2.1.1 Study area

Southeast Asian peatlands store 42 Pg soil carbon across an area of 271 000 km² (Hooijer et al., 2010). More than 97 % of these peat soils are located in lowlands (Hooijer et al., 2006). The development of peatlands in Southeast Asia is favoured by its tropical climate with high precipitation rates that range between 120 mm in July and 310 mm in November with an annual mean of 2700 mm yr⁻¹ (Yatagai et al., 2020). Due to land-use changes like deforestation and the conversion into plantations, today less than one-third of those Southeast Asian peatlands remain covered by peat swamp forests, while in 1990 it was 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 capture the influence of peatlands on the carbon dynamics in the rivers. The impact of sampling locations and seasonality is discussed in Appendix B.

Figure 1Map of river catchments with the location of peat areas. Blue lines indicate the main rivers. Blue shaded areas outline the river basins, and brown areas indicate peatlands. Coloured data points indicate the sampling stations of the individual campaigns.

The collective data for this study 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.

2.1.2 River expeditions and measured parameters

Data were derived from a total of 16 campaigns in Sumatra and Sarawak (Fig. 1, Table A1 in the Appendix). For the Indonesian rivers, 10 measurement campaigns between 2004 and 2013 were conducted. We use published data from Baum et al. (2007) for the Mandau, Tapung Kanan, and Tapung Kiri rivers; from Wit et al. (2015) for the Siak, Indragiri, Batang Hari, and Musi rivers; and from Rixen et al. (2016) for the Rokan and Kampar rivers. CO₂ measurements are available for the campaigns performed after 2008.

For the Malaysian rivers, measurements were performed in six campaigns between 2014 and 2017. We use data published by Müller-Dum et al. (2019) and Martin 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 and March and July 2017 at the Simunjan, Sebuyau, and Maludam rivers. Measurements of DOC, CO₂, and O₂ concentrations as well as water pH, water temperatures (T), and gas exchange coefficients (k₆₀₀) for these additional campaigns were performed in the same manner as during the 2014 Maludam campaign (Müller et al., 2015). However, due to instrumental problems, the CO₂, O₂, and pH data measured at the Simunjan River in 2016 were not available for our analysis. Table 3 lists the averaged river parameters, including the catchments' peat coverages and atmospheric CO₂ fluxes.

During the January 2016 and March and July 2017 campaigns, concentrations of particulate inorganic carbon (PIC) in the form of CaCO₃ were measured in addition to the other parameters. These data are not included in the before-mentioned studies. Therefore, we describe the measurement principle here. Discrete water samples, taken from approximately 1 m below the water surface, were filtered through pre-weighed and pre-combusted glass fibre filters (0.7 µm) to sample particulate material within the water volume. To determine the particulate carbon (organic and inorganic), the samples were catalytically combusted at 1050 ^∘C, and combustion products were measured by thermal conductivity using an Euro EA3000 elemental analyser. The PIC was determined from the difference between this total particulate carbon and particulate organic carbon that was measured after addition of 1 M hydrochloric acid in order to remove the inorganic carbon from the sample.

2.1.3 River catchment size and peat coverage

River catchment sizes were derived from Hydro-SHEDS (Lehner et al., 2008) at 15 s resolution in WGS 1984 Web Mercator Projection. Sub-basins belonging to the catchments were identified using the HydroSHEDS 15 s flow direction data set and added to the main basins. The estimated accuracy of final catchment lines is 0.4 %.

Catchment peat coverage was derived from peat maps downloaded from https://www.globalforestwatch.org/ (last access: 10 December 2018) for Indonesia and Malaysia. The Indonesian peatland map was published by the Indonesian Ministry of Agriculture (MoA, 2012). The Malaysian peat map was made available by (Wetlands International, 2004) and is based on a national inventory by the Land and Survey Department of Sarawak (1968). Both maps include peatlands in different conditions, from undisturbed peat swamp forest to disturbed peat under plantations, which is nowadays widespread in those countries. Peat coverage was determined from the areal extent of peatlands in the catchment divided by catchment size. Peat coverages derived using other peat maps are compared in Appendix C.

2.2.1 Gas exchange between rivers and the atmosphere

Atmospheric CO₂ fluxes from rivers were calculated from CO₂ gas exchange coefficients and river CO₂ concentrations according to

Exchange coefficients for CO₂ ($k_{{\text{CO}}_{\mathrm{2}}}\left(T\right)$) were calculated from k₆₀₀ and water temperature according to Wanninkhof (1992) as

An exponent of $n=\mathrm{1}/\mathrm{2}$ (valid for rough surfaces; Zappa et al., 2007) was used for the rivers. The temperature T is given in degrees Celsius. pCO${}_{\mathrm{2}}^{\text{a}}$ is the atmospheric partial pressure of CO₂ (≈400 µatm), and $K_{{\text{CO}}_{\mathrm{2}}}$ describes the temperature-dependent Henry coefficient for CO₂, which was calculated according to Weiss (1974) as

$k_{{\text{CO}}_{\mathrm{2}}}$ and $K_{{\text{CO}}_{\mathrm{2}}}$, derived for the individual rivers, are listed in Table A2.

Atmospheric O₂ fluxes ($F_{{\text{O}}_{\mathrm{2}}}$) were derived analogously to $F_{{\text{CO}}_{\mathrm{2}}}$, with $k_{{\text{O}}_{\mathrm{2}}}\left(T\right)$ calculated according to Wanninkhof (1992) as

and Henry coefficients for O₂ ($K_{{\text{O}}_{\mathrm{2}}}$) calculated according to Weiss (1970) as

$k_{{\text{O}}_{\mathrm{2}}}$ and $K_{{\text{O}}_{\mathrm{2}}}$ for the individual rivers in this study are also listed in Table A2.

2.2.2 Decomposition rates and their dependency on pH and O₂

The decomposition rate of DOC (R) is defined as molecules of CO₂ that are produced per available molecule of DOC during a specific time step and thus represents the proportionality factor between the CO₂ production rate and the DOC concentration:

As discussed before, R can be limited by O₂ concentrations and by pH. We use an O₂ limitation factor that is based on the Michaelis–Menten equation ($L_{{\text{O}}_{\mathrm{2}}}=\frac{{\text{O}}_{\mathrm{2}}}{K_{\text{m}}+{\text{O}}_{\mathrm{2}}}$) as suggested by Pereira et al. (2017). For pH limitation, we consider an exponential limitation factor ($L_{\text{pH}}^{\text{exp}}=\exp \left(\mathit{\lambda }\cdot \left(\text{pH}-{\text{pH}}_{\mathrm{0}}\right)\right)$) as suggested by Williams et al. (2000) and a linear limitation factor ($L_{\text{pH}}^{\text{lin}}=\frac{\text{pH}}{{\text{pH}}_{\mathrm{0}}}$) as suggested by Sinsabaugh (2010). Considering the definition of pH as the negative decadic logarithm of H⁺ activity ({H⁺}), the exponential limitation factor is equivalent to a linear correlation with ${\left\{{\text{H}}^{+}\right\}}^{\frac{\mathit{\lambda }}{\ln \left(\mathrm{10}\right)}}$.

The CO₂ production rates due to DOC decomposition for the linear and the exponential pH limitation approach are thus defined as follows.

R_max is the maximum decomposition rate. K_m is the Michaelis constant for O₂ inhibition. It is also called the half-saturation constant and gives the O₂ concentration at which O₂ limits decomposition by 50 % (Loucks and Beek, 2017). λ is the exponential pH inhibition constant, and pH₀ 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). Calculations of pH₀ based on our data and the exponential pH approach are described in Appendix D4. They yield an optimum pH of approximately 7.2 and thus agree well with the pH₀ of 7.5 used in this study.

$L_{{\text{O}}_{\mathrm{2}}}$ and L_pH can take values between 0 and 1. Thus, Eq. (7) is only valid for pH ⩽ pH₀. For higher water pH, a different approach would be needed. However, for the rivers in this study Eq. (7) is sufficient since their pH is <7.5 (Table 3). The limitation factors represent the fraction of decomposition that remains after the limitation by the parameter. Later on, we refer to the fraction by which decomposition is limited, which is (1−L_pH) for pH limitation and ($\mathrm{1}-L_{{\text{O}}_{\mathrm{2}}}$) for O₂ limitation. The total fraction by which pH and O₂ limit decomposition is given by ($\mathrm{1}-L_{\text{pH}}\cdot L_{{\text{O}}_{\mathrm{2}}}$). When O₂ concentrations and water pH are high enough not to limit the decomposition rate, Eq. (7) simplifies to Eq. (6) with R=R_max.

2.2.3 Least-squares optimization to quantify the pH and O₂ impact on decomposition rates

As mentioned before, we base our calculations on the assumption that DIC concentrations in peat-draining rivers result from an equilibrium between CO₂ emissions and CO₂ production by decomposition. Thus, we optimized the parameters in Eq. (7) such that the production of CO₂ in the water volume beneath a specific surface area equals the atmospheric CO₂ flux through this area. The CO₂ production is calculated by multiplication of Eq. (7) with the product of river depth d and surface area A, and the CO₂ emissions are calculated by multiplication of Eq. (1) with the surface area A:

Analogously, river O₂ concentrations result from an equilibrium between the atmospheric O₂ flux and O₂ consumption due to decomposition. During decomposition, the O₂ consumption is proportional to the CO₂ production ($\mathrm{\Delta }{\text{O}}_{\mathrm{2}}=-b\cdot \mathrm{\Delta }{\text{CO}}_{\mathrm{2}}$). The proportionality factor b is usually <1 since a fraction of the O₂ used for decomposition is taken from the oxygen content in the dissolved organic matter (Rixen et al., 2008). Thus, the equilibrium between O₂ consumption within the water volume and O₂ flux through the surface area can be written as

In order to compare these dependencies to measured data, Eq. (8) and Eq. (9) were analytically solved for CO₂ and for O₂, respectively. The resulting equations based on linear pH limitation ($L_{\text{pH}}^{\text{lin}}=\frac{\text{pH}}{{\text{pH}}_{\mathrm{0}}}$) are listed in Table 1. The analogously derived equations for CO₂ and O₂ based on the exponential pH approach $\left(L_{\text{pH}}^{\text{exp}}=\exp \left(\mathit{\lambda }\cdot \left(\text{pH}-{\text{pH}}_{\mathrm{0}}\right)\right)\right)$ are listed in Table 2.

Table 1Equations to derive CO₂ and O₂ based on the linear pH approach.

Equations to derive CO₂ from measured temperature (T), DOC, pH, and O₂ as well as to derive O₂ from measured T, DOC, and pH. R_max, K_m, and b, derived via least-squares optimization using measured DOC, pH, T, O₂, and CO₂ data of the investigated rivers, are listed in Table 5.

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Table 2Equations to derive CO₂ and O₂ based on the exponential pH approach.

Equations to derive CO₂ from measured temperature (T), DOC, pH, and O₂ as well as to derive O₂ from measured T, DOC, and pH. R_max, K_m, λ, and b, derived via least-squares optimization using measured DOC, pH, T, O₂, and CO₂ data of the investigated rivers, are listed in Table 5.

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Based on these equations, least-squares optimizations were performed to derive the decomposition parameters R_max, b, K_m, and λ such that CO₂(DOC, pH, O₂, T) and O₂(DOC, pH, T) are simultaneously optimized for the measured parameters of DOC, pH, T, CO₂, and O₂.

The equations in Tables 1 and 2 depend on the river gas exchange coefficients for CO₂ ($k_{{\text{CO}}_{\mathrm{2}}}$) and O₂ ($k_{{\text{O}}_{\mathrm{2}}}$), which both depend on k₆₀₀. Those exchange coefficients are poorly constrained and spatially as well as temporally extremely variable. The k₆₀₀ values we list in this study are based on a variety of techniques, including floating chamber measurements (Müller et al., 2015), calculations based on wind speed and catchment parameters (Müller-Dum et al., 2019), and balance models of water parameters (Rixen et al., 2008). Although all of those estimates remain highly uncertain, we find a fairly good agreement between k₆₀₀ and river depths (d, Fig. A1). We therefore use a fixed ratio of $k_{\mathrm{600}}/d=(\mathrm{7.0}\pm \mathrm{0.5})\times {\mathrm{10}}^{-\mathrm{6}}{\mathrm{s}}^{-\mathrm{1}}$ for the least-squares optimizations rather than individual exchange coefficients and depths of the rivers.

4.2.1 Functional dependency of decomposition on O₂

The two Michaelis constants for O₂ limitation of decomposition, derived for the linear and exponential pH limitation approaches, differ strongly (Table 5). As discussed before, the Michaelis constant represents the O₂ concentration at which O₂ availability limits decomposition by 50 %. In literature, Michaelis constants between 1 and 40 µmol L⁻¹ are suggested for the O₂ impact on phenol oxidase, depending on the phenolic species (Fenoll et al., 2002).

The linear pH limitation approach yields a Michaelis constant of $K_{\text{m}}\approx \mathrm{390}\mathrm{\mu }\mathrm{mol}{\mathrm{L}}^{-\mathrm{1}}$. This constant is higher than the O₂ concentration in atmospheric equilibrium ($\approx \mathrm{280}\mathrm{\mu }\mathrm{mol}{\mathrm{L}}^{-\mathrm{1}}$), which implies an oxygen deficit at atmospheric conditions that does not exist (Vaquer-Sunyer and Duarte, 2008). However, though the derived K_m value for this linear pH limitation is unrealistically high, this does not necessarily negate the linear pH approach. High parameter interdependence between K_m and R_max complicate the computation of these decomposition parameters (Sect. D1). To disentangle the impact of the intercorrelated parameters, additional least-squares optimizations at fixed K_m values ranging from 1 to 40 µmol L⁻¹ (Fenoll et al., 2002) were performed (Sect. D2). These optimizations result in maximum decomposition rates of R_max = (1.4–2.4) $\mathrm{\mu }\mathrm{mol}{\mathrm{mol}}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$ and O₂ consumption factors of $b=(\mathrm{102}-\mathrm{109})\mathit{\%}$ and therewith do not agree with literature values of these parameters ($R_{\text{max}}\mathit{⩾}\mathrm{3}\mathrm{\mu }\mathrm{mol}{\mathrm{mol}}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$ and b≈80 %; Sinsabaugh et al., 2008; Rixen et al., 2008).

The exponential pH limitation approach yields a Michaelis constant of $K_{\text{m}}\approx \mathrm{6}\mathrm{\mu }\mathrm{mol}{\mathrm{L}}^{-\mathrm{1}}$. This value is in good agreement with the literature data of 1 to 40 µmol L⁻¹ (Fenoll et al., 2002). Its large uncertainty (>400 %, Table 5) is mainly caused by relatively high concentrations of O₂ in the rivers. Due to exchange with atmospheric O₂, the concentrations in all rivers exceed the median O₂ threshold to lethal hypoxic conditions of 50 µmol L⁻¹ (Vaquer-Sunyer and Duarte, 2008). Thus, the O₂ limitation in peat-draining rivers is relatively small (between 3 % and 10 %, Table A4). Consequentially a majority of the decomposition 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 % (Table A4).

4.2.2 Functional dependency of decomposition on pH

Our results indicate the exponential pH limitation of decomposition to be more realistic than the linear pH limitation. The exponential limitation better represents river CO₂, especially for high CO₂ concentrations which are most strongly affected by the pH limitation. The exponential limitation is additionally supported by the unrealistically high O₂ limitation resulting from the linear pH approach. The strong collinearity between decomposition parameters in the linear pH limitation approach complicates the interpretation of the parameters mentioned above. Additional calculations of the parameters R_max and b for fixed K_m disagree with literature data and thus further disprove the linear approach (Sect. D2).

The exponential pH coefficient results in $\mathit{\lambda }=\mathrm{0.5}\pm \mathrm{0.1}$. Thus, in terms of H⁺ activity the correlation is given by ${\left\{{\text{H}}^{+}\right\}}^{\frac{\mathrm{0.5}}{\ln \left(\mathrm{10}\right)}}$, which roughly equals the fifth root of H⁺ activity. The derived limitation coefficient is similar to coefficients reported for high-latitude peat soils (λ=0.65 and 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 pH and water pH are important regulators of global carbon emissions.