Modeling exports of dissolved organic carbon from landscapes: a review of challenges and opportunities

Inland waters receive large quantities of dissolved organic carbon (DOC) from soils and act as conduits for the lateral transport of this terrestrially derived carbon, ultimately storing, mineralizing, or delivering it to oceans. The lateral DOC flux plays a crucial role in the global carbon cycle, and numerous models have been developed to estimate the DOC export from different landscapes. We reviewed 34 published models and compared their characteristics to identify challenges in model applications and opportunities for future model development. We classified these models into three types: indicator-driven, hydrology-forced, and process-based DOC export simulation models. They differ mainly in their environmental inputs, simulation approaches for soil DOC production, leaching from soils to inland waters, and transit through inland waters. It is essential to consider landscape characteristics, climate conditions, available data, and research questions when selecting the most appropriate model. Given the substantial assumptions associated with these models, sufficient measurements are required to benchmark estimates. Accurate accounting of terrestrially derived DOC export to oceans requires incorporating the DOC produced in aquatic ecosystems and deposited with rainwater; otherwise, global export estimates may be overestimated by 40.7%. Additionally, improving the representation of mineralization and burial processes in inland waters allows for more accurate accounting of carbon sequestration through land ecosystems. When all the inland water processes are ignored or assuming DOC leaching is equivalent to DOC export, the loss of soil carbon through this lateral flux could be underestimated by 43.9%.


Introduction
The land-to-ocean carbon flux through inland waters connects the terrestrial and marine carbon reservoirs, and accounting for this land-to-ocean component of the carbon cycle is crucial in reconciling the discrepancy between top-down estimates of landatmosphere carbon exchange and bottom-up estimates of land carbon stock changes [1][2][3].Initially, dissolved organic carbon (DOC) is transported from soils to inland waters through runoff, representing a significant component of this lateral carbon flux [4,5].In aquatic ecosystems, a portion of the terrestrially derived DOC is either mineralized and released to the atmosphere or buried in sediments, with the remainder eventually delivered to coastal oceans [6,7].Previous studies estimated that the annual global flux of DOC ultimately delivered to coastal oceans ranges from 132 to 360 Tg C, with an average of 211 Tg C per year (table S1).
To account for the DOC export (E DOC ) from different landscapes, calculating the product of the average riverine DOC concentration (C DOC ) and total river discharge (Q) for a given period is a common approach (E DOC = C DOC × Q) [8].River discharge can be continuously monitored at the landscape outlet by measuring both the stream velocity and the cross-sectional area, or alternatively, it can be estimated using hydrological models [9,10].Numerous methods, including in situ measurements, remote sensing products, and estimation models, can be used to obtain the riverine DOC concentration [11,12].However, each approach has its advantages and disadvantages concerning methodological limitations and sources of error.In situ measurements of riverine DOC concentrations are generally low-frequency, short-term, and insufficient at representing the DOC concentration for the entire cross-section of the river [13].Riverine DOC concentrations can be inferred by the riverine chromophoric dissolved organic matter (CDOM) concentrations [14].However, the complex optical properties of inland waters, ice cover, and limited datasets combine to limit the applicability of remote sensing images in estimating riverine CDOM concentrations [15].Another challenge is the atmospheric conditions, including haze, aerosols, and humidity, which can obscure the low waterleaving radiances and reduce reliabilities of remotelysensed riverine CDOM concentrations [16].Models can provide long-term estimates of riverine DOC concentrations, but they require reliable measurements to calibrate their parameters and validate their results [17].In addition to using the product of DOC concentrations and river discharges, numerous simulation models can directly estimate the total DOC export from a landscape [18,19].
Modeling the DOC export from a landscape involves three critical processes: production in soils, leaching from soils to inland waters, and transit through inland waters [20,21].Soil DOC originates from the degradation of soil organic matter, exudation from roots, rainwater deposition, and the movement of organic compounds via vegetation throughfall [22][23][24].DOC production rate and content in the soil are influenced by various environmental factors such as temperature and available nitrogen [25][26][27].The leaching of DOC from soils to inland waters is predominantly governed by the soil sorption/desorption capability and hydrological force [28,29].As DOC transits through inland waters, a fraction may be mineralized or buried, with rates being affected by water conditions such as water temperature, microbial abundance, and residence time [30,31].
Numerous models have been developed to estimate the DOC export by incorporating different climate variables and key hydrological and biogeochemical processes.These models have been implemented to estimate long-term DOC exports from various landscapes and examine their spatio-temporal patterns.Therefore, a thorough comparison and evaluation of these models is essential for their application and for enhancing their simulation capabilities.In this study, we conducted a comprehensive review and comparison of published models designed for estimating DOC export, aiming to address these challenges and potential opportunities.

Materials and methods
For this study, we searched 34 models using Google Scholar, Web of Science, and ScienceDirect with keywords 'dissolved organic carbon' , 'DOC' , 'export' , 'flux' , 'model' , and 'simulation' .These models, developed between 1994 and 2021, have been applied to estimate the DOC export across various scales, ranging from individual catchments to the global level (table S2).If a model was not given a specific name in the original paper, we defined a name using the initials of its critical input environmental factors or its significant DOC flux processes.For example, Clair et al [32] employed the basin area, slope index, and precipitation to predict the annual DOC export from a basin; we thus named this model 'ASP' .Birkel et al [33] developed a model intertwining hydrology and biogeochemistry, with a focus on hydrological connectivity and soil biogeochemistry, leading us to name it 'HB-DOC' .
Considering their core structure and estimation methodologies, we categorized the 34 models into three distinct types: indicator-driven, hydrologyforced, and process-based models.Indicator-driven models rely on either univariate (using a single environmental factor) or multivariate regression (using multiple environmental factors) to estimate the DOC export from a landscape.Unlike the other two types, hydrology-forced models do not directly estimate the DOC export from a landscape over a specified time frame.Instead, they determine the DOC export as the product of the river discharge and its average DOC concentration over a given period.These models consist of two modules: one estimates the river discharge from a landscape, and the other determines the corresponding average riverine DOC concentration.Process-based models offer an all-encompassing method by representing the complete terrestrial ecosystem.Apart from hydrological processes, they encompass biogeochemical functions like vegetation photosynthesis, biomass distribution, respiration, and the decomposition of soil organic carbon.
Moreover, we reviewed, summarized, and compared model characteristics including input drivers, the simulation time step, the definition of single simulation units, the environmental factors strongly related to the DOC flux, and the methods employed to simulate critical hydrological and biogeochemical processes.Given that environmental factors including temperature, precipitation, available nitrogen, and land cover type have strong relationships with the lateral DOC flux and are commonly integrated into these simulation models, we examined and summarized these factors for each model.Crucially, we delved into the key processes of DOC production in soils, its leaching from soils to inland waters, and its transit through inland waters, identifying challenges in model applications and opportunities in future model development (figure 1).

Model classification
Seven models were classified as indicator-driven models (table 1).They typically operate on an annual time step, except for the Soil C:N model, for which the simulation time step is not applicable.Fourteen models were categorized as hydrology-forced models.Most of these operate on a daily simulation time step, though DISC-CARBON and DCWBM-OLS operate monthly.It is important to note that the Generic Model and Landscape-Mixing lack a hydrology module for discharge simulations and instead rely on field measurements.Due to the similarity in their estimation method to other hydrological DOC models, we categorized them as hydrologyforced models.In addition, SWAT-DOC uses a simplified version of the environmental policy integrated climate (EPIC) model for simulating vegetation growth but does not encompass the entire terrestrial ecosystem [34].Consequently, we have categorized it as a hydrology-forced model.Ten models fall under the process-based category.Specifically, they can capture the relationship between soil DOC production and net primary production.TEM 6.0 and TRIPLEX-HYDRA operate on a monthly time step, the rest run on a daily basis.To describe an individual simulated land unit, both indicator-driven and hydrology-forced models often use terms such as "catchment", "watershed", or "basin" (table 1).These terms refer to a drainage landscape that channels water from rain or snow melt into the inland water system.However, these terms do not have distinctions based on the size of the study area.In contrast, process-based models, often referred to as "column" models, simulate the DOC flux either for a singular site (one grid) or for a region comprising multiple grids of a consistent size.

Model input drivers
Temperature and precipitation have significant influences on the entire land-to-ocean terrestrially derived DOC flux process.Lower temperatures have the potential to reduce both DOC production in soils and its decomposition rate in waters [60,61].An increase in precipitation increases runoff, subsequently bolstering the hydrological force responsible for transporting more DOC from soils to inland waters [62].Simultaneously, rapid river flows caused by heavy precipitation can decrease the water retention time, leading to a reduction in the mineralization and burial of DOC within inland water ecosystems [63].These two factors are integrated into several indicatordriven models, but they are integral to the functionality of hydrology-forced and process-based models (figure 2).Notable exceptions include the landscapemixing and the generic model, which lack a hydrology module and instead depend on observed river discharge.In hydrology-forced models, temperature and precipitation are crucial inputs, driving the simulation of river discharge [64].For process-based a A site or single grid simulation.models, these variables not only shape runoff estimations but also play roles in various biogeochemical processes, from photosynthesis to soil organic carbon decomposition [52,55].Increased nitrogen supply boosts net primary production, thereby enriching the soil with organic carbon, a substrate essential for DOC production [27].However, an increased nitrogen supply also elevates soil acidity, subsequently diminishing the activity of soil microbes that play an important role in DOC production [65].In addition, nitrogenabundant aquatic systems generally experience high rates of DOC decomposition [66].Nitrogen is rarely incorporated into indicator-driven and hydrologyforced models (except for SWAT-DOC), but four process-based models incorporate the nitrogen cycle in their DOC export simulations (figure 2).The four models mainly emphasize the influence of nitrogen on terrestrial ecosystem processes, including the rate of photosynthesis, vegetation growth, biomass distribution, and decomposition of soil organic carbon [21].However, they ignore the influence of nitrogen in inland water ecosystems regarding DOC mineralization.
Land cover is crucial for indicator-driven models and is a necessary input for all process-based models when estimating DOC export (figure 2).However, its function varies significantly between the two model types.Wetlands within a drainage region are significant contributors to the DOC in inland waters; thus, a decrease in wetland area can dramatically reduce DOC export from a landscape [67].This significant relationship is incorporated into indicator-driven models.On the other hand, process-based models require land cover information that specifies the proportion of different vegetation types, such as the fraction of coniferous forest.This information is vital in process-based models, as it determines the simulation approach for each vegetation type.Eight of these hydrology-forced models require land cover information as input data, which the hydrology module utilizes to estimate the discharge.

Soil DOC production
Across three types of models, the methods used for estimating soil DOC production and pool size are categorized into five distinct groups (figure 2, table S2).The first method (sufficient DOC) assumes that the amount of soil DOC is sufficient to be moved by runoff and has no influence on the DOC leaching from soils to inland waters (n = 10).The second method (input SOC) assumes that the soil organic carbon is static.It uses existing soil carbon data as an indicator in the empirical regression model to directly estimate the DOC export or as input data to further estimate the soil DOC pool (n = 3).The third method (DOC concentration) is based on the field-measured soil DOC density to roughly model the soil DOC pool size (n = 1).The fourth method (Soil-DOC regression) directly the soil DOC density by using environmental factors in conjunction with an empirical regression model (n = 10).Using soil moisture and temperature as indicators is the most popular way to simulate the dynamics of the soil DOC pool (table S2).The fifth method (Entire ecosystem) estimates the soil organic matter content through simulating the entire terrestrial system including plant growth, litter fall, and soil organic carbon dynamics, which is used by all process-based models (n = 10).

Terrestrial-aquatic DOC leaching
Four distinct methods are employed in these models to simulate the DOC leaching from soils to inland waters or the riverine DOC concentration (figure 2, table S2).Since hydrology-forced models utilize riverine DOC concentration to estimate DOC export, and given that this concentration is influenced by the leaching process, we summarized the methods for estimating riverine DOC concentration in this section.The first method infers the DOC leaching from soils to inland waters by modeling the soil DOC sorption/desorption capacity, a critical determinant of the leaching process (n = 10).The second method postulates that the DOC flux is regulated by the soil hydraulic conductivity and the runoff rate (hydraulic force) (n = 19).Consequently, either the soil water content or runoff is employed to estimate the riverine DOC concentration or total DOC leaching.The third method adopts an empirical leaching model, integrating environmental variables such as glacier area and soil type (table S2), to predict the riverine DOC concentration (n = 3).The fourth method leverages the time-dependent or independent correlation between river discharges and riverine DOC concentrations, known as the C-Q pattern (n = 4).Each model applies one or a combination of these methods to simulate the DOC leaching from soils to inland waters.

Inland water DOC transit
Of the three types of models, ten account for the potential fates of terrestrially derived DOC in inland waters, including at least one of the major processes: DOC burial or DOC mineralization (table S2).However, only three (i.e.DOC-FE, TAF-DOC, and DOC-3-ForHyM) estimate the amount of DOC buried in the sediment.These ten models employ five distinct approaches to model the fates of terrestrially derived DOC in inland waters (figure 2, table S2).The first approach uses the water residence time or travel time in aquatic ecosystems coupled with the rate of microbial DOC mineralization (n = 4).The second approach uses either the measured decay rate or the fraction of mineralized DOC as input parameters to estimate the mineralized DOC during its transit (n = 1).The third strategy employs a temperature-dependent DOC mineralization rate function to estimate the amount of DOC decomposed during transit (n = 3).The fourth approach uses a loss rate to project the overall DOC reduction during transit, potentially accounting for both mineralized and buried DOC (n = 1).Finally, the fifth method leverages the open water area within a drained landscape and combines it with an empirical regression method to model the quantity of DOC that is either mineralized or buried (n = 1).

Challenges in model application
Indicator-driven models depend on one or multiple key environmental factors and can adequately represent the overall DOC export from a landscape [19].Due to their dependence on given relatively static indicators, such as land cover information (figure 2), they may not fully capture climate influence, ecosystem dynamics, seasonal trends, and inter-annual dynamics (figure 3).Hydrology-forced models can reliably simulate the discharge from a landscape [47].However, when modeling the riverine DOC concentration based on the estimated discharge, they could not incorporate the influence of ecosystem dynamics and climate change on soil DOC production.In contrast, process-based models simulate biogeochemical process dynamics for the entire terrestrial ecosystem and so can estimate soil DOC production and pool size according to the influence of climate variables (table S2).As one-dimensional 'column' models, they have a limited spatial representation of the interface between terrestrial and aquatic ecosystems.
The observed diluting response, where DOC concentration decreases during high flow events [68, 69], may be attributed to insufficient soil DOC or strong soil sorption capacity.In addition, Zarnetske et al [23] suggested that watersheds with less than 20% wetland coverage might be more source-limited.Consequently, excluding modeling soil DOC production and pool size could lead to an overestimation of DOC export during high flow events or in watersheds with limited wetland coverage (figure 3).While using soil organic carbon or DOC concentration as input data might mitigate the diluting response, characterizing the impact of climate on soil DOC dynamics remains challenging.Additionally, the need for intense location-specific measurements can increase the workload for model input data preparation.The soil-DOC regression approach can incorporate specific climate factors, but it necessitates substantial measurements for parameter calibration (figure 3).Process-based models, which simulate the entire terrestrial ecosystem, can holistically represent soil DOC production and account for its climate-induced dynamics (figure 3).However, variations exist among these models in their estimations of soil DOC production and pool size.They may use the soil organic matter degradation approach, include carbon displaced by the washout of organic compounds during vegetation throughfall, assume a fraction of soil organic matter is DOC, or apply a temperature-dependent DOC production rate (table S2).Moreover, fully representing the entire terrestrial ecosystem requires numerous parameters and input data, which can significantly increase the model setup workload.
Incorporating soil sorption/desorption in estimating the DOC leaching is another useful way to eliminate the diluting response.Given that the rates of DOC sorption and desorption are influenced by factors such as temperature, moisture, pH, and the concentrations of cations and anions in the soil water [70], this approach offers a way to capture the effects of climate change on DOC leaching.However, the model parameters need calibration based on location-specific characteristics such as soil types (figure 3) [71].While hydraulic force and C-Q pattern approaches prioritize runoff over soil properties, they fall short in eliminating the diluting response and depicting the impacts of climate change on DOC leaching [69].Additionally, given that the DOC concentration is an instantaneous measurement, obtaining a reliable C-Q relationship demands extensive measurements of both the DOC concentration and the corresponding river discharge (figure 3) [13].The empirical leaching method, which uses single or multiple indicators to model DOC leaching, is highly sensitive to landscape characteristics [33].This sensitivity can limit its applicability to different regions.
Current models typically employ factordependent (e.g.residence time, temperature, water area) rates of mineralization and burial, measured mineralization rates, or a total loss rate to simulate DOC burial and mineralization, either through photolytic or microbial processes (figure 2).While factor-dependent approaches focus on a single key determinant, they often overlook the interplay among climate conditions, microbial abundance, flow velocity, and the air-water and water column interfaces (figure 3).Using a measured decay rate, which is a static parameter, may not adequately capture the fluctuations in climate and water conditions [47].Though the loss rate can encompass both mineralization and burial, it does not distinctly partition these two potential fates [17].Given that DOC sediment in inland waters can act as a long-term carbon sink, this approach might lead to an underestimation of the carbon sequestration through land ecosystems.
Due to these limitations, benchmarks are essential for validating the simulated DOC exports.The dominant approach is using measured DOC exports at the watershed outlet.This is calculated as the product of average DOC concentration and total discharge over a specified period.In addition, hydrology-forced models can assess their estimates by comparing both discharges and DOC concentrations.Process-based models might use measured carbon pool sizes, such as aboveground biomass and soil organic carbon, or carbon fluxes such as gross primary production and net ecosystem exchange, to validate their performance in simulating the entire terrestrial ecosystem [72].However, DOC leaching, mineralization, and burial are rarely validated in existing simulations.While ignoring the validation of these processes and only validating the DOC export might obtain reliable estimated DOC exports from a landscape, it raises the concern that terrestrial-aquatic DOC leaching could be either overestimated or underestimated.

Opportunities in model development
Existing models primarily consider the degradation of soil organic matter as the primary source of soil DOC.However, DOC production, whether exuded by roots, transported with the washout of organic compounds in vegetation throughfall, or derived from rainwater, is rarely included (figure 1, table S2).Current research offers substantial data concerning soil DOC concentration [73-76], rainwater DOC deposition (table S3), root exudation [77, 78], and the washout of organic compounds in vegetation throughfall [79, 80], which can enhance and validate soil DOC estimates.By adopting a comprehensive approach to modeling and validating both soil DOC production and pool size, the performance of current models can be greatly enhanced.This is especially advantageous for regions with limited wetlands and for areas that frequently experience heavy precipitation.
Rather than quantifying the DOC leaching from each individual soil layer, current models commonly assume that all DOC entering inland waters originates from a singular soil layer (table S2).However, DOC leaching rates can vary significantly between different soil layers.Distributing the soil organic carbon across multiple soil layers and assuming an exponential DOC production rate with depth provides a useful method for differentiating DOC carbon pools in various soil layers [29,81].To obtain the rate of DOC leaching from each soil layer, the initial mass isotherm is an efficient approach.This method quantifies the fraction of DOC in each soil layer that moves from the soil to inland waters through plotting the amount of DOC retained or released per mass of soil against the initial amount of DOC added to the soils [82].This approach presents opportunities to enhance modeling simulation, but it necessitates extensive experiments and measurements.
Most of these models assume streams and rivers as pipes and simply deliver the terrestrially derived DOC directly and unaltered via flow to the coastal ocean; however, field inventories reveal that the transportation process of DOC through aquatic ecosystems is more complex [83].In inland waters, microbes biomineralize DOC to inorganic carbon and release it into the atmosphere [84].Chromophoric DOC, the light-absorbing fraction of terrestrially derived DOC, can be mineralized by solar radiation [85].Moreover, it is probable that DOC can reach the lake bottom and be buried in the sediment [86].Additionally, the in-water production of DOC from aquatic plants and algae [87], as well as inputs from rainwater [88], is of higher importance than previously thought.Numerous studies have been undertaken to quantify DOC mineralization and burial [84,89,90].Synthesizing these studies offers opportunities for developing state-of-the-art approaches to model the processes of DOC transit in inland waters.
To investigate the influence of these aquatic processes on the land-to-ocean terrestrially derived DOC flux, we synthesized existing studies and formulated a global terrestrially derived DOC flux budget (figure 4).Our findings indicate that global inland waters receive approximately 21 ± 7 TgC/year of DOC from rainwater, with around 8 ± 3 TgC/year eventually delivered to coastal oceans (tables S3 and S4).The DOC ultimately exported to coastal oceans includes 53 ± 25 TgC/year produced by aquatic ecosystems (table S5).Current research estimates the annual global DOC exported to coastal oceans to be 211 ± 65 TgC/year (table S1).Therefore, the contribution of terrestrially derived DOC to this export is estimated to be 150 ± 37 TgC/year (table S6).Our synthesis suggests that 40% of terrestrially derived DOC is exported to coastal oceans, while 25% gets buried in sediments and 30% is mineralized during its transit through inland waters (table S6).Therefore, we estimated that about 376 ± 92 TgC/year of DOC leaches from soils to inland waters (figure 4, table S6).Within the inland waters, approximately 132 ± 32 TgC/year of DOC is mineralized and released into the atmosphere, and about 94 ± 23 TgC/year is buried in sediments.Consequently, on a global scale, neglecting aquatic DOC production and DOC contributions from rainwater might lead to an overestimation of the exports of terrestrially derived DOC to coastal oceans by 40.7% (table S6).Additionally, when all the inland water processes including aquatic DOC production, contributions of DOC from rainwater, DOC mineralization, and DOC burial are overlooked (assuming DOC leaching is equivalent to DOC export), the loss of soil carbon through this lateral flux could be underestimated by 43.9% (table S6).
Disturbances such as fire, hurricanes, and forest harvesting substantially impact the DOC flux [91].Through combusting a large quantity of soil organic carbon, which is the substrate of soil DOC production, fires significantly reduce the soil DOC production [92].In addition, forest harvesting significantly diminishes the soil organic matter, which in turn leads to a decrease in soil DOC production, resulting in a reduced amount of terrestrially derived DOC [93].Hurricanes produce heavy precipitation, which affects the performance of models based on the dilution C-Q pattern [9] and potentially brings substantial DOC with rainwater to the inland waters [94].It is difficult to incorporate these disturbances in indicator-driven models and hydrologyforced models, whereas process-based models have the potential ability to include these disturbances.Currently, the effects of disturbances on DOC export are rarely comprehensively represented in modeling studies.The frequency of fires and hurricanes is projected to increase with global warming [95], and so it will be necessary to model these disturbances in future studies to better characterize the dynamics of DOC export.

Conclusions
By reviewing, analyzing, and comparing 34 published DOC export simulation models, we identified challenges for selecting the most appropriate model to estimate the DOC export from a landscape, such as the available environmental factors, target simulation time step, and landscape characteristics.Our findings indicate that assuming sufficient soil DOC while ignoring the production process can lead to an overestimation of DOC export in source-limited regions.Therefore, process-based models, which simulate the entire terrestrial ecosystem, are the optimal choice.Additionally, in regions subject to frequent heavy precipitation, models that can comprehensively simulate soil DOC production and desorption process are crucial.These models effectively eliminate the diluting effect, where DOC concentration decreases during high flow events, ensuring more reliable results.Moreover, current simulation models for estimating the DOC transit through inland waters rely heavily on numerous assumptions about unmeasured or unknown quantities, rates, and mechanisms.Although benchmarks collected at the river outlet are generally used to validate the results, overlooking processes of DOC in inland waters may not have a significant influence on the estimation of DOC eventually exported from a landscape.However, this neglect could lead to inaccurate estimates of both soil DOC loss and terrestrially derived DOC exported from the landscape.Therefore, our analysis of existing measurements and the development of a detailed budget for global land-to-ocean terrestrially derived DOC flux present opportunities for enhancing current models and validating estimates.

Figure 1 .
Figure 1.Key processes considered for estimating the DOC export from a landscape, as reviewed in this study.

Figure 2 .
Figure 2. Reviewed environmental factors include temperature (T), precipitation (P), nitrogen input or available soil nitrogen (N), and land cover type (LC).Summarized approaches used to model the DOC production in the soil (DOCp), leaching from soils to inland waters (DOC l ), and transit through inland waters (DOCt).

Figure 3 .
Figure 3. Overview of challenges faced by different modeling approaches.Modeling DOC production faces challenges like integrating climate change impacts, addressing dilution response, estimating the soil DOC pool, and representing the terrestrial ecosystem, alongside data requirements and parameterization.In modeling DOC leaching, challenges include the influence of climate change, dilution response, representing soil properties, and requirements for measurements and relationship analysis.For DOC transit modeling, the key challenges are the influence of climate change, the effect of microbial abundance, variation in decay rates, the impact of flow speed on retention time, and accurate attribution of fates.

Figure 4 .
Figure 4. Budget for global land-to-ocean flux of the terrestrially derived DOC (See Tables S1 and S2-S6 for details on the estimations.).tDOC = terrestrially derived DOC, aDOC = DOC produced by aquatic plants and algae, rDOC = DOC deposition in rainwater, MtDOC = mineralized terrestrially derived DOC in inland waters, BtDOC = buried terrestrially derived DOC in inland waters, EtDOC = exported terrestrially derived DOC to coastal oceans.

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