A semi-distributed process-based hydrological model (WSFS: Watershed Simulation and Forecasting System; Kolhinen et al., 2026), is included in Vemala (Fig. 1). The spatial simulation unit in runoff simulations is a sub-catchment, called third level sub-catchment, with a mean size of 60 km² (Catchment areas, Syke, 2025a, Fig. A1). For surface water routing and water quality simulations, these sub-catchments are divided into a fourth level of detail (Fig. A1) to take into account the variation of characteristics affecting hydrology and nutrient and carbon loading. Small brook or fourth level sub-catchments are defined by a river width greater than 2 m (Metadata: Shoreline10 from Syke and National Land Survey of Finland, NLS). The median size of the catchments in Vemala is 0.8 km² with 80 % of the catchments smaller than 2 km² (WSFS-Vemala, Syke, 2025f).

The unsaturated soil layer is represented by a 2-layer soil moisture model (surface and sub-surface), and a soil saturated layer characterizing groundwater. Water infiltrates from the surface layer to the sub-surface layer if the soil moisture content exceeds field capacity. The sub-surface layer produces the main part of the runoff to rivers and lakes and of the percolation to the groundwater (Jakkila et al., 2014). Runoff is produced from the surface layer only when the ground is frozen. Vemala simulates 40 different land-use and soil type combinations based on national soil (Natural Resources Institute Finland and Geological Survey of Finland, 2025) and land cover datasets (Corine land cover 2018, Syke, 2025b). This description enables the simulation of hydrological processes that vary on mineral and organic soils, accounting for distinct hydraulic conductivities and water holding properties of mineral and peat soils. Finnish soil maps (Natural Resources Institute Finland and Geological Survey of Finland, 2025; Fig. 2c) are used for soil type distribution. Specifically, six soil types organic, clay, till, silt, sand, and rocky soils have been used as input to the model for each small brook catchment. Corine Land Cover data (Syke, 2025b; Fig. 2b) was used to classify each small brook catchment into land use classes field, forested, bog, or built areas. This classification is essential for simulating evapotranspiration accurately.

There are considerable differences in hydrological conditions and organic carbon content in mineral and peat soils, leading to different TOC leaching patterns. These differences have been considered both in the hydrological and the terrestrial TOC process-based models (Fig. 1). In peat soils, shallow groundwater can contribute the most to runoff through baseflow, especially during prolonged dry periods (Mozafari et al., 2023). Shallow water tables with small range of fluctuation are characteristic for peat soils. Shallow groundwater can have significantly higher DOC concentrations than deep groundwater. This pattern probably results from occurrence and movement of shallow groundwater through the organic-rich surficial deposits (Gibson et al., 2000). By definition, peat soils contain more organic matter (>40 %, Lemola et al., 2018) than mineral soils, and SOC (solid organic C) vertical distribution is different in mineral and peat soils. In mineral soils the SOC content generally decreases with depth, whereas in organic soils it increases with depth (Hiederer, 2009).

Vemala TOC terrestrial model (Fig. 1) builds on Vemala-N model (Huttunen et al., 2016) and INCA-C model (Futter et al., 2007). The model represents two C storages in the soil: SOC and DOC. These pools are defined separately for different soil types and land use classes. The main inputs to the model are annual litter fall and the initial C storage in soil. Carbon exchanges between the SOC and DOC pools are represented through the following processes:

SOC can be disassociated into DOC, and DOC can be reassimilated into SOC.

The model distinguishes six land use and soil type combinations: agriculture on clay, coarse and peat soils, forest on mineral soils and on ditched peatlands as well as natural peat soils. Carbon mass balance of SOC and DOC storages for two soil layers (unsaturated soil layer and groundwater layer) is simulated daily. DOC produced in the unsaturated layer is percolated to the groundwater layer. Percolation is simulated in the hydrological model for each combination of land use and soil type class separately. Leaching of DOC (kg⁻¹ ha⁻¹ d⁻¹) is calculated as follows: mass of DOC in layers (kg ha⁻¹) is divided by soil moisture or groundwater storage (mm) to obtain the simulated concentration. DOC concentration is then multiplied by daily runoff (mm d⁻¹) from each soil layer to obtain the DOC load (kg ha⁻¹ d⁻¹) transported out from each layer (Eqs. 1 and 2): 1DOCleaching,1=mDOC,1soilmoisture+cfmoisture⋅runoff12DOCleaching,2=mDOC,2groundwaterstorage+cfgw⋅gwflow2 With, cf_moisture and cf_gw the plant unavailable water and groundwater adjustment parameters, which are manually calibrated for each land use/soil texture class. At the national scale, the spatial variability in the input data has been considered in the TOC model. Methodology of the calculation of the initial C content in agricultural soils is given in Appendix B and is based on field parcel data from soil laboratory Viljavuuspalvelu oy which contains soil organic matter (SOM) class (vm – low, m – medium, rm – rich, erm – very rich, mm – mull, Tm – peat soil; Table B1). Initial C content in mineral forest soils is based on Finnish multisource national forest inventory data (Mäkisara et al., 2016). Simulated initial C content decreases exponentially with the soil layer depth in mineral soils (Wen et al., 2020), whereas in peat soils carbon content is constant with depth. Annual litter fall data for forests is obtained from PREBAS model results for 16×16 m grids for all Finland and added to the soils in Vemala TOC model as daily input during autumn months. PREBAS combines carbon acquisition through photosynthesis, tree growth and soil carbon processes (Minunno et al., 2019). DOC production rates for peat soils are based on Laurén et al. (2019), and temperature dependency coefficient Q10 values, that describes relative change of C release rate under a 10° change in soil temperature, are calibrated. Soil temperature is simulated based on simulation of the energy flux between air, snow and soil layers, and distribution of energy to freeze the soil frost or to change soil temperature in the soil layers. DOC loads simulated by the TOC terrestrial model are calibrated against TOC observations in inland waters. TOC is mostly under a dissolved form (Mattsson et al., 2005) in Finnish rivers. Therefore, TOC is assumed to be fully dissolved and represents DOC in Vemala.

Vemala TIC terrestrial model development (Fig. 1) is based on a regression model between TIC concentration, using alkalinity as a proxy, and runoff per soil type. TIC is assumed to be fully dissolved and thus represents DIC. The alkalinity load per soil type (Alk_n,load, mol d⁻¹) is calibrated with runoff from each soil type (qr_n) in the catchment area (Eq. 3): 3Alkn,load=γn⋅qrnεn with γn and εn the alkalinity coefficients for each soil type (n). Negative alkalinities are excluded from this model. The range of alkalinities per soil types was defined using the mean values measured by Korkka-Niemi (2001) from well waters in Finland and a variation of ±20 % from the mean values (Table 1).

The Vemala biogeochemical submodel (Korppoo et al., 2017) simulating the co-impact of nitrogen and phosphorus on algal growth and therefore eutrophication, was developed to couple organic carbon to inorganic carbon processes and simulate total carbon cycling. The aim is to simulate organic carbon long-term sedimentation or sequestration and CO₂ emissions to the air separately within the aquatic ecosystem (Fig. 3). The new state variables are TIC, alkalinity and pH. TIC represents the sum of three fractions (CO₂, HCO3-, CO32-), TOC the sum of four fractions (DOCH₃, DOCH2-, DOCH²⁻ and DOC³⁻; Hruska et al., 2003), and pH the hydrogen ions H⁺ (Eq. 4): 4pH=-log⁡H+ The processes affecting C and simulated in Vemala are mineralisation that transforms TOC into TIC, photosynthesis that consumes TIC for algal growth, lysing, grazing and viruses that release TOC to the water, algal sedimentation as TOC, TOC compaction in the sediments representing long-term sedimentation, and exchange of CO₂ through the water-air interface (Fig. 3). In Finnish waters, most of the TOC is dissolved (Kortelainen et al., 2006; Mattsson et al., 2005) and thus direct sedimentation of TOC is neglected in the model and TOC is considered equivalent to DOC. However, TOC sedimentation happens through phytoplankton settling, thus feeding the sediments with organic matter. Other processes linked to DOC sedimentation are omitted from the model at this point.

The availability of TIC for release to the atmosphere depends on pH, alkalinity and TOC. pH models consider the acidity of the main acids in the water. The simple structure of pH models in freshwater use carbonate, oxide ions and protons to define the alkalinity (e.g. Munhoven, 2020; Marescaux et al., 2020). However, this type of model proved too simplistic for Finnish waters with high DOC and low concentrations of inorganic carbon (Abril et al., 2015). Hruska et al. (2003) quantified the acidity of dissolved organic carbon using three dissociation constants (pKa₁ = 3.04, pKa₂ = 4.51, pKa₃ = 6.46, Fig. C1) and a site density, which represents the number of carboxylic groups per milligram of DOC, of 10.2 ± 0.6 microequiv mg⁻¹ of DOC for Swedish experimental sites. The pH buffering by DOC is thus significant in the pH range of 3.5–6.5. DOC can thus be simplified to a triprotic model with four fractions. DOCH₃ is omitted from this model as it is outside the range of pH for natural freshwaters. The resultant alkalinity definition in this model can be expressed in terms of TIC and TOC as we consider the total C fully dissolved in Finnish waters as (Eq. 5): 5Alk=α1+2α2TIC+OH--H++β1+2β2+3β3TOC With α1 and α2 the respective proportion of HCO3- and CO32- ions in TIC (mmol L⁻¹) and β1, β2 and β3 the respective proportion of DOCH2-, DOCH²⁻ and DOC³⁻ ions in TOC (mmol L⁻¹). OH⁻ (mmol L⁻¹) and H⁺ (mmol L⁻¹) are the concentrations of hydroxide ions and protons and Alk refers to alkalinity (mmol L⁻¹). The proportion of CO₂ compared to TIC in the water depends on pH, alkalinity and TOC. This equilibrium between TOC, TIC, Alk and pH is solved using the Newton-Raphson algorithm after reformulating Eq. (5) to solve for [H⁺] using a polynomial equation as in Munhoven (2013) (Appendix C: pH model). Once pH is determined, CO₂ concentration in the water is calculated. The CO₂ gas exchange rate (FCO2, in mgC m⁻² d⁻¹) at the water-atmosphere interface is calculated using (Eq. 6): 6FCO2=kCO2×CO2-CO2atm with the concentration of CO₂ in the water column (CO₂, mgC m⁻³) and at equilibrium with the atmospheric CO₂ (CO_2atm, mgC m⁻³; Eq. (12)) and kCO2 the gas transfer rate at the water-atmosphere interface (m d⁻¹, Eq. 7): 7kCO2=k600×Schmidt600-0.6667×1-zice with k600 the transfer velocity (Eq. 9 for the transfer velocity in a lake or Eq. 10 for the transfer velocity in a river) for the Schmidt number (cm h⁻¹), Schmidt is the Schmidt number for CO₂ (Eq. 8) and zice the fraction of the lake covered by ice. This equation assumes that ice works as a cap on lakes impeding the exchange of gas at the water-atmosphere interface. 8Schmidt=1911.1-118.11×Tc+3.4527×Tc2-0.041320×Tc3 with Tc the temperature in Celsius (Wanninkhof, 1992). 9k600lake=max⁡(0.0,-1.318+2.067×xwind) k600lake is the transfer velocity for the Schmidt number 600 (cm h⁻¹) for CO₂ and xwind the wind speed at 10 m height (m s⁻¹) from Jonsson et al. (2008) for lakes. 10k600river=13.82+0.35⋅vel with vel the water velocity (cm s⁻¹) and k600river the transfer velocity for the Schmidt number 600 (cm h⁻¹) for rivers up to a width of 100 m (Eq. 10, Alin et al., 2011).

The atmospheric concentration of CO₂ has steadily increased in the past decades (Fig. C2). Data from the ICOS website (Integrated Carbon Observation System ICOS RI, licensed under CC4BY) allowed the modelling of the daily CO₂ concentration in the atmosphere (Eq. 11, r2=0.89). 11pCO2=362+2.3×Year-1997+15×sin⁡Date+60365.2425×2×π with pCO2, the atmospheric CO₂ (in ppm) as simulated based on the Hyytiälä and Pallas stations in Finland, Year is the simulation year and Date is the day of the year (1–365). 12CO2atm=pCO2×K0×MC×patm×dens In which CO_2atm is the CO₂ concentration at saturation in the water (mgC m⁻³) and Ko the solubility of CO₂ in the water (molC kg⁻¹ atm⁻¹), Mc the molar mass of carbon (12 gC mol⁻¹) and patm the atmospheric pressure and pCO₂ the atmospheric concentration of CO₂ (Eq. 11), and dens the density of the water as a function of the temperature (Chen and Millero, 1976).

The Vemala calibration process used a modification of the direct search Hooke-Jeeves optimisation algorithm as described in Huttunen et al. (2016) and considers both loads and concentrations during parameter optimisation. The model was calibrated over the period January 2004 to December 2023, while the period January 1990 to December 2003 was used for the validation of the model. The Nash-Sutcliffe criterion (NSE, Nash and Sutcliffe, 1970) was used to evaluate the model performance for loads; the NSE values were calculated separately for the calibration and validation. The NSE coefficient ranges from -∞ to 1. A coefficient of 1 corresponds to a perfect match between simulated and observed loads, while a coefficient of 0 presents a model that is as accurate as the mean of the observed data. To evaluate the performance of the model in terms of concentrations the coefficient of determination for linear regression (r2, Krause et al., 2005) and the percent bias (PBIAS, Gupta et al., 1999) were calculated.

Vemala calibration is a process starting with the calibration of first the hydrological submodel followed by the terrestrial submodels and ending with the biogeochemical submodel. Vemala TOC model is calibrated in two steps: first, there is a manual calibration of parameters for each of the six land use classes against annual TOC exports reported in literature. Table D1 shows the annual exports of TOC used in guiding the manual calibration. However, it is very hard to find national scale TOC export values because TOC export highly variates depending on soil types, vegetation and along a South-North gradient in Finland. Export equations by Finér et al. (2021) are used for forests on mineral soils and peatlands, however these equations only consider the South-North gradient. The second step of the calibration is an automatic calibration of two parameters – coefficients for adjusting DOC production rates for upper and lower soil layer. Vemala TIC terrestrial model is calibrated via the alkalinity proxy. Alkalinity calibration is done automatically with two parameters for each soil type (γn and εn in Eq. 3) at the Vantaanjoki catchment scale using all the alkalinity observations over the period 2004–2023 (Fig. 5b). Finally, water quality observation points monitored regularly in the catchment are used in the calibration of the biogeochemical model (Korppoo et al., 2017).

The biogeochemical deterministic model developed in this study is built on well-known enzyme-catalysed reactions (e.g. Michaelis-Menten) that focus on simulating the limiting reactions of the system affected by environmental conditions (e.g. light, temperature, flow). The range of parameters used in this application have been described in Korppoo et al. (2017) and are based on experimental measures or range from the literature. In this study, we run a sensitivity analysis of the latest processes added to the model in this development and affecting carbon cycling: mineralisation that transforms TOC into TIC, phytoplankton growth that through photosynthesis consumes TIC and through phytoplankton mortality releases TOC to the water, and exchange of CO₂ through the water-air interface. To evaluate the model's responsiveness to these processes, we varied the associated parameters by ±20 % around their calibrated values. This approach allows us to assess the robustness of the model and identify which processes exert the greatest influence on carbon loss from the aquatic system.

The Vantaanjoki catchment covers 1680 km² in southern Finland (Fig. 2a), just north of the city of Helsinki and includes Tuusulanjärvi lake (Fig. 2b and c). The river flows southwards and discharges into the Gulf of Finland. For model purposes, Vantaanjoki is divided into 48 third-level sub-catchments which are further subdivided into 989 small brook catchments with average size of 148 ha (e.g. Fig. A1). Land cover is dominated by forests on mineral soils (50 %). Forests on peat soils account for 7 % of the area, agricultural fields for 22 %, and lakes for 3%. Urban areas cover the remaining 18 % of the catchment (Corine Land Cover 2018, Syke, 2025b, and and Peatland drainage status, Syke, 2025d, Fig. 2b). The soil types are distributed between north and south with northern areas characterized by sand/till/silt/organic mostly covered by forests while the south is defined by clay overlay allowing for more agriculture to take place. Overall, clay is the main soil type (37 %) followed by rock, sand and till (22 %, 12 % and 11 %, respectively) while organic soils and silt both cover 8 % of the total catchment area (Fig. 2c). The average rainfall over the 10 year period 2014–2023 is 720 mm. In southern Finland hydrology is characterized by the highest flow peaks occurring in spring during snowmelt and in autumn when rainfall is more abundant.

Tuusulanjärvi catchment area is 91 km² of which 50 % is covered by clay, 21 % by rock and 12 % by till (Fig. 2c). Lake coverage accounts for another 9 % of the area, while forest (33 %), agriculture (31 %) and urban (27 %) areas are equally distributed (Fig. 2b). Tuusulanjärvi Lake itself covers 5.9 km² and has a volume of 18 million m³ with a retention time of over 200 d and is the largest lake in the Vantaanjoki catchment. The lake is hypereutrophic (Schönach et al., 2018).

The WSFS-Vemala model is developed and applied using long-term hydrological and water quality observations from national monitoring programmes maintained by the Finnish Environment Institute (Syke). Discharge data are obtained from the HYDRO dataset (Syke, 2025c), which consists of continuous flow measurements from gauging stations across Finland. Water quality data, including total organic carbon, total inorganic carbon, alkalinity, pH, nitrogen, phosphorus and phytoplankton are obtained from the VESLA dataset (Syke, 2025e), which is based on routine grab sampling and laboratory analyses following standardized national protocols. Sampling frequency typically ranges from monthly to seasonal, depending on site and variable.

For Vantaanjoki catchment, nine discharge stations and ten lake water level stations are used for the runoff parameter calibration of the hydrological model in Vantaanjoki catchment (Table 2). Because lakes cover only a small fraction of the catchment area and are relatively small in size, the discharge observations are given greater weight in the calibration process. The calibration is performed by minimizing the difference between daily simulated and observed discharge in all points simultaneously. The points with larger discharge get higher weight in the optimization function.

Both TOC observations and TOC calculated from COD_Mn observations were used in model calibration and validation. TOC data were estimated from COD_Mn data that correlates well with TOC in Finland (Kortelainen, 1993). As TOC data for rivers and lakes are scarce and COD_Mn have been more often analysed, this approach enables to use larger datasets and improved model performance. Equation (13) is fitted for Vantaanjoki catchment with COD_Mn and TOC observations from 1990–2022 (VESLA dataset, Syke, 2025e). 13TOC=0.797×CODMn+1.076,r2=0.89,n=4193 TIC observations (mgC L⁻¹) were scarce all over Finland and thus alkalinity (Alk in mmol L⁻¹) measurements were used as a proxy using the expression (Rantakari and Kortelainen, 2008 with an r2=0.95, Eq. 14): 14TIC=0.996⋅Alk⋅1000+19.3⋅121000 TOC and TIC are measured on unfiltered samples in Finland, while DOC and DIC are very rarely sampled. Water quality observation points monitored regularly in the catchment are used in the calibration of the Vemala model. Vantaa 4,2 6040 is the most frequently monitored water quality observation point downstream of the catchment with 15 or more observations per year (Fig. 5a). Based on the observations available in the VESLA dataset (Syke, 2025e); over the period 1990–2023, the mean (± standard deviation) total phosphorus, total nitrogen, TOC and TIC concentrations were 102 µg L⁻¹ (±61), 2.3 mg L⁻¹ (±0.9), 12.3 mg L⁻¹ (±3.5) and 10 mg L⁻¹ (±2.7) respectively and for alkalinity and pH the averages were 0.79 (±0.23) and 7.27 (±0.28). The ecological status of Vantaanjoki and Tuusulanjärvi is considered satisfactory (Syke).

Additionally, samples were collected from the main tributaries and outlet of the Tuusulanjärvi lake during 2023. The samples were analysed at the MetropoliLab Oy for total organic carbon (SFS-EN 1484:1997), total inorganic carbon (SFS-EN 1484:1997), pH (SFS 3021:1979) and alkalinity (VYH87).

In Vantaanjoki, the simulated TOC specific loading for different land use/soil classes compares well with values reported in the literature. Vemala simulates 3 tC km⁻² yr⁻¹ TOC load from agriculture on mineral soils, which is in line with Manninen et al. (2018) who reported 2.5–5.2 tC km⁻² yr⁻¹ DOC load from cultivated fields on mineral soils. The DOC load has been reported to increase with increasing topsoil carbon content (Manninen et al., 2018). Vemala simulates a TOC load of 3.6 tC km⁻² yr⁻¹ from forests on mineral soils, which corresponds with Rantakari et al. (2010) findings 2.3–4.0 tC km⁻² yr⁻¹ of TOC load from forests on upland soils. TOC load from peat soils varies over a wide range depending on whether it is natural or drained, nutrient rich or oligotrophic and of the thermal gradient from south to north. Mean simulated TOC load for Vantaanjoki catchment from natural and drained peat soils were 7.8 and 9.2 tC km⁻² yr⁻¹ respectively, which are lower than 10.1 and 16.8 tC km⁻² yr⁻¹ calculated by export coefficient equations based on temperature sums for Vantaanjoki (Finér et al., 2021).

There is an increasing trend in both simulated and observed TOC concentrations in Tuusulanjärvi for the period 1990–2023. Observed mean TOC concentrations in 1990's has increased by 16 % for the decade 2010–2020. The increasing TOC trends in various waterbody types, streams, lakes, rivers and coastal waters, has also been reported in Finland by Räike et al. (2024). According to Räike et al. (2024), the main reasons for increasing trends of TOC transport to waterbodies are decrease in acid sulphate deposition, increase in temperature, runoff, tree biomass and management of drained peatlands. According to the Yasso07 model simulations, total litter fall input to the forest soils has increased by about 10 % since 1990's (Lehtonen and Heikkinen, 2016). Although, there is practically no new peatland drainage being carried out in Finland; remedial drainage is still conducted, and previously drained peatlands continue to be managed for forestry, both of which contribute to increased TOC leaching. Already performed peatland drainage has possibly a long-term effect on increasing TOC trends (Nieminen et al., 2021).

Vemala performs well in simulating the loads of TIC, alkalinity and pH over both the calibration and validation periods with NSE higher than 0.6 at the outlets of Tuusulanjärvi and Vantaanjoki. There is however, one exception, with the NSE calculated for alkalinity over the validation period being negative (-0.5). In Tuusulanjärvi and Vantaanjoki, the observed alkalinity increase between the calibration and validation periods can be partly explained by an increased buffer capacity of freshwaters following a decrease in acid deposition (e.g. Vuorenmaa, 2007; de Wit et al., 2016) from the late 1980s onwards. Sulphate deposition load declined significantly by 60 %–70 % over the period 1986–2003 in southern Finland (Vuorenmaa, 2007). In addition, soil weathering rates are sensitive to increasing temperatures, with predicted increases in alkalinity and pH of Finnish surface waters under climate change scenarios (Aherne et al., 2012). The Vemala model simulates alkalinity as a conservative tracer and therefore does not consider the above secular changes due to acid deposition and temperature. Moreover, it omits the impact of nitrification, denitrification and other processes affecting alkalinity as implemented in other carbon models (e.g. Marescaux et al., 2020). The importance of these processes on the overall alkalinity model would however be limited with findings from Marescaux et al. (2020) showing a contribution to alkalinity export from instream processes of less than 4 %. At this stage of the model development, it is thus justified to simulate alkalinity in the river network as a tracer. Vemala must rely on variables with national coverage for its development at the national scale, however observed TIC dataset (VESLA, Syke) is very limited. Thus, alkalinity that is well correlated with TIC and is supported by comprehensive monitoring data across Finland is a good proxy to simulate TIC in Finland.

The TIC loading at the outlet of the catchment is well simulated, although TIC concentrations overall are underestimated in Vemala. In Tuusulanjärvi, some of the tributaries are presenting an increased TIC concentration in the summer up to 27 mgC L⁻¹, while others present a low concentration throughout the year. In our model, TIC input loading is associated with rock weathering using alkalinity and soil types rather than accounting for mineralisation of organic carbon in the soil. TIC load from bedrock and clay soils is higher than from coarse soils (sand and silt) as analysed from well waters in Finland (Korkka-Niemi, 2001). Elevated summer concentrations can be explained by elevated groundwater flow, point sources from urban areas or wastewater treatment plants. Runoff from agricultural land may increase DIC loading compared to forested land due to liming. In Sweden, Humborg et al. (2010) estimated that 4 % of the carbonate and bicarbonate export to the sea in Sweden was from pollution, mainly from liming of agricultural land, which covers 8 % of Sweden. However, it is difficult to assess the extent of the liming effect on agricultural land on the stream water pH and thus inorganic C dissolved in the water (Huotari et al., 2013). Point sources of TIC are not included in this model nor is the mineralisation process producing DIC in the soil at this stage of the model development. Overall, the simplified representation of TIC loading based on soil types and runoff in Vemala represents well the variability of TIC loading between different catchments as well as the intra-annual variability of TIC concentrations, even though the overall loading is underestimated. In the future, the terrestrial TOC model could be coupled more tightly with the TIC model to simulate mineralisation processes and greenhouse gas emissions from land areas.

The simulation of the transfer velocity of CO₂ across the water-air interface, represented by k600, is crucial in the calculation of CO₂ emissions and requires the introduction of physical/topographic features like wind speed and water velocity to reduce the uncertainty associated with k600 estimates at the catchment scale (Alin et al., 2011; Rocher-Ros et al., 2019). In this study, k600 was defined separately for lakes and rivers and correlated respectively to wind speed (Jonsson et al., 2008) and water velocity (Alin et al., 2011). Average values of k600 in Tuusulanjärvi over both periods (k600=6.1–7.8 cm h⁻¹ annual averages) are comparable to other measurements from lakes like Heiskanen et al. (2014) who calculated an average k600 of 7 cm h⁻¹ in a small boreal lake during autumn. Alin et al. (2011) presented a k600 range between 5–55 cm h⁻¹ in rivers with a water velocity between 0.05–1 m s⁻¹. In Vantaanjoki, the average water velocity ranges between 0.02–0.35 m s⁻¹ over the period 1990–2023 (WSFS-Vemala, Syke, 2025f), resulting in a range of k600 between 14–26 cm h⁻¹. This is below the range used to characterise rivers in Sweden (k600=26–64 cm h⁻¹, Humborg et al., 2010), however, the velocity in the Swedish streams was much higher, ranging from 1–4 m s⁻¹, which would explain our lower estimates of k600.

The average annual CO₂ emissions rate for Tuusulanjärvi of 25 gC m⁻² yr⁻¹ is comparable to other studies, for instance, using the equation related to open water rainfall from Rantakari and Kortelainen (2005) provides an average annual CO₂ emission rate of 24 gC m⁻² yr⁻¹. Our estimate also compares to other studies like the estimate, based on continuous CO₂ concentrations in the water (April 2005–October 2006), of 30–44 gC m⁻² yr⁻¹ from a meso-eutrophic, slightly acidic headwater lake in southern Finland (Huotari et al., 2009). However, our estimate is about half the estimate for its lake size class (1–10 km²) of 56 gC m⁻² yr⁻¹ but corresponds to a lake class with an area greater than 100 km² in the study from Kortelainen et al. (2006). Kortelainen et al.'s study did not account for residence time, eutrophication or acidity levels that can considerably influence carbon emissions from lakes.

The overall river network carbon emissions of 223–260 gC m⁻² yr⁻¹ were low compared to calculations based on the size of the rivers like in Humborg et al. (2010: 473–3032 gC m⁻² yr⁻¹, depending on the Strahler stream order). This discrepancy can first be explained by the discrepancy in the average velocity of rivers between the two papers as we have presented with the k600 values. These high emissions have also been reported by Rocher-Ros et al. (2019: median 1290 and mean 2790 gC m⁻² yr⁻¹) or Raymond et al. (2012: mean 3358 gC m⁻² yr⁻¹). However, in peat areas, lower CO₂ emissions have been reported like Rocher-Ros et al. (2019: 40 gC m⁻² yr⁻¹) or Dinsmore et al. (2010: 39 gC m⁻² yr⁻¹). TIC concentrations in Finnish waters can play a role in the lower estimates of CO₂ emissions. Indeed, in boreal environments DOC flux represents up to 80 % of the carbon export to the Baltic Sea (Räike et al., 2016), while worldwide DIC export to the Sea is equivalent to DOC (Hope et al., 1994) and can even represent up to 80 % of the carbon flux in UK rivers (Jarvie et al., 2017). In boreal catchments characterised by non-carbonate bedrocks, inland waters are low in alkalinity and in inorganic carbon explaining the lower CO₂ emissions. Finally, the lower estimates of carbon emissions in the streams could also be explained by an underestimation of TIC in the water column. The underestimation of TIC is due to a simplification of the TIC loading, which is in this model based uniquely on soil types and not incorporating the added diffuse sources of TIC from agriculture, peat or urban areas, nor the point sources like wastewater treatment plants.

The older version of the Vemala model, simulating TOC only as a separate variable and including a retention term for both carbon emission and carbon sedimentation in the lake, simulated a TOC retention of 108 tC yr⁻¹ equivalent to 20 % of the TOC loading to the lake (Vemala, Huttunen et al., 2016). This value is lower than the combined total carbon loss from the lake in our new estimates (147 tC yr⁻¹) that includes not only carbon retention in the sediments but also carbon emissions to the atmosphere. Thus, over a third of the total carbon loss is omitted in the previous version of the model showing the importance of simulating TIC as well as TOC in carbon emission calculations. In this simulation, a large part of the total carbon is sedimented through phytoplankton sedimentation. However, only a relatively small fraction undergoes long-term burial (3 % of TC), referred in this model as “compacted”, thus most of the sedimented TOC is mineralised in the surface of the sediments and returns to the water column as TIC. The capture of carbon in the sediments (3 gC m⁻² yr⁻¹) is lower than in other lakes of similar sizes (1–10 km²: 7.2 gC m⁻² yr⁻¹) according to Pajunen (2000). The carbon cycling in inland waters has significantly changed due to human activities (Tranvik et al., 2009) and this link should be further explored using this model. It would be important to expand this study to the national scale to get the total estimate of carbon balance and flows in the aquatic environment, taking into account the variety in characteristics and loading of lakes and rivers. This would improve currently available estimates on GHG fluxes from Finnish surface waters, which are based on generalised emission coefficients (Holmberg et al., 2023). Evaluation of the regional-scale impacts of future changes in climate or land-use could also be improved (e.g. Forsius et al., 2017). Water residence times and nutrient concentrations are key predictors for organic carbon reactivity and CO₂ emissions from inland surface waters (Evans et al., 2017). WSFS-Vemala through its biogeochemical submodel links nutrients to phytoplankton growth and carbon cycling in inland waters to further study these fundamental links between eutrophication and GHG emissions in the future.

In the Vemala biogeochemical model, mineralisation is at the core of the carbon cycling in the water, which explains the sensitivity of the model to this process (Fig. 10). The mineralisation process is simulated as affected by temperature following a sigmoid function (Korppoo et al., 2017). Future climate change scenarios will thus have an impact on the simulated mineralisation dynamics in the aquatic ecosystem. Mineralisation not only influences carbon dynamics but also affects nutrient availability and phytoplankton growth, making it a key driver of biogeochemical interactions in the system. The co-dependency of various variables to the mineralisation rates allows for a reduction in the uncertainty of the calibrated parameters as mineralisation rates are calibrated to fit not only TOC but also organic nitrogen and phosphorus. This demonstrates the benefit of deterministic process-based models that rely on well documented enzyme reaction rates as well as the simulation of interconnected variables affected by the same processes in the aquatic ecosystem. The sensitivity analysis highlights the performance of the model to represent well all variables in the water column considering the sensitivity of each output to each calibrated parameter.