Southeast Asian peatlands store 42 Pg soil carbon across an area of 271 000 km2 . More than 97 % of these peat soils are located in lowlands . 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 mmyr-1 . 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 . Southeast Asian rivers mostly originate in mountain regions and cut through coastal peatlands on their way to the ocean (Fig. ). 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 .

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. ). 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.

Data were derived from a total of 16 campaigns in Sumatra and Sarawak (Fig. , Table  in the Appendix). For the Indonesian rivers, 10 measurement campaigns between 2004 and 2013 were conducted. We use published data from for the Mandau, Tapung Kanan, and Tapung Kiri rivers; from for the Siak, Indragiri, Batang Hari, and Musi rivers; and from 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 and for the Rajang River and by 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 . 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  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.

River catchment sizes were derived from Hydro-SHEDS 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 . The Malaysian peat map was made available by 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 .

Atmospheric CO2 fluxes from rivers were calculated from CO2 gas exchange coefficients and river CO2 concentrations according to 1FCO2=kCO2(T)⋅CO2-KCO2(T)⋅pCO2a. Exchange coefficients for CO2 (kCO2(T)) were calculated from k600 and water temperature according to as 2kCO2=k600⋅1911.1-118.11⋅T+3.4527⋅T2-0.041320⋅T3600-n. An exponent of n=1/2 valid for rough surfaces; was used for the rivers. The temperature T is given in degrees Celsius. pCO2a is the atmospheric partial pressure of CO2 (≈400 µatm), and KCO2 describes the temperature-dependent Henry coefficient for CO2, which was calculated according to as 3ln⁡KCO2=-58.0931+90.5069⋅100T+22.2940⋅ln⁡T100. kCO2 and KCO2, derived for the individual rivers, are listed in Table .

Atmospheric O2 fluxes (FO2) were derived analogously to FCO2, with kO2(T) calculated according to as 4kO2=k600⋅1800.6-120.10⋅T+3.7818⋅T2-0.047608⋅T3600-n and Henry coefficients for O2 (KO2) calculated according to as 5ln⁡KO2=-58.3877+85.8079⋅100T+23.8439⋅ln⁡T100. kO2 and KO2 for the individual rivers in this study are also listed in Table .

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: 6R=ΔCO2DOC⋅Δt⇒∂CO2∂t=R⋅DOC. 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 (LO2=O2Km+O2) as suggested by . For pH limitation, we consider an exponential limitation factor (LpHexp=exp⁡λ⋅pH-pH0) as suggested by and a linear limitation factor (LpHlin=pHpH0) as suggested by . 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 H+λln⁡(10).

The CO2 production rates due to DOC decomposition for the linear and the exponential pH limitation approach are thus defined as follows. 7∂CO2∂tlin=Rmax⋅LO2⋅LpHlin⋅DOC=Rmax⋅O2Km+O2⋅pHpH0⋅DOC∂CO2∂texp=Rmax⋅LO2⋅LpHexp⋅DOC=Rmax⋅O2Km+O2⋅exp⁡λ⋅pH-pH0⋅DOC Rmax is the maximum decomposition rate. Km 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 % . 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 . Calculations of pH0 based on our data and the exponential pH approach are described in Appendix . They yield an optimum pH of approximately 7.2 and thus agree well with the pH0 of 7.5 used in this study.

LO2 and LpH can take values between 0 and 1. Thus, Eq. () is only valid for pH⩽pH0. For higher water pH, a different approach would be needed. However, for the rivers in this study Eq. () is sufficient since their pH is <7.5 (Table ). 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-LpH) for pH limitation and (1-LO2) for O2 limitation. The total fraction by which pH and O2 limit decomposition is given by (1-LpH⋅LO2). When O2 concentrations and water pH are high enough not to limit the decomposition rate, Eq. () simplifies to Eq. () with R=Rmax.

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. () 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. () with the product of river depth d and surface area A, and the CO2 emissions are calculated by multiplication of Eq. () with the surface area A: 8d⋅A⋅Rmax⋅LO2⋅LpH⋅DOC=A⋅kCO2(T)⋅CO2-KCO2(T)⋅pCO2a.

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 (ΔO2=-b⋅ΔCO2). 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 . Thus, the equilibrium between O2 consumption within the water volume and O2 flux through the surface area can be written as 9-b⋅d⋅A⋅Rmax⋅LO2⋅LpH⋅DOC=A⋅kO2(T)⋅O2-KO2(T)⋅pO2a.

In order to compare these dependencies to measured data, Eq. () and Eq. () were analytically solved for CO2 and for O2, respectively. The resulting equations based on linear pH limitation (LpHlin=pHpH0) are listed in Table . The analogously derived equations for CO2 and O2 based on the exponential pH approach LpHexp=exp⁡λ⋅pH-pH0 are listed in Table .

Based on these equations, least-squares optimizations were performed to derive the decomposition parameters Rmax, b, Km, 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  and depend on the river gas exchange coefficients for CO2 (kCO2) and O2 (kO2), 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 , calculations based on wind speed and catchment parameters , and balance models of water parameters . Although all of those estimates remain highly uncertain, we find a fairly good agreement between k600 and river depths (d, Fig. ). We therefore use a fixed ratio of k600/d=(7.0±0.5)×10-6s-1 for the least-squares optimizations rather than individual exchange coefficients and depths of the rivers.

The two Michaelis constants for O2 limitation of decomposition, derived for the linear and exponential pH limitation approaches, differ strongly (Table ). 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 40µmolL-1 are suggested for the O2 impact on phenol oxidase, depending on the phenolic species .

The linear pH limitation approach yields a Michaelis constant of Km≈390µmolL-1. This constant is higher than the O2 concentration in atmospheric equilibrium (≈280µmolL-1), which implies an oxygen deficit at atmospheric conditions that does not exist . However, though the derived Km value for this linear pH limitation is unrealistically high, this does not necessarily negate the linear pH approach. High parameter interdependence between Km and Rmax complicate the computation of these decomposition parameters (Sect. ). To disentangle the impact of the intercorrelated parameters, additional least-squares optimizations at fixed Km values ranging from 1 to 40µmolL-1 were performed (Sect. ). These optimizations result in maximum decomposition rates of Rmax = (1.4–2.4) µmolmol-1s-1 and O2 consumption factors of b=(102-109)% and therewith do not agree with literature values of these parameters (Rmax⩾3µmolmol-1s-1 and b≈80%; ).

The exponential pH limitation approach yields a Michaelis constant of Km≈6µmolL-1. This value is in good agreement with the literature data of 1 to 40µmolL-1 . Its large uncertainty (>400 %, Table ) 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 50µmolL-1 . Thus, the O2 limitation in peat-draining rivers is relatively small (between 3 % and 10 %, Table ). 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 ).

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 Rmax and b for fixed Km disagree with literature data and thus further disprove the linear approach (Sect. ).

The exponential pH coefficient results in λ=0.5±0.1. Thus, in terms of H+ activity the correlation is given by H+0.5ln⁡(10), 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 . 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.