both CO2 and CH4 flux estimates. Our model calibration and validation suggests that the WT-based approach, which does not consider anaerobic zones in the unsaturated soil zone, may lead to biased predictions of CO2 and CH4 fluxes relative to the oxygen-based approach. Similarly, at a larger scale, Bohn and Lettenmaier (2010) indicated that the WT formulation (uniform or wet-dry formulations) used in the earth system models would cause significant biases (±100 % or more) on the estimates of CH4 flux from wetlands in western Siberia.

It should be noted that our oxygen-based approach is only a first step in identifying the importance of soil aerobic and anaerobic zones in thick organic soil profiles. After the aerobic and anaerobic zones are identified, how to accurately simulate fluxes of CO2 and CH4 also will depend on how to mathematically represent the factors and processes that control C decomposition and transport. In our model application, we assumed that C decomposition was dependent only on soil temperature, moisture, and oxygen conditions. Many other important factors and processes including soil redox potential, pH, electron acceptors, plant-mediated transport, and microbial dynamics (Davidson and Janssens 2006; Limpens et al. 2008) are not considered in our modeling exercises, which may be responsible for the large discrepancies between the simulated and observed fluxes of CO2 and CH4. Since the time series of CH4 and CO2 fluxes utilized in this study were temporally limited, there might be uncertainty in calculating the growing-season fluxes with sub-daily environmental measurements, which might also help explain the discrepancies between observations and simulations of our oxygen-based approach.

The oxygen-based approach can be easily incorporated into existing ecosystem and earth system models and the corresponding physical parameters of our model can also be easily measured and obtained from laboratory studies (e.g., measurements of SWRC). Unfortunately, there are limited experimental data available to calibrate and validate our model simulations. As a result, our model simulations might differ from reality and different model parameters and factors (e.g., O2 consumption rate, SWRC, soil pore size distribution, soil biogeochemistry, and ratios among production of aerobic CO2, anaerobic CO2, and CH4) might cause different model simulation results. Therefore, additional experimental and observational data (e.g., O2 profile) are required to examine and improve the performance of the oxygen-based model.

Future work should quantify O2 consumption rates and explore whether this is a key biological parameter controlling the simulated fraction of anaerobic zones. There are three potential methods (experiments and/or modeling) that would directly or indirectly determine O2 consumption rates. The first potential method is to use controlled laboratory experiments to measure the changes in dissolved and gaseous O2 concentration with time under different environmental conditions (e.g., moisture, temperature, and O2 concentration). Another approach would be to use laboratory or field experiments coupled with numerical modeling. This could be done by first measuring the micro-profiles of O2 concentration (and other gases and chemicals) in soil pores with micro-sensors (e.g., Nielsen et al. 2010; Sayama et al. 2005) and then calculating the O2 consumption rates based on the measured micro-profiles with numerical modeling(e.g., Nielsen et al. 2010). Finally, a useful approach might also be to couple modeling to in situ measurements of ecosystem variables. This could be achieved by first incorporating the oxygen-based model into ecosystem or earth system models and then calibrating the incorporated model with measured ecosystem variables and states (e.g., CO2 and CH4 flux) to inversely estimate the oxygen-consumption rate. The last approach is similar to the traditional model calibration and validation procedures that are used to estimate C decomposition rates by ecosystem and earth system models (e.g., Thornton and Rosenbloom 2005). In general, while measurement of O2 consumption rates are fairly difficult, we argue that improved data would benefit not only predictions of C fluxes as outlined in this study, but also other issues related to soil ecology, soil microbiology, and soil biogeochemistry.

Field experiments that simultaneously measure the net flux and depth profiles of CO2, CH4, and O2 along with vertical variation in soil temperature, moisture, redox potential, and possible microbial community dynamics would assist in the calibration and validation of our oxygen-based approach, but also would likely improve traditional WT-based ecosystem and earth system models. For example, most ecosystem models use the measured flux of CO2 and CH4 from soil to atmosphere to calibrate and validate the model performance. Some ecosystem models also compare the simulated profiles of soil temperature and moisture with measured data. However, very few ecosystem models compare simulated profiles of CO2, CH4, and O2 with depth to measured profiles, yet these comparisons are needed to verify if the models are correctly parameterized or structured, especially for microbial dynamics and C decomposition. Future studies that collect such data in general will be helpful in gaining better insight into processes occurring in subsurface soils, and connections to surface processes such as C emissions.

Our oxygen-based model not only has the potential to replace the traditional WT-based approach, but also has other potential applications. For example, interactions among soil microorganisms and effects on biogeochemistry remain one of the most important missing components in earth system models (Allison et al. 2010; Lawrence et al. 2009; Treseder et al. 2012). In order to incorporate soil microorganisms into earth system models (as an additional C pool and/or a driving factor of C decomposition), it becomes critical to first reliably simulate soil habitat (e.g., soil water and aeration). These soil conditions then could be used as a cornerstone to simulate microbial physiology (i.e., conditions leading to nutrient immobilization, growth, respiration, etc.), population dynamics, and microbially-mediated processes (i.e., sulfate reduction, nitrification/denitrification) in the unsaturated and saturated soil zones. Our oxygen-based approach might offer an initial platform for exploring microbial interactions within the soil and their potential to alter biogeochemical cycles (Treseder et al. 2012).

Acknowledgments

This work was supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Climate and Environmental Science Division under contract DE-AC02-06CH11357, by the National Science Foundation (NSF) for the APEX project (DEB-0425328, DEB-0724514, DEB-0830997), and by the USGS Climate Research & Development Program. Additional funding and considerable logistic support were provided by the Bonanza Creek LTER Program, which is jointly funded by NSF (DEB-1026415) and the USDA Forest Service, Pacific Northwest Research Station (PNW01-JV112619320-16).

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