The ORCHIDEE LSM comprehensively simulates the cycling of energy, water, and carbon in terrestrial ecosystems (Krinner et al., 2005). The hydrological processes (e.g., rainfall interception, evapotranspiration, and soil water dynamics) and plant photosynthesis in ORCHIDEE are simulated at a time step of 30 min. The carbon cycle processes (e.g., maintenance and growth respiration, carbon allocation, litter decomposition, SOC dynamics, plant phenology and mortality) are simulated at daily time step. In its default configuration, ORCHIDEE represents 13 land cover types, with one for bare soil and 12 for lands covered by vegetation (eight types of forests, two types of grasslands, two types of croplands). Given appropriate land cover maps and parametrization, the number of plant functional types (PFTs) to be represented can, however, be adapted (Zhang et al., 2020).

Our previous implementations of lateral DOC transfer (Lauerwald et al., 2017) and POC delivery from upland to river network (Zhang et al., 2020) were both based on the ORCHIDEE branch ORCHIDEE-SOM (Camino-Serrano et al., 2018, Fig. S1), which provides a depth-dependent description of the water and carbon dynamics in the soil column. Specifically, the vertical soil profile in ORCHIDEE-SOM is described by an 11-layer discretization of a 2 m soil column (Camino-Serrano et al., 2018). Water flows between adjacent soil layers are simulated using the Fokker–Planck equation that resolves water diffusion in non-saturated conditions (Campoy et al., 2013; Guimberteau et al., 2018). Free gravitational drainage occurs in the lowest soil layer when actual soil water content is higher than the residual water content (Campoy et al., 2013). Following the CENTURY model (Parton et al., 1988), ORCHIDEE-SOM represents two litter pools (metabolic and structural) and three SOC pools (active, slow, and passive) that differ in their respective turnover times. The decomposition of each carbon pool is calculated by first-order kinetics based on the corresponding turnover time, soil moisture and temperature as controlling factors, and the priming effects of fresh organic matter (Guenet et al., 2016, 2018). Soil DOC is represented by a labile and a refractory DOC pool, with a high and low turnover rate, respectively. Each DOC pool may be in the soil solution or adsorbed on the mineral matrix. The products of litter and SOC decomposition enter the free DOC pool, which in turn is decomposed following first-order kinetics (Kalbitz et al., 2003) and returns back to SOC. Adsorption and desorption of DOC follow an equilibrium distribution coefficient calculated from soil clay and pH. Free DOC can be transported with the water flux simulated by the soil hydrological module of ORCHIDEE. However, DOC adsorbed to soil minerals can neither be decomposed nor transported (Camino-Serrano et al., 2018). All the described processes occur within each soil layer. At each time step, “the flux of DOC leaving the soil is calculated by multiplying DOC concentrations in soil solution with the runoff (surface layer) and drainage (bottom layer) flux simulated by the hydrological module” (Camino-Serrano et al., 2018, p. 939). More detailed information about the simulation of soil hydrological and biogeochemical processes in ORCHIDEE-SOM can be found in Guenet et al. (2016) and Camino-Serrano et al. (2018).

By merging the model branches ORCHILEAK and ORCHIDEE-MUSLE, the new branch ORCHIDEE-Clateral combines the novel features of both sources (DOC and POC) described above. The development of ORCHIDEE-Clateral is complemented by a representation of the sediment and POC transport through the river network that is completely novel and described below.

In this study, ORCHIDEE-Clateral was applied over Europe and parts of the Middle East (-30∘ W–70∘ E, 34–75∘ N), where extensive observation datasets are available to calibrate and evaluate our model (Table 1). The return period of daily bankfull flow (Pflooding, year), which represents the average interval between two flooding events, is used in this study to produce the forcing file of Srivmax from a pre-run of ORCHILEAK. Note that Pfloodingis generally shorter than the return period of real flooding events, as the flooding may occur on several continuous days and all the flooding waters occurring on these continuous days are generally regarded as belonging to the same flooding event (Fig. S2 in the Supplement). To our knowledge, existing observational data on Pflooding are still very limited. Therefore, following Schneider et al. (2011), we also use a constant Pflooding to simulate the bankfull flows from European rivers and the observed long-term (1961–2000) average bankfull flow rate (m3 s-1) at 66 sites obtained from Schneider et al. (2011) to calibrate Pflooding (the optimized value is 0.1 year, Table 2). To our knowledge, there are still no large-scale observation data on the sediment delivery rates from land to river networks in Europe. Therefore, following Zhang et al. (2020), the parameters a, b, c, and d in Eqs. (1) and (2) (Table 2) were calibrated for 57 European catchments (Fig. S3d) against the modeled sediment delivery data obtained from the European Soil Data Centre (ESDAC, Borrelli et al., 2018). The sediment delivery data from the ESDAC product were derived from WaTEM/SEDEM model simulations using high-resolution data for topography, soil erodibility, land cover, and rainfall. This model was calibrated and validated using observed sediment fluxes from 24 European catchments (Borrelli et al., 2018).

Parameters controlling sediment transport, deposition, and re-detachment (i.e., ω, crivdep, cflddep, cebed, and cebank, Table 2) in stream and flooding reservoirs were calibrated against the observed long-term averaged sediment discharge rate (Table 1). We also conducted an analysis to test the sensitivity of the simulated riverine sediment and carbon discharges to these parameters following the method used in Tian et al. (2015). The sensitivity of simulation results was evaluated based on the relative changes in simulated riverine sediment and carbon discharges to a 10 % increase and decrease in each parameter (Table 2). The result of the sensitivity analysis shows that the simulated riverine sediment and POC discharges are most sensitive to crivdep in Eq. (10), followed by ω in Eq. (8) (Fig. S4). Compared to crivdep and ω, the simulated riverine sediment and POC discharges are less sensitive to cflddep, cebed, and cebank. With 10 % changes in cflddep, cebed, or cebank, the changes in riverine sediment and POC discharges are generally less than 3 %. In addition, the changes in simulated riverine DOC and CO2 discharges are mostly less than 1 % with 10 % changes in ω, cflddep, cebed, and cebank. Nonetheless, a 10 % change in crivdep can lead to a change of about 5 % in the simulated riverine CO2 discharge (Fig. S4).

After parameter calibration, ORCHIDEE-Clateral was applied to simulate the lateral transfers of water, sediment. and organic carbon in European rivers over the period 1901–2014. Before this historical simulation, ORCHIDEE-Clateral was run over 10 000 years (spin-up) until the soil carbon pools reached a steady state. In the “spin-up” simulation, the PFT maps, atmospheric CO2 concentrations, and meteorological data during 1901–1910 were used repeatedly as forcing data. The final simulated water discharge rates in European rivers were evaluated using observation data at 93 gauging sites (locations see Fig. S3a) from the Global Runoff Database (GRDC, Table 1). The simulated bankfull flows were evaluated against observed long-term (1961–2000) average bankfull flows at 66 sites (Fig. S3b) from Schneider et al. (2011). The simulated riverine sediment discharge rate is evaluated using observation data from the European Environment Agency and existing publications (see Table 1) at 221 gauging sites (Fig. S3c). The riverine total organic carbon (TOC), POC, and DOC concentrations provided by the GLObal RIver Chemistry Database (GLORICH, Hartmann et al., 2019) at 346 sites (Fig. S3d) were used to evaluate the simulated riverine POC and DOC concentrations. Note that observations in the GLORICH database, which are measured at gauging sites with drainage area <1.0×104 km2, were excluded from our model evaluation because these small catchments cannot be represented by the coarse river network scheme at 0.5∘ (ca. 55 km at the Equator). Among the retained 346 gauging sites, TOC concentrations were measured at 188 sites, and DOC was measured at 314 sites. POC was measured at only two sites (Bad Honnef with 51 measurements and Bimmen with 78 measurements) in the Rhine catchment and one site (Rheine, 36 measurements) in the Ems catchment (Fig. S3d).

Based on our simulation results, the average annual sediment delivery from upland to the river network caused by water erosion in Europe (-30∘ W–70∘ E, 34–75∘ N) during 1901–2014 is 2.8±0.4 Pg yr-1 (Fig. 8a). From northern to southern Europe, the sediment delivery rate from upland to the river increases from less than 1.0 g m-2 yr-1 in the Scandinavia Peninsula, which is covered by mature boreal forests (Fig. S12a), and in the Northern European Plain to more than 600 g m-2 yr-1 in the mountainous regions of the Apennine Peninsula, Balkan Peninsula, and the Middle East (Figs. 9a, S13a). In total across Europe, 63.2 % (1.8±0.2 Pg yr-1) of the sediment delivered into the river network is deposited in river channels and floodplains, and the remaining 36.8 % (1.0±0.1 Pg yr-1) is exported to the sea (Fig. 8a). Generally, large rivers, like the Danube, Volga, and Ob rivers, carry more sediment to the sea than small rivers (Fig. 9b, c). But several relatively small rivers in the Middle East and the Po river in northern Italy also carry a similarly large amount of sediment to the sea, as the upland soil erosion rates are very high (>200 g m-2 yr-1) in these catchments (Fig. 9a, c). Spatial distribution of the sediment deposition is controlled by the stream routing scheme and the spatial distribution of floodplains (Fig. 10b). In northern and central Europe, the area-averaged sediment deposition rates (i.e., calculated as the amount of annual sediment deposition in each 0.5∘×0.5∘ grid cell divided by the grid cell area) in river channels and floodplains are mostly less than 100.0 g m-2 yr-1 (Fig. 9d). In the downstream part of the Danube, Po, and several rivers in the Middle East, the sediment deposition rate can exceed 800.0 g m-2 yr-1. From 1901 to the 1960s, the annual total sediment delivery from uplands to the whole river network of Europe declined significantly (p<0.01, independent sample t test) from about 3.0 Pg yr-1 to about 2.3 Pg yr-1 (Fig. S14a). From 1960 to 2014, the annual sediment delivery rate did not show a significant trend but revealed large interannual variations.

Along with soil erosion and sediment transport, the average annual POC delivery from upland to the river network in the whole of Europe during 1901–2014 is 10.1±1.1 Tg C yr-1 (Fig. 8b). 41.0 % of the POC delivered into the river network is deposited in river channels and floodplains, 2.9 % is decomposed during transport, and the remaining 56.1 % is exported to the sea. Spatial patterns of the area-averaged SOC delivery rate and POC discharge rate basically follow that of sediment (Fig. 10a, c). Although the sediment discharge rates in some rivers in the Middle East can be as high as that in the Danube or Volga river (Fig. 9c), the POC delivery rates in these rivers are much smaller than in the larger ones (Fig. 10c). This is mainly due to the lower SOC stocks in the Middle East compared to those found in the Danube and Volga catchments (Fig. S7). We also note that different from the sediment delivery, the annual total POC delivery from upland to the river network in Europe did not show a significant declining trend from 1901 to the 1960s (Fig. S14b). The increase in SOC stock (Fig. S14c) may have partially offset the decline in sediment delivery rate.

Leaching results in an average annual DOC input of 13.5±1.5 Tg C yr-1 from soil to the river network in Europe, and the in situ DOC production caused by wet deposition and the decomposition of riverine POC as well as submerged litter and soil organic carbon under flooding waters amounts to 2.2±0.7 Tg C yr-1 (Fig. 8c). 28.1 % of the total riverine DOC then infiltrates the floodplain soils, 12.9 % is decomposed during riverine transport, and the remaining 59.0 % is exported to the sea. The spatial distribution of the DOC leaching rate is very different from that of POC (Fig. 10b). From northwestern Europe to southeastern Europe and the Middle East, the DOC leaching rates decrease from over 6 g C m-2 yr-1 to less than 1.0 g C m-2 yr-1. DOC discharge rates in major European rivers, such as the Rhine, Danube, Volga, Elbe, and Ob, are mostly higher than 100 Tg C yr-1 (Fig. 10d). Comparatively, the DOC discharge rates in southern Europe and the Middle East are significantly lower (<60 Tg C yr-1).

The average annual leaching rate of CO2 sourced from the decomposition of upland litter and soil organic carbon (incl. DOC) in the whole of Europe is 14.3±2.2 Tg C yr-1 (Fig. 8a). Decomposition of the submerged litter and organic carbon in floodplains and the decomposition of riverine POC and DOC add an in situ CO2 production amounting to 7.5±2.7 and 4.1±0.5 Tg C yr-1, respectively. Most of this CO2 (80.2 %) feeding stream waters is then released back to the atmosphere quickly, in such a way that only 15.8 % of the CO2 is exported to the sea, and 4.0 % infiltrates the floodplain soils.

Representing the lateral carbon transport in an LSM is helpful to estimate the terrestrial carbon cycle more accurately. From the year 1901 to 2014, soil erosion and leaching combined resulted in a 5.4 Pg loss of terrestrial carbon to the European river network, with this amount corresponding to about 5 % of the total SOC stock (106 Pg C, Fig. S7a) in the 0–30 cm soil layer. The average annual total delivery of organic carbon (POC + DOC) during the same period is 47.3±6.6 Tg C yr-1 (Fig. 8), which is about 4.7 % of the net ecosystem production (NEP at 993±255 Tg C yr-1, defined as the difference between the vegetation primary production – NPP – and the soil heterotrophic respiration – Rh – due to the decomposition of litter and soil organic matter, i.e., NEP = NPP - Rh) and 19.2 % of the net biome production (NBP at 243±189 Tg C yr-1, defined as the difference between NEP and the land carbon loss – Rd – due to additional disturbances, e.g., harvest, land cover change, and soil erosion, and leaching, i.e., NBP = NEP - Rd - DOC and POC to the river) (Fig. 11b). The annual total export of carbon to the sea surrounding Europe is 19.0±1.4 Tg C yr-1, which amounts to 1.9 % and 8.7 % of the NEE and NBP, respectively.

Besides direct transfers of organic carbon from soil to aquatic systems, the lateral transport of water, sediment, and carbon can also affect the land carbon budget in several indirect ways. First, the lateral redistribution of surface runoff can affect the land carbon budget by altering soil wetness. Our simulation results reveal that the lateral redistribution of runoff can significantly change local soil wetness, especially in floodplains (Fig. S13b), where the increase in soil wetness can be larger than 10 % (Fig. S16b). Soil wetness is a key controlling factor of plant photosynthesis (Knapp et al., 2001; Stocker et al., 2019; Xu et al., 2013). Benefiting from the increase in soil wetness, the NPP in many grid cells with a large area of floodplain increased by more than 5 % (Fig. 11b), although the NPP over the whole of Europe only increased by 1 % (Fig. 11). Changes in soil wetness can further alter soil temperature (Fig. S16a). As soil wetness and temperature are the two most important controlling factors of organic matter decomposition, the lateral redistribution of runoff can affect the local land carbon budget by changing the Rh. Moreover, in ORCHIDEE-Clateral, the turnover times of litter and SOC under flooding waters (assumed to experience anaerobic conditions) are set to be one-third of the litter and SOC turnover times in upland soil (Reddy and Patrick, 1975; Neckles and Neill, 1994; Lauerwald et al., 2017). Accounting for flooding thus decreases the decomposition rate of litter and SOC stored in floodplain soils.

Second, soil erosion and sediment deposition can affect the land carbon budget by altering the vertical distribution of litter and soil organic carbon. At the net erosion sites of the uplands, the loss of surface soil results in some of the belowground litter and SOC that were originally stored in deeper soil layers emerging to the surface soil layers, and it also results in a fraction of the belowground litter becoming aboveground litter. In the floodplains, the newly deposited sediment becomes part of the surface soil layer, and the belowground litter and SOC in the original surface soil layer are transferred down to the deeper soil layers. As the temperatures and fresh organic matter inputs (sourced from the aboveground litterfall and dead roots), which can impact SOC decomposition rates through the priming effect (Guenet et al., 2010, 2016), in different soil layers are different, changes in the vertical distribution of belowground litter and SOC can therefore lead to changes in the overall decomposition rate of the organic matter in the whole soil column.

Third, soil aggregates mostly break down during soil erosion and sediment transport, and the riverine POC thus loses some of its physically protection from decomposition (Hu and Kuhn, 2016; Lal, 2003). Some modeling studies have assumed that at least 20 % of the eroded SOC would be decomposed during soil erosion and transport processes (Lal, 2003, 2004; Zhang et al., 2014). However, the estimation by Smith et al. (2001) using a conceptual mass balance model suggests that only a tiny fraction of the eroded POC is decomposed and released as CO2 to the atmosphere. Using laboratory rainfall simulation experiments, van Hemelryck et al. (2011) estimated a 2 %–12 % mineralization of the eroded SOC from a loess soil, and X. Wang et al. (2014) estimated a mineralization of only 1.5 %. In ORCHIDEE-Clateral, the passive SOC pool is regarded as the SOC associated with soil minerals and protected by soil aggregates. The turnover time of the passive POC in the river stream and flooding waters is assumed to be the same as that of the active POC (0.3 year). Our simulation results suggest that the fraction of total riverine POC that is decomposed during lateral transport from uplands to the sea is 2.9 % in Europe (Fig. 8b), which is larger than the POC decomposition fraction (0.9 %) when the turnover time of the passive POC in rivers is assumed to be the same as that of the passive POC (i.e., no soil aggregates break down). The acceleration of POC decomposition rate due to the breakdown of soil aggregates can thus slightly affect the estimate of the regional land–atmosphere carbon flux. Moreover, the riverine POC and DOC can be transported over a long distance and finally settle or infiltrate floodplains or river channels (especially estuarine deltas) where the local environmental conditions might be quite different from those encountered in the uplands from where these C pools originate. These changes in environmental conditions can affect the decomposition rate of the laterally redistributed organic carbon (Abril et al., 2002).

Comparison between the simulation results from ORCHIDEE-Clateral with activated and deactivated erosion and river routing modules indicates that ignoring lateral carbon transport processes in LSMs may lead to significant biases in the simulated land carbon budget (Figs. 11 and S14). Although the omission of lateral carbon transport in ORCHIDEE-Clateral only resulted in a 1 % decrease in simulated average annual total NPP in Europe during 1901–2014 and a 1 % increase in annual total Rh, the annual total NBP (NEP–Rd–DOC and POC to the river) is overestimated by 4.5 %. Over the same period, the lateral carbon transport only induced a 0.09 % decrease in the total SOC and DOC stock in Europe (Fig. S15c), but their spatial distribution was significantly altered (Fig. 12e, f). For instance, in some mountainous regions, the soil erosion induced a reduction of the SOC stock by more than 8 %. On the contrary, the sediment and POC deposition in some floodplains led to an increase in SOC stock by more than 8 % (Fig. 12f).

Consistent with previous studies (Stallard, 1998; Smith et al., 2001; Hoffmann et al., 2013), our simulation results reveal the importance of sediment deposition in floodplains for the overall SOC budget. From 1901 to 2014, erosion and leaching over Europe totally induced a loss of 3.03 Pg organic carbon (POC + DOC) from uplands to the river network, and only 0.65 Pg of this carbon was redeposited onto the floodplains. The total stock of soil organic carbon in Europe thus should have decreased by 2.38 Pg C. However, due to the decrease in decomposition rate of the buried organic carbon (including in situ and ex situ carbon) in floodplain soils, the total stock of soil organic carbon in Europe only decreased by 0.91 Pg C. Floodplains in Europe have protected a total of 2.12 (= 3.03–0.91) Pg of soil organic carbon from being transported to the sea or released to the atmosphere in forms of CO2. Although the sequestration of organic carbon in floodplains cannot make up all of the soil organic carbon (POC + DOC) loss, the increased organic carbon stock in floodplains (2.12 Pg C) is much higher than the soil POC loss (0.86 Pg C) induced by soil erosion.

In the present version of ORCHIDEE-Clateral, the lateral transfers of sediment and carbon are simulated using a simplified scheme due to the fragmented nature of large-scale forcing (e.g., geomorphic properties of the river channel) and validation data (e.g., continuous sediment and carbon concentration data in river streams and deposition–erosion rates in river channels). We recognize that this simplification induces significant uncertainties in model outputs, especially regarding changes in lateral sediment and particulate carbon transfers under climate change and direct human perturbations. Several physics-based algorithms have been proposed to accurately calculate the TC of streamflows (Arnold et al., 1995; Molinas and Wu, 2001; Nearing et al., 1989). These algorithms mostly require detailed information about the stream power (e.g., flow speed and depth), geomorphic properties of the river channel (e.g., slope and hydraulic radius), and the physical properties of the sediment particles (e.g., median grain size) (Neitsch et al., 2011). They are good predictors to estimate TC in rivers with detailed observation data on local stream, soil, and geomorphic properties. Unfortunately, it is not practical to implement those algorithms in ORCHIDEE-Clateral due to the lack of appropriate forcing data at large scale as well as the relatively rough representation of streamflow dynamics compared to hydrological models for small basins. For example, runoff and sediment from all headwater basins in one 0.5∘ grid cell of ORCHIDEE-Clateral are assumed to flow into one single virtual river channel. Although the total river surface area in each grid cell is represented (obtained from forcing file, Table 1, Lauerwald et al., 2015), the length, width, and depth of the river channel are unknown. Furthermore, in reality, there can be multiple river channels in the area represented by each grid cell, and these channels might flow in different directions.

We also noticed that previous studies have derived empirical functions of upstream drainage area (e.g., Luo et al., 2017) or upstream runoff (e.g., Yamazaki et al., 2011) to calculate the river width and depth, allowing simulation of the water flow in the river channel using physically based algorithms. Unfortunately, to obtain a good fit of the simulated river discharges against observations, the parameters in the empirical functions for calculating river width and depth generally need to be calibrated separately for each catchment (Luo et al., 2017), an approach that is incompatible with large-scale simulations like those performed here. Without such calibration, the simulated geometrical properties of the river channel and runoff are prone to large uncertainties, thus rendering the simulation of sediment transport at continental or global scale using physically based algorithms a more challenging task. Given the difficulty of simulating the detailed hydraulic dynamics of streamflow at large spatial scale, we thus apply a simple approach (Eq. 8) to calculate the sediment transport capacity. Overall, we encourage future studies to produce large-scale databases on the geomorphic properties of global river channels (e.g., river depth and width) and to develop large-scale sediment transport models capable of producing more realistic and accurate simulations of sediment deposition, re-detachment, and transport processes, as well as including the exchanges of water, sediment, and carbon between river streams and floodplains.

The simulation of the soil DOC dynamics and leaching in our model needs to be further improved to better simulate the seasonal variation of riverine DOC and TOC concentrations. The concentration of soil DOC and the DOC decomposition rate during the lateral transport process in the river network are the two key factors controlling DOC concentration in river flow. As only a small fraction (<20 %) of the riverine DOC is decomposed during lateral transport (Fig. 8), the overestimated (Fig. 6) seasonal amplitude in riverine DOC (and TOC) concentrations is likely caused by the uncertainties in the simulated seasonal dynamics of the leached soil DOC. The current scheme used in our model for simulating soil DOC dynamics has been calibrated against observed DOC concentrations at several sites in Europe (Camino-Serrano et al., 2018). Although the calibrated model can overall capture the average concentrations of soil DOC, it is not able to fully capture the temporal dynamics of DOC concentrations (Camino-Serrano et al., 2018). Given this, it is necessary to collect additional observation data on the seasonal dynamics of soil DOC concentration to further calibrate the soil DOC model. In addition, averaged over the various DOC and SOC pools we distinguish in the soils, DOC represents a much more reactive fraction of soil carbon (with a turnover time of several days to a few months) than SOC (with a turnover time of decades to thousands of years). Therefore, soil DOC concentrations experience large seasonal variations, while SOC concentrations generally are much more stable and show very limited seasonal dynamics. Overall, seasonal variations in riverine POC concentrations are mainly controlled by the seasonal dynamics of soil erosion rates rather than by the seasonal SOC dynamics, which explains a partial decoupling in the behavior of POC compared to that of DOC.

Although most processes related to lateral carbon transport have been represented in ORCHIDEE-Clateral, there are still omitted processes and large uncertainties in our model. For example, many studies suggest that a substantial portion of the eroded sediment and carbon is deposited downhill at adjacent lowlands as colluviums rather than being exported to the river (Berhe et al., 2007; Smith et al., 2001; Hoffmann et al., 2013; Wang et al., 2010). As the deposition of sediment and carbon within headwater basins can also significantly alter the vertical SOC profile and soil micro-environments (e.g., soil moisture, aeration, and density) (Doetterl et al., 2016; Gregorich et al., 1998; Wang et al., 2015; Zhang et al., 2016), omission of this process may result in uncertainties in the simulated vegetation production and SOC decomposition. In addition, the impact of artificial dams and reservoirs on riverine sediment and carbon fluxes is also not represented in our model. Construction of dams generally leads to increased water residence time, nutrient retention, and sediment and carbon trapping in the impounded reservoir (Habersack et al., 2016; Maavara et al., 2017), and it can also affect the downstream flooding regime and frequency (Mei et al., 2016; Timpe and Kaplan, 2017). Estimation by Maavara et al. (2017) suggests that the organic carbon trapped or mineralized in global artificial reservoirs is about 13 % of the total organic carbon carried by global rivers to the oceans. To more accurately simulate the lateral carbon transport, we plan to include the soil and carbon redistribution within headwater basins and the effects of dams and reservoirs on riverine sediment and carbon fluxes in our model in the near future.

The effects of lateral redistribution of water and sediment on vegetation productivity has not been fully represented in our model. As shown above, our model is able to represent the impacts of lateral water redistribution on vegetation productivity though modifying local soil wetness (Figs. 12 and S16). However, in addition to modifying soil wetness, many studies have indicated that soil erosion and sediment deposition can affect vegetation productivity by modifying soil nutrient (e.g., nitrogen – N and phosphorus – P) availability (Bakker et al., 2004; Borrelli et al., 2018; Quine, 2002; Quinton et al., 2010). Recently, terrestrial N and P cycles have already been incorporated into another branch of ORCHIDEE (i.e., the ORCHIDEE-CNP developed by Goll et al., 2017). By coupling our new branch and ORCHIDEE-CNP, it will be possible to develop a more comprehensive LSM that can also simulate the effects of lateral N and P redistribution on vegetation productivity.

Although soils are the major source of riverine organic carbon, domestic, agricultural, and industrial waste, as well as river-borne phytoplankton, can also make significant contributions (Abril et al., 2002; Meybeck, 1993; Hoffmann et al., 2020). Moreover, previous studies have shown that sewage generally contains highly labile POC, while most aquatic production is generally mineralized within a short time (Abril et al., 2002; Caffrey et al., 1998). Omission of organic carbon inputs from manure and sewage could potentially lead to an underestimation of CO2 evasion from the European river network. Inclusion of these additional carbon sources should thus help improve simulation of aquatic CO2 evasion.

Uncertainties in our simulation results also stem from the forcing data (Table 1) applied in our model. The routing scheme of water, sediment, and carbon is driven by a map of streamflow direction at 0.5∘ spatial resolution (Guimberteau et al., 2012). Comparison between this flow direction map and the flow direction map derived based on a high-resolution (3") DEM shows discrepancies between the two river flow networks (Fig. S6). As the flow direction directly determines the area of each catchment and the route of river flows, errors in forcing data for flow direction may thus induce uncertainties in the simulated riverine water, sediment, and carbon discharges. Land cover maps are another source of uncertainty. For instance, croplands generally experience significantly larger soil erosion rates than grasslands and forests (Borrelli et al., 2017; Nunes et al., 2011; Zhang et al., 2020). However, croplands in ORCHIDEE are only represented in a simplified way by segmenting them into C3 and C4 crops based on their photosynthesis characteristics. Therefore, our simulations based on land cover data with only two broad groups of crops might not be able to fully capture the seasonal dynamics of planting, canopy growth rate, and harvesting for all crop types. Furthermore, the effects of soil conservation practices, which would decrease erosion rates, are ignored in our model. Panagos et al. (2015) have shown that contour farming as well as stone wall and grass margin techniques have been applied in Europe to reduce the risk of soil erosion. However, these soil conservation practices only reduce the average erosion rate in the European Union by 3 %. Excluding soil conservation practices should thus have a limited impact in our simulation results.

Further model calibration, evaluation, and development are necessary for improving our model. Due to the limitation of observation data, we calibrated the parameters controlling sediment transport, deposition, and re-detachment (i.e., ω, crivdep, cflddep, cebed, and cebank in Table S1) in streams and flooding reservoirs only against the observed sediment yield. Even though our model can overall capture the lateral transfers of sediment and carbon in many rivers in central and northern Europe, more observation data are crucially needed to further evaluate the performance of our model, in particular in southern Europe. In addition, it is still unknown whether our model can satisfactorily simulate intermediate processes such as sediment deposition in river channels and floodplains, as well as the rate of river channel erosion. It is also unknown whether our model would perform satisfactorily in regions with very different climates than Europe such as the tropical region. Thus, in the future, an important aim will be to further calibrate our model against more detailed observation data (e.g., sediment deposition rate in river channels and floodplains) and extend the model application to regions of contrasting climate, vegetation, and topography. Moreover, the GLORICH database (Hartmann et al., 2019) only provides instantaneous observations of riverine organic carbon concentrations, and it is therefore difficult to evaluate the model's ability to reproduce temporal trends. Therefore, future modeling efforts should be combined with data mining efforts targeting the collection of continuous (e.g., daily) and long-term observational data on organic carbon content and fluxes in streams and rivers.