Carbon balance of a restored and cutover raised bog : implications for restoration and comparison to global trends

The net ecosystem exchange (NEE) and methane (CH4) flux were measured by chamber measurements for five distinct ecotypes (areas with unique eco-hydrological characteristics) at Abbeyleix Bog in the Irish midlands over a 2-year period. The ecotypes ranged from those with highquality peat-forming vegetation to communities indicative of degraded, drained conditions. Three of these ecotypes were located in an area where peat was extracted by hand and then abandoned and left to revegetate naturally at least 50 years prior to the start of the study. Two of the ecotypes were located on an adjacent raised bog, which although never mined for peat, was impacted by shallow drainage and then restored (by drain blocking) 6 years prior to the start of the study. Other major aspects of the carbon (C) balance, including dissolved organic carbon (DOC), dissolved inorganic carbon (DIC), and open-water CO2 evasion, were quantified for a catchment area at the study site over the same 2-year period. The ecotype average annual ecotype C balance ranged from a net C sink of−58±60 g C m−2 yr−1, comparable to studies of intact peatlands, to a substantial C source of+205±80 g C m−2 yr−1, with NEE being the most variable component of the C balance among the five ecotypes. Ecotype annual CH4 flux ranged from 2.7±1.4 g C-CH4 m−2 yr−1 to 14.2± 4.8 g C-CH4 m−2 yr−1. Average annual aquatic C losses were 14.4 g C m−2 yr−1 with DOC, DIC, and CO2 evasion of 10.4 g C m−2 yr−1, 1.3 g C m−2 yr−1, and 2.7 g C m−2 yr−1, respectively. A statistically significant negative correlation was found between the mean annual water table (MAWT) and the plot-scale NEE but not the global warming potential (GWP). However, a significant negative correlation was observed between the plot-scale percentage of Sphagnum moss cover and the GWP, highlighting the importance of regenerating this keystone genus as a climate change mitigation strategy in peatland restoration. The data from this study were then compared to the rapidly growing number of peatland C balance studies across boreal and temperate regions. The trend in NEE and CH4 flux with respect to MAWT was compared for the five ecotypes in this study and literature data from degraded/restored/recovering peatlands, intact peatlands, and bare peat sites.

(S1) For this model, GPPmax is the maximum rate of primary production at light saturation, and b is the light intensity at which the GPP is half of GPPmax. The negative sign is for sign convention to account for carbon uptake to the peatland. This model has been used in some studies (e.g. Laine et al., 2006, Strack et al., 2014 with a constant GPPmax,, which has the advantage of being simple with few fitting parameters. However, the assumption of a constant GPPmax (tested in Table S1) fails to account for much of the variability found in the field data for this study.
To account for the seasonal variability in GPPmax, previous studies (e.g. Wilson et al., 2013;Wilson et al. 2016b) have added a green leaf area term to the GPP model, where green leaf area was determined in the field using a metric presented in Wilson et al. (2007). Green leaf area was found to vary in a sinusoidal way through-out the year and is different for each species of plant (Wilson et al., 2007). However, green leaf area is an unusual and somewhat labor intensive piece of field data to collect on a large scale, especially when collars contain a diverse mixture of plant species. Further, the total green leaf area for a plot has to be estimated or modeled based on a sub-sample of plants in the plot, with a potential for measurement bias.
Thus, for this work, rather than use green leaf area, Julian day of the year was introduced into the model according to Eq. S2.
= −( + * sin (( + 215) 365 * 2 )) ⁄ (S2) In Eq. S2, the a and c terms are an empirical parameters fit to the field data for each collar. The a term is equivalent to the average annual GPPmax, and the c term is the relative seasonal variation in GPPmax throughout the year.
Additionally, the modelled GPP was scaled by a temperature effect and a water table effect. The temperature effect on GPP included in Eq. 1 (i.e. exp(T5cm*d)) is similar to results from previous studies (e.g. Piechl et al. 2014). The water table effect on GPP included in Eq. 1 (i.e. (1 + * )) was taken from Wilson et al., (2016b). Combining Eq. S2 and Eq. S1 together with the temperature and water level scaling effects gives the base model for calculating GPP (Eq. 1).
Numerous other variations of the temperature effect, water table effect, and seasonal effect on GPPmax were also tested to the fit of the field data (Table S1), but the combination in Eq. 1 was found best explain the variation in the field data for each of the 29 collars based on a number of metrics (r 2 , SSQ of the residuals, slope). Table S1. Some example variations of empirical GPP models, which were tested to the fit of the field data in developing Eq. 1. With exponential temperature and linear water table effect = −( + * sin ( 365 * )) * ⁄ + * ( 5 * ) * (1 + * )

ER Modelling
Ecosystem respiration (ER) is modeled according to the T5cm and WT. The model used in this study (i.e. Eq. 2 in the main body of the paper) was taken directly from Wilson et al., (2016b). The present study uses the model for a very similar purpose to Wilson et al., (2016b); that is scaling up chamber measurements to model ER over annual time scale in the Irish climate. As with GPP modeling, numerous empirical models were tested to the fit of the field data (Table S2), and Eq. 2 best explained the variation of the field data. A more complex model was tested for modelling ER, which included a sinusoidal variation with respect to Julian day of the year (bottom row of Table S2) similar to Eq. 1. This effect was included because the ER would be expected to be at least partially related to the green leaf area, which would vary over the year. In this case, the more complex model did explain the variation in the field data slightly better than Eq. 2, but this was at the expense of 2 additional fitting parameters. Thus, the slight improvement in fit of this model did not justify the higher degree of complexity.

Tables on NEE model information
The empirical fitting parameters in Eq. 1 and Eq. 2 along with the standard error and statistical significance of the fitting parameters were determined using Minitab 2018©. Table S3 and Table  S4 give information on model fitting statistics such n-values, STDEV of the residuals, r 2 , range of the data, and slope of modelled vs. measured data for each of the 29 collars, for the Eq. 1 and Eq. 2, respectively. Table S5 and S6 give the best fit model parameters along with standard error and statistical significance of those parameters for each of the 29 collars, for Eq. 1 and Eq. 2, respectively.

Methane modelling
Due to equipment issues, the CH4 flux field measurements were collected from May 11, 2017 to January 5, 2018 rather than the entire calendar year of 2017. This meant that the sampling period had a bias toward the warmer part of the year, which likely would have higher CH4 emissions. To account for this bias in sampling period, the collar average CH4 flux was scaled by a factor of 0.80. This factor was derived from an empirical model based on field measurements, which was developed to determine the temporal variations in CH4 flux. This empirical model is described here: The field data were first normalized by dividing each measurement by the collar average CH4 flux. Then, the normalized CH4 flux data from all collars (n=230) were pooled together.
With this pooled data set, the variations in CH4 flux were modelled as a function of the JDAY and the T5cm according to Eq. S3. This equation was adjusted to fit the field data based on the r 2 value and the sum of the squares of the residuals, and is composed of an exponential temperature effect multiplied by a seasonal effect. These separate components of the model over 2016 and 2017 can be seen in Fig. S1. It was found that soil temperature alone did not account for the temporal variations in CH4 flux as well as a temperature effect multiplied by JDAY effect.
where CH4 flux is in g-C-CH4 m -2 hr -1 , and k is a scaling factor. It was found from Eq. S3 that the average CH4 flux over the entire 2017 calendar year was 0.80 times the average modelled CH4 flux of the field sampling dates. This scaling factor was thus used to account for the bias in sampling period. As a check, the modelled values were re-scaled by the collar average flux and compared to the measured CH4 flux values with an overall r 2 of 0.61 and a slope near unity (0.98) (Fig. S2).

Supplemental Section 2. Collar and ecotype aspects of the carbon balance measured in this study
Other Carbon losses or gains -(g-C m -2 yr -1 )                Range of fluxes given only. DOC flux estimated but not measured in the field. CH4 flux estimated but not directly measured at this site. CH4 flux for bare peat areas not directly reported in the paper, it is calculated from the total reported landscape flux, the flux for vegetated areas, and the percent vegetation cover. Estimated from plots presented in paper DOC fluxes are not measured at the outflow of the catchment and are exceptionally low.