Most tidal estuaries are alluvial estuaries (Regnier et al., 2013b), which are defined as estuarine systems with movable beds, consisting of material from marine and terrestrial origin, and a measurable freshwater inflow (e.g., Hobbie, 2000; Savenije, 2005, 2012). The global distribution of alluvial estuaries is roughly equivalent to that of the tidal estuaries as defined in the estuarine coastal typology of Dürr et al. (2011). The approach developed here builds on this intercompatibility, already mentioned in Regnier et al. (2013b). In tidal estuaries, two different zones can be identified along their longitudinal gradient: a lower zone, the so-called saline estuary, whose dynamics are essentially controlled by mixing with marine waters, and an upstream zone, referred to as the tidal river, where processes are mainly driven by the freshwater input from rivers (e.g., Jay et al., 1990; Dalrymple et al., 1992; Regnier et al., 2013b). Alluvial estuaries are characterized by a mutual dependency of the estuarine geometry and hydrodynamics. The magnitude of the water flow entering or leaving the estuarine channel is entirely controlled by its shape (Pethick, 1984). In turn, the water movement, mainly driven by tides and freshwater discharge, leads to a redistribution of the unconsolidated sediments that determines the shape of the estuary. This dynamic interplay between hydrodynamics and morphology results in a continuum of estuarine shapes that cover the entire spectrum between two end-member cases: (1) systems with rapidly converging banks towards the land and (2) systems characterized by parallel banks (Savenije, 1992). Although the exact shape of alluvial estuaries can vary, they nonetheless show common geometrical characteristics that are compatible with an idealized representation of the estuarine geometry (Savenije, 2005, 2012). The tidally averaged estuarine width B‾ (in m) typically shows an exponential decrease in the landward direction (e.g., Pethick, 1992; Lanzoni and Seminara, 1998; Savenije, 1992, 2005), while the tidally averaged estuarine depth H‾ (in m) remains nearly constant along the estuarine gradient (Savenije, 1992, 2005, 2012): B‾(x)=B0⋅exp⁡-xb,H‾(x)=H0, where x (in m) is the distance from the estuarine mouth, B0 and H0 denote the estuarine width and depth (in m) at the estuarine mouth (x = 0), respectively, and b is the width convergence length (in m), defined as the distance over which the estuarine width reduces to 37 % (e-1) of its value at the mouth. The shape of alluvial estuaries can, thus, be fully defined by the width convergence length, b, and the channel depth, H0 (Savenije, 2012). The ratio between these two geometrical key parameters is generally defined as the dimensionless estuarine shape number, S (Savenije, 1992): S=bH0. The hydrodynamic characteristics of alluvial estuaries may, in turn, be directly related to their main hydrodynamic forcings, such as tidal influence and freshwater inflow (Wright et al., 1973) by means of the dimensionless hydrodynamic Canter–Cremers estuary number N (Simmons, 1955): N=Qb⋅TP≈Qb⋅TA0⋅E, where Qb denotes the bankfull discharge or, in other words, the temporary maximum river discharge (in m3 s-1) that is associated with a state of maximum flow velocity and, thus, to the maximum ability to shape the estuary (Savenije, 2012). T is the tidal period (in s). P is the tidal prism (in m3), which represents the volume of saline water entering the estuary over a tidal period, T, and can be approximated by the product of the cross-sectional area at the estuarine mouth A0 (in m2) (A0 = B0 ⋅ H0) and the tidal excursion length E (in m), defined as the maximum distance a water particle travels during a tidal period T. By using a regression analysis based on measurements from 16 alluvial estuaries worldwide, Savenije (1992) showed that the estuarine shape number (S; Eq. 3) is related to the hydrodynamic Canter–Cremers number (N; Eq. 4) through a power law relationship, resulting in the dimensionless hydro-geometrical relationship: bH0=12 500⋅Qb⋅TA0⋅E0.26. Certain hydro-geometrical characteristics, such as the tidal period T, the tidal excursion E and the estuarine depth at the mouth H0 can be approximated by characteristic values. For instance, E is usually close to 10 km for a semi-diurnal (T ≈ 12 h) tidal estuary, while an alluvial estuary flowing in a coastal plain generally reveals a tidally averaged depth (H‾) of about 7 m (Savenije, 1992; Volta et al., 2014). Note that, for estuaries in which the freshwater discharge is known, a new formulation proposed by Gisen and Savenije (2015) can be used to estimate the estuarine depth. On the other hand, other characteristics, such as the bankfull discharge Qb, the width convergence length b, and the cross-sectional area at the estuarine mouth A0, are system-specific characteristics, depending on the hydrological regime of the estuarine watershed and on the local balance between riverine and marine energies. Therefore, they cannot be easily approximated. The width convergence length, b, and the bankfull riverine discharge, Qb, can thus be considered key parameters for defining the hydro-geometrical character of alluvial estuaries and for predicting their salt intrusion profiles (Savenije, 2005, 2012). Important transport and mixing properties can be directly related to these hydro-geometrical characteristics. Hence, Eq. (5) not only provides a universal theoretical framework for analyzing the tight link between geometry, hydrodynamics and transport but also offers a theoretical basis for a classification of alluvial estuaries. Savenije (2005, 2012) identified two main estuarine types, which differ in terms of geometrical features, hydrodynamics characteristics and salt intrusion patterns:

funnel-shaped (or marine-dominated) estuaries that are typically characterized by a short width convergence length, b, and thus rapidly converging banks, a low freshwater discharge, a dome-shaped salinity profile with a small salinity gradient at the estuarine mouth and an intrusion of saltwater far upstream;

The identification of two end-member estuarine classes and an intermediate group, on the one hand, and the recognition of the first-order control of hydrodynamics on estuarine biogeochemistry (e.g., Alpine and Cloern, 1992; Nixon et al., 1996; Arndt et al., 2007, 2009; Laruelle et al., 2009), on the other hand, allow hypothesizing that each estuarine type might respond in a specific way to the tight coupling between geometry, hydrodynamics, transport and biogeochemistry. Hence, important biogeochemical properties in estuaries might, just as salinity profiles, be predicted on the basis of hydro-geometrical features (Fig. 2; Volta et al., 2014).

In this study, we explore the link between biogeochemical dynamics and key hydro-geometrical properties in three idealized, tidal alluvial estuaries characterized by variable marine/riverine influence by means of a reactive-transport model. For this purpose, three idealized geometries are defined to be representative of the two extreme classes and the intermediate types as described in Sect. 2.1 (marine- and riverine-dominated estuaries and intermediate cases). The width convergence length, b, recognized as a shape and hydrodynamic key parameter (see Sect. 2.1), is used to discriminate between the three estuarine types. First, a reference estuary, characterized by an idealized geometry resembling that tested in Volta et al. (2014), is defined. Then, its width convergence length (b = 30 km) is decreased and increased by 50 % in order to intensify the marine (b = 15 km) and the riverine (b = 45 km) character of the system, respectively. This allows defining two other idealized systems, which can be regarded as representative of the marine and river-dominated estuarine classes and between which the reference estuary can be considered an intermediate case. Henceforth, according to Regnier et al. (2013b) and Volta et al. (2014), the marine-dominated estuary, the reference case and the riverine-dominated estuary will be referred to as the marine, the mixed and the riverine estuary, respectively. The estuarine width at the seaward limit, B0, and the estuarine length, EL, of the marine and the riverine estuaries are adjusted so that their total, tidally averaged volume corresponds to that of the mixed estuary (V‾ ≈ 1.5 × 109 m3). This allows minimizing the effect of volume variations on the biogeochemical dynamics across the three estuarine types. As a result, the channel width of the marine-dominated estuary reduces, over a distance of 90 km, from 13 830 m at the estuarine mouth to 30 m close to the upper limit, whereas the width of the riverine-dominated estuary decreases, over a distance of 226 km, from 4760 m at the estuary mouth to 30 m at the upper limit. All estuaries are assumed to be coastal plain estuaries. Hence, their tidally averaged water depth is approximated to 7 m (see Sect. 2.1). Furthermore, it is assumed that the three idealized systems are subject to a semi-diurnal tidal forcing, thus resulting in an identical tidal excursion length, E, of approximately 10 km (see Sect. 2.1). Based on these geometrical characteristics, Eq. (5) can be used to calculate the bankfull discharge, Qb in m3 s-1, for each system. New formulations are now available to constrain the bankfull discharge from geometrical parameters (i.e., depth and width; see Gisen and Savenije, 2015) and they could be used in future applications of C-GEM. The geometrical features of the three idealized estuaries are illustrated in Fig. 3 and summarized, together with their hydrodynamic properties, in Table 1. Table 1 also reveals that both the estuarine shape (S, Eq. 3) and the hydrodynamic Canter–Cremers (N, Eq. 4) numbers of the three idealized systems cover the whole range of observed values for temperate tidal estuaries (2500 < S > 6000, N < 0.05; Savenije, 1992). As a consequence, they may be considered as representative of a large range of hydro-geometrical conditions observed in this type of estuaries. Note that higher values of S have been reported for tropical estuaries (Gisen et al., 2015).

Simulations presented in this study are performed by using the C-GEM modeling platform, fully described and available as supplementary material in Volta et al. (2014). C-GEM dynamically resolves hydrodynamics, transport and pelagic biogeochemistry using the numerical schemes described in Regnier and Steefel (1999) and explicitly accounts for variations induced by tides. Here, we use a version of C-GEM similar to that described in Volta et al. (2014), but its biogeochemical reaction network was extended to include a non-siliceous phytoplanktonic group and an inorganic carbon module.

The biogeochemical dynamics of the three representative estuarine systems are investigated and compared by means of four whole-system biogeochemical indicators: the net ecosystem metabolism (NEM), the CO2 exchange flux with the atmosphere (FCO2) and the total nitrogen and carbon filtering capacities (FCTN and FCTC, respectively).

A sensitivity analysis is carried out to assess the response of the biogeochemical indicators (FCTN, FCTC, FCO2 and NEM) in the three idealized estuaries to variations in aerobic degradation, denitrification and nitrification rate constants (kox, kdenit and knit, respectively). These parameters are selected because of the heterotrophic character of estuaries (Borges and Abril, 2011; Volta et al., 2014) and the significant effect of nitrification rates on water pH and, thus, on DIC speciation, water pCO2 and FCO2 (Regnier et al., 2013b). The generic rate constants (Table 5) are used as baseline values and are exponentially increased and decreased over 1 order of magnitude. That range of variation corresponds to the range of kox values reported in the literature and minimum and maximum values may be regarded as representative of refractory and labile organic carbon loads, respectively (see Sect. 3). Similarly, the outermost knit and kdenit values may be considered as representative of different ammonia-oxidizing and nitrate-reducing microbial communities, respectively. For each estuary, 10 parameter combinations are tested. An additional sensitivity test is also performed in which, kox and kdenit vary over 2 orders of magnitude as in the first test (SA1), but knit remains constant at its baseline value (Table 5). This second sensitivity analysis (SA2) allows assessing the relative importance of the heterotrophic and nitrification reactions on the estuarine biogeochemical indicators in the three idealized estuaries by comparing results from both series of tests. All the parameter values used in SA1 and SA2 are provided in Table A1.

Values for 18 biogeochemical parameters included in the biogeochemical reaction network of the C-GEM modeling platform (Table 3) were compiled by a literature review comprising 49 model applications for tidal estuarine systems in temperate regions (Table 5). The review comprises models of different complexity ranging from 0- to 3-D models, which were developed and applied to investigate different aspect of estuarine biogeochemistry, such as water quality control (e.g., HydroQual Inc., 1987; Lin et al., 2007), bacterial and phytoplankton dynamics (e.g., Robson and Hamilton, 2004; Macedo and Duarte, 2006; Gypens et al., 2013), or estuarine nutrient budgets (e.g., Soetaert and Herman, 1995; Arndt et al., 2009) at different timescales ranging from months to several years. The review covers the following 12 parameters, assumed to be temperature-independent:

Michaelis–Menten half-saturation constants (KDSi, KPO4, KNH, KNO3, KTOC, KO2,ox, KO2,nit, and KN in µM), which account for the dependency of biogeochemical reaction rates on substrate availability;

For the temperature-dependent parameters, corresponding temperature functions are also included in the review. The review reveals that the temperature dependence of the aerobic and the denitrification rate constants (kox and kdenit, respectively) is typically expressed as an exponential increase of the rate constants with temperature (e.g., Regnier et al., 1997; Hofmann et al., 2008; Arndt et al., 2009; Volta et al., 2014). On the other hand, the temperature dependence of autotrophic parameters, such as the nitrification rate constant (knit), the maximum specific photosynthetic rate (PmaxB), and the phytoplankton maintenance and mortality rate constants (kmaint and kmort, respectively) can be implemented as exponential functions, where the parameter value increases with temperature (e.g., Peterson and Festa, 1984; Le Pape and Ménesguen, 1997; Guillaud et al., 2000; Laruelle et al., 2009), or as Gaussian functions, where the value increases until an optimum temperature is reached and then progressively decreases (e.g., Garnier et al., 1995; Kim and Cerco, 2003; Gypens et al., 2013; Zheng et al., 2004).

A summary of the reviewed biogeochemical parameters, as well as their values, the location of the respective modeling studies and the corresponding reference, is provided in Tables B1 and B2. For the temperature-dependent parameters (Table B2), temperature functions are also reported.

A statistical analysis was performed to determine a generic biogeochemical parameter set representing the mean or the median of the respective published parameter values. Generally, the mean is considered a rigorous estimate of the central tendency of a set of normally distributed numerical scores. However, it is not a well-suited measure for data sets with a skewed distribution since it is largely influenced by outlier values. In this case, a numerical measure able to minimize the outlier influence on the generic trend, such as the median, should be preferred (Mendenhall et al., 2013). Here, the presence of outliers is used to determine whether a biogeochemical parameter may be approximated with the arithmetical mean or the median of a data set. If no outliers are detected, the literature parameter set can be considered normally distributed and thus the generic biogeochemical parameter can be approximated by the mean. Otherwise, when at least one outlier is identified, the distribution of values in the parameter set is assumed to be skewed and the generic biogeochemical parameter is calculated as the median of the literature values (Fig. 6). Parameter values are classified as outliers if they are larger than q3 + w ⋅ (q3 - q1) or smaller than q1 - w ⋅ (q3 - q1), where q1 and q3 are the 25th and 75th percentiles, respectively, while w is the maximum whisker length. The latter is set equal to 1.5, which corresponds to approximately 99 % coverage if the data are normally distributed and represents a rational compromise between a rigorous parameter value selection, which aims to identify a generic tendency of the literature parameter distributions without being influenced by values too high or too low compared to the rest of the sample, and the conservation of a statistically relevant number of parameter values.

For the sake of generalization, although in some modeling applications phytoplankton parameters were associated with specific groups, no distinctions between different phytoplankton species and/or groups were made during the analysis and any numerical value was assigned the same weight in the parameter estimation. Therefore, the generic set of phytoplankton parameters derived here should represent a generic estuarine phytoplankton group. Moreover, when a modeling study reported different aerobic degradation and denitrification rate constants (kox and kdenit, respectively) for differently reactive organic matter pools (e.g., Soetaert and Herman, 1995; Schroeder, 1997; Hofmann et al., 2008), the value considered in the parameter analysis corresponds to the average value of the two constants reported. Therefore, the generic values for kox and kdenit may be regarded as representative of organic matter decomposition through high-energy-yielding metabolic pathways.

A generic set of temperature functions, associated with temperature-dependent biogeochemical parameters, is derived by analyzing the T functions reported by the reviewed modeling applications. For phytoplankton temperature-dependent parameters, generic temperature functions were preferentially chosen over group-specific temperature formulations. For the phytoplankton maintenance rate constants (kmaint), all temperature functions reported in the literature referred to specific phytoplanktonic groups. In this case, the function associated with the largest number of different phytoplankton groups was considered the most generic and, thus, retained. On the other hand, although all temperature functions reported in the literature for aerobic degradation and denitrification rate constants are exponential, they nevertheless show different trends depending on the initial values and exponential factors applied. In this case, the formulation showing the average trend is selected as generic function (refer to Fig. B1). Finally, for the temperature function associated with the rate constant of nitrification (knit), the most frequently used function is chosen (refer to Table B2 for more details). For the generic temperature functions of biogeochemical parameters as implemented in C-GEM, refer to Table 3.

In an estuarine system, the interplay between tidal and fluvial influence results in important longitudinal variations in tidal amplitude and salinity (Fig. 7a and b). The comparison of the simulated longitudinal tidal amplitude and the salinity profiles for the three representative estuaries (Table 1) reflects the strong mutual dependency between estuarine geometry and hydrodynamic characteristics.

The distortion of the tidal wave in upstream direction (Fig. 7a) is mainly controlled by the balance between energy gain due to channel convergence and energy loss through friction. In the marine estuary, the strong convergence of the estuarine banks (short convergence length) compensates for the energy loss through friction and the tidal amplitude increases landward to 5.5 m at the upper estuarine boundary. In the mixed estuary, on the other hand, the weak amplification of the tidal amplitude indicates that the energy gain through convergence is almost balanced by the energy lost through friction. Upstream, tidal amplitude increases more rapidly to reach a maximum of about 5 m where convergence and friction effect are both of low magnitude. Beyond this point, close to the inland limit, the relative importance of the friction increases, owing to a relatively higher fluvial energy, and triggers a slight dampening of the tidal amplitude. In the riverine estuary, the weak channel convergence (long convergence length) combined with the dominant fluvial influence leads to a dampening of the tidal amplitude, in particular in the upper reach where frictional energy loss reaches a maximum. In summary, the marine and the mixed estuaries are typically characterized by a net energy gain through convergence and thus by a tidal amplitude amplification along their longitudinal gradients, whereas the large fluvial influence always induces a net reduction of estuarine energy by bottom friction and a consequent tidal damping in the riverine system.

In alluvial estuaries, the salinity intrusion is controlled by the balance between upstream dispersion and downstream advective transport and, thus, by the system's geometric and hydrodynamic properties (Savenije, 2005, 2012). Simulated salinity profiles for the three idealized systems (Fig. 7b) reflect this dependency. Despite identical lower boundary conditions (S = 34 at 50 km beyond the estuarine mouth; see Sect. 2.3.5), the shape of the simulated salinity profile and, in particular, the salinity gradient close to the estuarine mouth, as well as the salt intrusion length, reveal the characteristic differences generally observed across the different estuarine types (Savenije, 1992, 2005, 2012). These differences can be largely attributed to the relative significance of the tidal versus the fluvial influence in each system. The marine estuary is characterized by a dominant tidal influence and, thus, a small salinity gradient close to the mouth (ΔS = 7), a concave salinity profile and a long salinity intrusion length of almost the 75 % of the total estuarine length (EL). On the other hand, in the mixed estuary, tidal and fluvial influences are of roughly equal importance and the salinity gradient close to the mouth is thus larger than in the marine estuary (ΔS = 17). Moreover, the larger fluvial influence, results in a recession shape profile and a shorter salinity intrusion length of 40 % of the EL. Similarly, the riverine estuary displays a recession-shape salinity profile. However, the salinity gradient at the estuarine mouth is much larger (ΔS = 24) and the salinity intrusion shorter (20 % of the EL) than in the mixed system due to the large riverine discharge and the smaller tidal exchange.

In alluvial estuaries, the main features of the longitudinal distribution of suspended particulate matter (SPM) can be linked to the mechanical energy provided by the tides and the riverine discharge (Jay et al., 1990; Dalrymple et al., 1992). The longitudinal SPM profiles simulated in the marine and the mixed estuary reveal similar SPM trends (Fig. 7c). In both cases, SPM concentrations increase in the lower estuary due to the progressive compression of the incoming flood into a smaller cross-sectional area and to a consequent increase in the flood-tidal current speed and reach locally high values where the total energy (fluvial + tidal) is maximal, while, further upstream, SPM concentrations decrease to a minimum at the so-called balance point, where fluvial and tidal energy contributions are of similar but low magnitude. In the upper reaches, SPM concentrations are largely controlled by the riverine influence. The progressive decrease in fluvial energy from the upper estuarine limit to the sea induces a reduction of erosion and a consequent increase in deposition rates. As a result, decreasing SPM from the upper limit to the energy balance point is simulated. On the other hand, the riverine estuary reveals two turbidity maxima separated by a zone of low SPM concentrations, corresponding to the energetic balance point (Fig. 7c). As for the marine and the mixed cases, the progressive increase in SPM from the downstream limit upwards is essentially related to the progressive compression of the marine inflow into a progressively smaller volume. Nonetheless, in the upper reaches, maximum SPM concentrations are likely induced by the high river discharges promoting net erosion, as well as by the strong volumetric reduction associated with the large tidal wave dampening (Fig. 7a). A quantitative comparison of the SPM concentrations simulated in the three representative estuaries (Fig. 7c) reveals that the marine system shows very low SPM levels. The latter are likely related to the strong funnel character of this system that, bearing relatively steeper and larger volumetric variations along the estuarine gradient (Fig. 3), entails a larger dilution effect on SPM concentrations. Overall, modeled SPM distributions agree well with the conceptual, mechanical energy patterns described by Dalrymple et al. (1992), who identified two high-energy zones separated by a low-energy area (the balance point) in tidal estuaries. Moreover, they indicate that the extent of these zones along the three idealized estuaries, as well as their sediment loads, can be strongly affected by different hydro-geometrical characteristics.

The potential effects of future environmental changes on the biogeochemical functioning of estuaries are assessed by comparing the biogeochemical indicators (NEM, FCO2, FCTN and FCTC) simulated under baseline conditions (year 2000) with those simulated using a future scenario representing the year 2050 (Table 7). Results and integrated rates for the reactions influencing the NEM are summarized in Table 8. Compared to the biogeochemical boundary conditions of the baseline run, the future scenario using the global orchestration projections (Seitzinger et al., 2010) predicts an increase in PO4 and dissolved inorganic nitrogen (DIN = NH4 + NO3) loads from rivers (+57 and +29 %, respectively), as well as a decrease in TOC, DSi and SPM (-6, -1 and -17 %, respectively). Simulation results indicate that, in 2050, NEM will still be dominated by heterotrophic degradation and all estuaries will remain largely net heterotrophic (Table 8), although a slight improvement of the estuarine trophic status (less negative NEM values compared to baseline conditions) is simulated. These results essentially reflect the effect of increasing nutrient and decreasing TOC and SPM concentrations on primary production and heterotrophic degradation reactions. In particular, the larger nutrient and light availability, promoting higher NPP rates, and the smaller organic carbon input from rivers, sustaining lower degradation rates, translate into a less negative NEM in all three idealized systems in the future (Table 8). In quantitative terms, the magnitude of NEM variations in the three estuaries is always smaller than 6 %, because the influence of NPP on the overall carbon balance, as well as the predicted drop in organic carbon inputs from rivers, is marginal.

Table 8 also reveals that the CO2 outgassing flux from the three idealized estuarine systems will decrease in the future. While such trends may appear to contradict a simulated increase in water pCO2 (data not shown) and decrease in pH (Fig. 12a), the higher atmospheric pCO2 expected in 2050 (468 µatm) actually leads to a net decrease in the pCO2 gradient at the air–water interface and to an acidification of the estuarine water masses. As a consequence, the three estuaries will become less important CO2 sources for the atmosphere in 2050 because the atmospheric CO2 increase will largely offset the estuarine CO2 increase (Fig. 12b, Table 8). Furthermore, Table 8 indicates that the mixed and the riverine estuaries reveal low sensitivities to increased atmospheric CO2 concentrations (-8 and -4 % in CO2 evasion for the mixed and the riverine cases, respectively), while the marine estuary shows a larger reduction in CO2 outgassing (-20 %). Although all estuaries remain net CO2 sources for atmosphere in 2050 when the exchange rate is integrated over the entire estuarine volume, a reversal trend is simulated in the downstream zone of the marine estuary, which will become a net sink for atmospheric CO2 (Fig. 12b). On the other hand, the mixed and the riverine systems will remain atmospheric CO2 sources all along their longitudinal profiles. These results essentially reflect the different influences of the adjacent coastal zone on the estuarine biogeochemistry in the three systems. If simulations are carried out until year 2100, assuming a pCO2 gradient as high as 234 µatm at the marine boundary and an atmospheric pCO2 of 660 µatm (Moss et al., 2010), the downstream zone of the marine estuary could become strongly undersaturated with respect to the atmospheric equilibrium and largely compensate for CO2 outgassing in the upper reaches (Fig. 12b). For instance, volume-integrated CO2 exchange rate over the entire domain indicates that the marine estuary might become a sink for atmospheric CO2 in 2100. Furthermore, a sink zone could develop in the mixed estuary in 2100, while the riverine system will remain a net source (Fig. 12b).

By definition, FCTC depends on CO2 outgassing and on the TC riverine input flux. Therefore, the overall decrease in CO2 emissions simulated in the future in the three idealized systems translates into consistent reductions in FCTC (Table 8). Finally, simulation results also reveal that the efficiency of the three estuaries in removing nitrogen will decrease in the future (FCTN in Table 8), because the projected increase in riverine nitrogen loads (+29 %) is comparatively larger than the enhanced nitrogen removal through denitrification simulated in each idealized estuary (D in Table 8). The outcomes of our scenarios are in overall agreement with the future increase in carbon and nitrogen export to the coastal ocean predicted at global scale (e.g., Kroeze and Seitzinger, 1998; Bauer et al., 2013). Although these projections can only be regarded as a first-order estimate for future trends because of the great deal of uncertainty in predicting future conditions, our findings highlight that, by the end of the century, changes in carbon and nutrient loads from the catchments may lead to a significantly smaller impact on the overall estuarine C balance than the atmospheric CO2 increase. Furthermore, the latter may be such that estuaries under strong marine influence could experience a shift from being net CO2 sources to net CO2 sink, in a manner similar to that already advocated for the coastal ocean (e.g., Mackenzie et al., 2004; Bauer et al., 2013; Regnier et al., 2013a).