CO 2 emissions from peat-draining rivers regulated by water p H

. Southeast Asian peatlands represent a globally signiﬁcant carbon store that is destabilized by deforestation and the transformation into plantations, causing high carbon dioxide (CO 2 ) emissions from peat soils and increased leaching rates of peat carbon into rivers. While these high carbon leaching rates and consequently high DOC concentrations indicate global model studies assumed that CO 2 emissions from peat-draining rivers would be high, estimates based on ﬁeld data suggest they are only moderate. In this study we offer an explanation for this phenomenon and show that carbon decomposition is hampered 5 by the low p H in peat-draining rivers, which limits CO 2 production in and emissions from these rivers. We ﬁnd an exponential p H limitation that shows good agreement with laboratory measurements from high latitude peat soils. Additionally, our results suggest that enhanced input of carbonate minerals increase CO 2 emissions from peat-draining rivers by counteracting the p H limitation. As such inputs of carbonate minerals occur due to human activities like deforestation of river catchments, liming in plantations and enhanced weathering projects, our study points out an important feedback mechanism of those practices.


Introduction
Rivers and streams emit high amounts of carbon dioxide (CO 2 ) to the atmosphere (Cole et al., 2007), but estimates of these emissions (0.6 − 1.8 PgC yr −1 ) are highly uncertain (Aufdenkampe et al., 2011;Raymond et al., 2013). Studies agree that more than three-quarters of the global river CO 2 emissions occur in the tropics (Raymond et al., 2013;Lauerwald et al., 2015).
River CO 2 emissions are controlled by the partial pressure difference between CO 2 in the atmosphere and in the river water 15 (Raymond et al., 2012), whereby riverine CO 2 is fed by decomposition of organic matter that is leached from soils (Wit et al., 2015). Model-based studies suggest Southeast Asia as a hotspot for river CO 2 emissions (Lauerwald et al., 2015;Raymond et al., 2013) due to the presence and degradation of carbon-rich peat soils.
About half of the known tropical peatlands are located in Southeast Asia, whereby 84 % of these are Indonesian peatlands, mainly on the islands of Sumatra, Borneo and Irian Jaya (Page et al., 2011). Already in 2010, land use changes affected 90% 20 of the peatlands located on Sumatra and Borneo (Miettinen and Liew, 2010) and turned them from CO 2 sinks to CO 2 sources (Hooijer et al., 2010). Enhanced decomposition in disturbed peatlands additionally increases the leaching of organic matter from soils into peat-draining rivers Moore et al., 2013). According to Regnier et al. (2013), land use its tropical climate with high precipitation rates that range between 120 mm in July and 310 mm in November with an annual mean of 2,700 mm yr −1 (Yatagai et al., 2020). Due to deforestation and conversion into plantations, today less than one-third of those Southeast Asian peatlands remain covered by peat swamp forests, while in 1990 it were more than three-quarters (Miettinen et al., 2016). Southeast Asian rivers mostly originate in mountain regions and cut through coastal peatlands on their way to the ocean (Fig. 1). Measurement data included in this study were obtained in river parts that flow through peat soils to 60 capture the influence of peatlands on the carbon dynamics in the rivers. The collective data were derived from four rivers on Borneo (Sarawak, Malaysia) and six rivers on Sumatra (Indonesia).
The investigated rivers on Borneo are the Rajang, Simunjan, Sebuyau and Maludam and the rivers surveyed on Sumatra are the Rokan, Kampar, Indragiri, Batang Hari, Musi and Siak (Fig. 1). We additionally include data from the Siak's tributaries Tapung Kiri, Tapung Kanan and Mandau. River peat coverages range from 4 % in the Musi catchment to 91 % in the Maludam catchment, whereby the bigger rivers that originate in the uplands generally have lower peat coverages than smaller coastal rivers.

Campaigns and measurements
Data were derived from a total of 16 campaigns in Sumatra and Sarawak (Tab. A1). For the Indonesian rivers, ten measurement campaigns between 2004 and 2013 were conducted. We use published data from Baum et al. (2007)  For the Malaysian rivers, measurements were performed in six campaigns between 2014 and 2017. We use data published by Müller-Dum et al. (2018) for the Rajang river and by Müller et al. (2015) for the Maludam campaigns in 2014 and 2015. Additional campaigns for this study were conducted in March 2015 at the Simunjan and Sebuyau rivers as well as in January 2016,

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March 2017 and July 2017 at the Simunjan, Sebuyau and Maludam rivers. Measurements of DOC, CO 2 and O 2 concentrations as well as pH, water temperatures (T ) and gas exchange coefficients (k 600 ) for these additional campaigns were performed in the same manner as during the 2014 Maludam campaign (Müller et al., 2015). However, due to technical problems, the CO 2 , O 2 and pH data measured at the Simunjan river in 2016 were ignored for our analysis. Table 1 lists the averaged river parameters, including the catchments' peat coverages and atmospheric CO 2 fluxes.

Additional parameters and catchment properties
Atmospheric CO 2 fluxes from the rivers were calculated from exchange coefficients and CO 2 concentrations according to

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whereat k CO2 (T ) was calculated from k 600 according to Wanninkhof (1992). pCO a 2 is the atmospheric partial pressure of CO 2 (≈ 400 µatm) and K CO2 describes the temperature dependent Henry coefficient for CO 2 , which was calculated according to Weiss (1974). The atmospheric O 2 fluxes (F O2 ) were derived analogously with k O2 (T ) calculated according to Wanninkhof (1992) and Henry coefficients for O 2 calculated according to Weiss (1970).

Quantification of the pH and O 2 impact on decomposition rates
The decomposition rate of DOC (R) is defined as molecules of CO 2 that are produced per available molecules of DOC during 105 a specific time step and thus represents the proportionality factor between the CO 2 production rate and the DOC concentration: As discussed before, R can be limited by O 2 concentrations and by pH. We used an O 2 limitation factor that is based on the Michaelis-Menten equation (L O2 = O2 Km+O2 ) as suggested by Pereira et al. (2017). For pH limitation, we consider two 110 approaches suggested in literature that are represented by an exponential limitation factor (L pH = exp (λ · (pH − pH 0 ))) as suggested by Williams et al. (2000) and by a linear limitation factor (L pH = pH pH0 ) as suggested by Sinsabaugh (2010).
For the exponential pH approach the CO 2 production rate due to DOC decomposition is given by where R max is the maximum decomposition rate, K m is the Michaelis constant for O 2 inhibition that is also called the half 115 saturation constant and gives the O 2 concentration at which O 2 limits decomposition by 50 % (Loucks and Beek, 2017), λ is the pH inhibition constant and pH 0 is a normalization constant that was set to 7.5 since this is reported to be the optimal pH for the activity of the decomposition impelling enzyme phenol oxidase (Pind et al., 1994;Kocabas et al., 2008). Equation (3) is only valid for pH pH 0 , as the limitation factor cannot be > 1. For higher water pH, a different approach would be needed.
However, for the rivers in this study Eq. (3) is sufficient since their pH is < 7.5 (Tab. 1). When O 2 concentrations and water 120 pH are high enough not to limit the decomposition rate, Eq.
The dissolved inorganic carbon (DIC) concentrations in peat-draining rivers, as a first approximation, result from an equilibrium between CO 2 emissions and CO 2 production by decomposition. Therefore, we optimized the parameters in Eq.
(3) such that the production of CO 2 in the water volume beneath a specific surface area equals the atmospheric CO 2 flux through this area.
The CO 2 production is calculated by multiplication of Eq.
(3) with the product of river depth d and surface area A and the CO 2 125 emissions are calculated by multiplication of Eq. (1) with the surface area A: Analogously, river O 2 concentrations result from an equilibrium between the atmospheric O 2 flux and O 2 consumption due to decomposition. During decomposition, the O 2 consumption is proportional to the CO 2 production (∆O 2 = −b · ∆CO 2 ). The proportionality factor b is usually < 1 since a fraction of the O 2 used for decomposition is taken from the oxygen content in 130 the dissolved organic matter (Rixen et al., 2008). Thus, the equilibrium between O 2 consumption within the water volume and O 2 flux through the surface area can be written as In order to compare these dependencies to measured data, Eq. (4) and Eq. (5) were analytically solved for CO 2 and for O 2 , respectively. The resulting equations are listed in Tab. 2. The analogously derived equations for CO 2 and O 2 that result from 135 the linear pH approach are listed in Tab. 3. Based on these equations, least squares optimizations were performed for the decomposition parameters R max , b, K m and λ such that CO 2 (DOC, pH, O 2 ) and O 2 (DOC, pH) are simultaneously optimized for the measured parameters of DOC, pH, T , CO 2 and O 2 . Table 2. Equations to derive CO2 and O2 for the exponential pH approach.
Equations to derive CO2 from measured DOC, pH and O2 as well as to derive O2 from measured DOC and pH. The parameters Rmax, Km, λ and b were derived by least squares optimization based on measured DOC, pH, T , O2 and CO2 data of the investigated rivers.
The equations in Tab. 2 and Tab. 3 depend on the river gas exchange coefficients for CO 2 (k CO2 ) and O 2 (k O2 ), which both depend on k 600 . Those exchange coefficients are poorly constrained and spatial as well as temporal extremely variable. The highly uncertain, we find a fairly good agreement between k 600 and river depths (d, Fig. A1). We therefore use a fixed ratio of k 600 /d = (7.0 ± 0.5) · 10 −6 s −1 for the least squares approximations. Table 3. Equations to derive CO2 and O2 for the linear pH approach.
Equations to derive CO2 from measured DOC, pH and O2 as well as to derive O2 from measured DOC and pH. The parameters Rmax, Km, λ and b were derived by least squares optimization based on measured DOC, pH, T , O2 and CO2 data of the investigated rivers.
3 Results excluded from the correlations due to strong deviations from the other campaigns that imply an additional process discussed in Sect. 4.3.
Ordinary least squares approximations were used to calculate linear correlations with DOC and pH and exponential correlations with CO2 and O2. Rivers included in a previous study investigating these correlations (Wit et al., 2015) are indicated by squares.

Correlation with peat coverage
The data presented in Tab. 1 yield a linear increase of river DOC concentration with peat coverage (Fig. 2a) as well as a negative linear correlation between river pH and peat coverage (Fig. 2b). The river CO 2 concentration shows a strong increase for peat coverages < 30 %. Yet, despite further increase in DOC concentrations, CO 2 concentrations in rivers with peat coverage > 30 % level off, resulting in a fairly constant CO 2 for peat coverages > 50 % (Fig. 2c). The river O 2 shows an opposite behaviour to 150 the CO 2 . O 2 concentrations initially decrease with increasing peat coverage and show a decline in the regression rate for high peat coverages, resulting in a minimum O 2 concentration of approximately 65 µmol L −1 (Fig. 2d).
However, the Simunjan seems to be an exception. Although we found that generally CO 2 concentrations stagnate for high peat coverages, extremely high CO 2 concentrations were measured during two campaigns in the Simunjan river (Fig. 2). In   In order to gain a better understanding of the pH and O 2 impacts on decomposition rates, we examined correlations of CO 2 and O 2 concentrations that were calculated based on the dependencies derived from both the linear (Tab. 3) and exponential (Tab. 2) approach of pH limitation with measured data. Figure 4 shows the correlation for linear pH limitation. Coefficients of determination for the CO 2 and O 2 correlations result to R 2 = 0.80 and R 2 = 0.87, respectively.
The decomposition parameters for this linear pH approach, derived via least squares approximation of the equation in Tab. 3   165 to measured data, result to a Michaelis constant for O 2 limitation of K m = (390 ± 509) µmol L −1 , a maximum decomposition rate of R max = (10 ± 11) µmol mol −1 s −1 and a fraction of O 2 consumption of b = (90 ± 25) %. These values represent pH limitations in the rivers that lower decomposition rates and therewith CO 2 production by between 6 % in the Batang Hari and   Tab. 2 which represent exponential pH limitation of decomposition rates. Each data point represents one river. Grey data points are excluded from the correlation since the data for these rivers (Kampar and Rokan) are based on less than three campaigns within the same season.
(3) and the parameters in Tab

Carbon dynamics in peat-draining rivers
The linear correlations observed between peat coverage and DOC (Fig. 2a) as well as pH (Fig. 2b) agree with results by Wit et al. (2015) and confirm the importance of peat soils as a major DOC source to these rivers, whereas the decomposition of DOC and leaching of organic acids from peat areas lower the pH. The initial increase of CO 2 conentrations (Fig. 2c) and decrease of O 2 concentrations (Fig. 2d) with peat coverage can be explained by increased DOC decomposition due to higher 185 DOC concentrations and also agrees with the results of Wit et al. (2015).
The CO 2 stagnation we observe for rivers of higher peat coverages (Fig. 2c) agrees with moderate CO 2 emissions that were stated for those rivers (Müller et al., 2015;Moore et al., 2013) and according to Eq. (3) can be explained by the pH limitation. A similar pattern of stagnating CO 2 concentrations has been observed in river sections of high DOC at the Congo river (Borges et al., 2015), indicating that the underlying process is valid not only for Southeast Asian rivers but for tropical peat-draining 190 rivers in general.

Exponential pH limitation of decomposition rates
As shown, we were able to reproduce the stagnation in CO 2 and O 2 concentrations by introducing O 2 and pH limitations for decomposition rates in the rivers. Model approaches of both exponential and linear pH limitation reproduce the observed stagnation in CO 2 and O 2 concentrations and result in reasonably good correlations with the measured concentrations ( Fig. 4   195 and Fig. 3).
The fractions of O 2 consumption by decomposition that we derived for both approaches, with b = (81 ± 10) % and b = (90 ± 25) %, agree with the fraction of 0.8 that was calculated based on the oxygen to carbon ratio in peat soils (Rixen et al., 2008).
The maximum decomposition rates of 4 µmol mol −1 s −1 for the exponential approach and 10 µmol mol −1 s −1 for the linear approach agree with global soil phenol oxidase activity data published by Sinsabaugh et al. (2008) that stated global average 200 soil phenol oxidase activity of 70.6 µmol h −1 per g organic matter. For a carbon content in organic matter of 38 mmol g −1 (Sinsabaugh, 2010) this represents approximately 0.5 µmol mol −1 s −1 , while sites of high phenol oxidase activity are listed with up to 3 µmol mol −1 s −1 (Sinsabaugh et al., 2008).
However, we assume the exponential limitation to be more realistic than the linear limitation as it is better in representing river CO 2 especially for high CO 2 concentrations which are most strongly effected by the pH limitation. This assumption is draining rivers is relatively small (between 3 and 10 %, Tab. 6) and consequentially a majority of the limitation is caused by the low pH in peat-draining rivers that we found to limit the decomposition rates in rivers of high peat coverage (low pH) by up to 85 % (Tab. 6).
The calculated exponential pH coefficient of λ = 0.5 ± 0.1 is similar to coefficients reported for high latitude peat soils (λ = 0.65 & λ = 0.77) that were determined via laboratory measurements of phenol oxidase activity (Williams et al., 2000). The fact that the exponential inhibition by pH can be found in those high latitude peat soils as well as in tropical peat-draining rivers suggests that the investigated correlations and processes are also relevant in other regions and that soil and water pH are important regulators of global carbon emissions.

Disruption of the pH limitation by carbonates
Typically, concentrations of particulate carbonate in peat-draining rivers are low (Wit et al., 2018). However we observed high 225 CaCO 3 concentrations for the Simunjan 2 campaigns, which show high DOC and CO 2 concentrations (Tab. 4). Possible causes for high carbonate concentrations during these campaigns could be increased erosion of mineral soils due to deforestation in mountain regions upstream or liming practices in plantations along the river. In either case, high carbonate concentrations at such a low pH indicate high dissolution of carbonates which might have counteracted a decrease in pH due to decomposition of DOC. This seems to have suspended the natural pH limitation of decomposition in peat-draining rivers which could explain 230 the high CO 2 concentrations observed during those two Simunjan campaigns (Tab. 4).

Implications and outlook
The stagnation in CO 2 we observe for high peat coverages provides an explanation for the disagreement between model studies that state extremely high CO 2 emissions from Southeast Asian rivers (Raymond et al., 2013;Lauerwald et al., 2015) and measurement-based studies that state rather moderate emission rates (Wit et al., 2015;Müller et al., 2015). The pH limitation 235 of decomposition that we derive to explain the observed CO 2 stagnation should be included to improve future model studies and accurately capture river CO 2 emissions from tropical peat areas.
The response on carbonate enrichment that we observe at the Simunjan river represents another important process that should be considered for anthropogenic activities like liming and enhanced weathering. Liming is a common practice to enhance soil fertility in plantations and enhanced weathering is a carbon dioxide removal strategy (Field and Mach, 2017) during which 240 atmospheric CO 2 is transformed into carbonates (Beerling et al., 2020). The resultant increase in carbonate concentrations and pH could cause a strong increase of decomposition rates and thereby CO 2 production and emission that would counteract the CO 2 uptake, which is not included in current estimates of enhanced weathering efficiencies (Taylor et al., 2016;Beerling et al., 2020).

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Our study shows that CO 2 concentrations in and emissions from Southeast Asian rivers stagnate for high peat coverages of the river catchments. Despite further increases in river DOC concentrations, CO 2 concentrations are fairly constant for peat coverages > 50 %. We found that this stagnation is caused by low water pH in rivers of high peat coverage that hampers decomposition rates. This process provides an answer to the question why, in contrast to the high DOC export, CO 2 emissions from tropical peat-draining rivers are more moderate.
We found an exponential limitation of decomposition by pH. Our calculations suggest that the low pH in rivers of high peat coverage reduces decomposition rates and thereby CO 2 production within the rivers by up to 85 %. Although this study is based on measurements in Southeast Asian peat-draining rivers, comparisons to laboratory studies of decomposition in temperate peat soils suggest that the investigated correlations and processes are also relevant in other regions and that soil and water pH are important regulators of global carbon emissions.

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As observed in the Simunjan river, one cause for increased water pH in peat-draining rivers can be the input of carbonates.
We found that CO 2 concentrations during the Simunjan campaigns that were accompanied by enhanced concentrations of suspended carbonates were significantly higher than those during campaigns of low carbonate concentrations, resulting in CO 2 emissions from this river that were increased by almost 100 %. We discussed that sources for enhanced carbonate concentrations can be rock weathering or soil erosion upstream of coastal peatland areas, or liming practices in plantations along the rivers, 260 which are common practice to improve plant growth on acidic soils.
This carbonate impact should be considered when discussing the efficiency of enhanced weathering, which is discussed as one of the possible measures to extract and bind anthropogenic CO 2 by transferring it to carbonate. The resultant pH increase, in regions of high peat coverage could lead to enhanced decomposition and thereby emissions of CO 2 from rivers and soils.
Further studies are needed to quantify the impact of the derived processes on enhanced weathering efficiencies.

Notes
Of the three available files, the product used was TROP_SUBTROP_PeatV21_2016_CIFOR.7z Those three products lead to highly different results (Tab. B2). We observed a tendency that CIFOR leads to smaller peat coverage than FAO and GFW. This is because CIFOR misses some, but not all peat areas that are known to be under industrial 280 plantations. Gumbricht et al. (2017) already pointed out that their model underestimates peatland area in Sumatra because peats are largely drained, which the model does not capture. However, in the Musi and Batang Hari catchment, CIFOR sees larger peat areas than FAO and GFW, which means that some peatlands might be missing in those maps. We decided to use the GFW maps for several reasons: 1) CIFOR seems to miss peat under industrial plantations, which is still relevant for river carbon dynamics. Therefore, we chose not to use the CIFOR maps. 2) Between GFW and FAO, GFW is more 285 recent than FAO for Indonesia. For Sarawak (Malaysia), both are based on the 1968 soil map by the Land Survey Department, but FAO uses a 10-fold coarser scale than the 1968 soil map (1:5,000,000 compared to 1:500,000). Thus, the GFW product was used. & 3) GFW maps are based on official information, and we believe that the local authorities would know best about the peatland distribution in their country.
Similar to the peat coverage, the publications from which we use data in our study all had different approaches to determining 290 catchment size -either including (Müller-Dum et al., 2018) or excluding (Wit et al., 2015) smaller sub-catchments. In our study, we aimed to unify those different approaches. Therefore, we recalculated catchment areas from one single data product (HydroSHEDS, (Lehner et al., 2006)) including sub-catchments that were identified using HydroSHEDS flow directions. The Simunjan catchment is included in the bigger Sadong catchment in HydroSHEDS. Therefore, it was manually delineated using HydroSHEDS flow directions.