The Kervidy–Naizin catchment is located in western France (48°0^′ N; 2°5^′ W) (Fig. 1) and forms part of the Agro-Hydro Systems (AgrHyS) Critical Zone Observatory (Fovet et al., 2018). It is a 4.82 km² headwater catchment of the 12 km² Naizin catchment (Fig. 1), which is drained by a second-Strahler-order intermittent stream that frequently dries up from July to October. The climate is temperate oceanic, with a mean ± standard deviation of annual temperature of 11±0.6 °C, annual cumulative rainfall of 894±170 mm yr⁻¹, and specific discharge of 350±140 mm yr⁻¹ from 2008–2016. The topography is relatively flat, with few slopes reaching a gradient of 5 %, and an elevation range of 98–140 m a.s.l. (above sea level). The soil is a silty loam 0.5–1.5 m deep, with well-drained Cambisols in the upslope zone and poorly drained Epistagnic Haplic Luvisols and Albeluvisols in the downslope riparian zone (FAO classification; WRB, 2006). At the global scale, Kervidy–Naizin is representative of headwater catchments underlain by bedrock in temperate climates. The bedrock consists of impervious, locally fractured Brioverian schists and lies below a fissured and fractured weathered layer of variable thickness 1–30 m deep (Molenat et al., 2005). A shallow, perennial groundwater body develops in the soil and weathered bedrock. In the upland domain, consisting of well-drained soils, the water table remains below the soil surface throughout the year, varying in depth from 1–5 m (Molenat et al., 2005). In the wetland domain, developed near the stream and consisting of hydromorphic soils (hereafter “riparian zone”), the water table is shallower, remaining near the soil surface generally from October to April/May each year. The seasonal fluctuation of the water table in this catchment has been described as a succession of three hydrological periods (Aubert et al., 2013; Lambert et al., 2013): (i) rewetting of riparian wetland soils after the dry summer season, (ii) rise of groundwater in the upland domain that leads to prolonged waterlogging of wetland soils and establishes a marked hydraulic gradient in groundwater between upland and wetland domains, and (iii) drawdown of groundwater that leads to drying of the stream (Humbert et al., 2015).

The land use of Kervidy–Naizin consists mainly of agriculture with intensive mixed crop–livestock farming, with maize (36 % of the area), cereals (32 %), and grasslands (13 %) and a high density of livestock (i.e. dairy cattle, pigs and poultry) of five livestock units ha⁻¹ (Benoit and Veysset, 2021) according to farm surveys performed in 2008 and 2013 and annual land-use surveys (Casal et al., 2018, 2019; Viaud et al., 2018). From 2002–2015, mean N inputs on the catchment equalled 257 kg ha⁻¹ yr⁻¹, coming from slurry and manure fertilization (69 %), inorganic fertilization (21 %, mainly ammonium nitrate), cattle excretion in pastures (5 %), and nitrogen (N) fixation (5 %) (Casal et al., 2019). Kervidy–Naizin is representative of intensive agricultural areas that have an excess of reactive N due to the application of livestock waste and inorganic fertilizers in excess of crop requirements.

In this landscape, most DOC and NO3- accumulate in riparian-zone soils and groundwater, respectively (Aubert et al., 2013; Strohmenger et al., 2020). Using end-member mixing analysis to identify DOC sources and quantify their contributions to the DOC stream in Kervidy–Naizin, Morel et al. (2009) estimated that 64 %–86 % of the DOC that entered the stream during storms, when much of the DOC export from soils to streams and rivers occurs (Lambert et al., 2014), came from riparian wetland soil. This result confirmed previous studies that found that riparian soils are the main source of DOC in most headwater catchments (Lambert et al., 2013). Morel et al. (2009) also demonstrated that this riparian wetland zone in Kervidy–Naizin behaved as non-limiting storage of DOC during flushing. Hillslope soils in this catchment also contribute to stream DOC export, but dissolved organic matter (DOM) in upland soils is supply-limited and seasonally depleted after groundwater rises. Upland DOC contribution decreases from ca. 30 % of the stream DOC flow at the beginning of the high-flow period to <10 % later in this period (Lambert et al., 2013, 2014). In addition, in a high-frequency, multi-solute 10-year monitoring (2000–2010) study of Kervidy–Naizin, Aubert et al. (2013) identified that NO3- accumulated in groundwater at a concentration of ca. 20.7 mg N–NO₃ L⁻¹ compared to 1.6 mg N–NO₃ L⁻¹ in riparian wetland.

Long-term analysis of the dynamics of nutrient concentrations and hydroclimatic variables at multiple timescales in Kervidy–Naizin highlighted contrasting dynamics of DOC and NO3- concentrations due to opposition in their spatial sources. DOC concentrations peaked under wet or storm flow conditions, when NO3- concentrations were lowest. In contrast, NO3- concentrations peaked under high-water-table and drier conditions, when DOC concentrations were lowest. This opposition between maxima and minima of daily DOC and NO3- concentrations can be interpreted as the result of relative mixing contributions of soil-surface riparian flows (i.e. DOC-rich and NO₃-poor) and upslope groundwater flows (i.e. NO₃-rich and DOC-poor) (Strohmenger et al., 2020).

We used daily aggregated meteorological and streamflow measurements collected from 2002–2017. The weather station in Kervidy–Naizin (Cimel Enerco 516i), located ca. 1 km from the outlet of the catchment (Fig. 1), records hourly rainfall, air and soil temperatures, air humidity, global radiation, wind direction, and wind speed, which allowed for calculation of potential evapotranspiration using the Penman equation (Penman, 1956). Stream level was recorded every minute at the outlet using a float-operated shaft-encoder level sensor and a data logger (Thalimedes OTT) and then converted to streamflow using a rating curve (Carluer, 1998).

Stream water was manually sampled daily at ca. 17:00 LT at the outlet station. These instantaneous grab samples were immediately filtered (pore size: 0.22 µm) on site and stored in the dark at 4 °C in propylene bottles. Analyses were performed within a maximum of 2 weeks. NO3- concentrations were measured by ionic chromatography (DIONEX DX 100; ISO 10304, 2007, precision: ±2.5 %). DOC was estimated as total dissolved carbon (C) minus dissolved inorganic C, both measured using a C analyser (Shimadzu TOC 5050A, precision: ±5 %).

Shallow-groundwater data were collected by a piezometer at mid-slope point (PG5, Fig. 1). The groundwater level at PG5, which has been measured every 15 min (Orpheus OTT) since 2000 using pressure probes, was used because its variations are representative of mean variations in the shallow groundwater in Kervidy–Naizin. The volumetric soil water content was measured in upland and riparian zones of the catchment using time domain reflectometry (TDR) probes. In the upland zone (Toullo station, Fig. 1), it was measured at three depths (i.e. 5, 20, and 50 cm), with three replicates per depth, at 30 min intervals from 1 January 2016 to 1 January 2019; these data were first averaged by depth and then aggregated into daily values. Although the Toullo station lies outside Kervidy–Naizin, we assumed that it could represent Kervidy–Naizin's soil moisture conditions in the upland zone. This assumption is supported by the fact that Kervidy–Naizin and Naizin are nested and have similar characteristics, such as soil types, slopes, and elevation (Matos-Moreira et al., 2017; Sorel et al., 2010). In the riparian zone (point PG2, Fig. 1), the volumetric soil water content was measured at a depth of 5 cm, with three replicates, at 30 min intervals from 3 December 2013 to 1 January 2017; these data were also averaged and then aggregated into daily values.

We used a parsimonious semi-distributed solute-transport model, implemented in Python, that was iteratively customized and tested within the DYNAMITE modular modelling framework (Fovet et al., 2015a; Hrachowitz et al., 2014, 2021). The processes are represented by linear or non-linear equations that connect the flows to model reservoirs (Beven, 2012). This representation of storage–discharge relationships directly connects water flows to biogeochemical processes, which facilitates simultaneous simulation of both water and solute flows (Birkel et al., 2017).

Global sensitivity analysis (GSA) was carried out to determine the effect of the model calibration scenarios on the most sensitive hydrological parameters. GSA allows us to identify the extent to which changes in different parameters influence changes in the hydrological model output and to determine the most important parameters (i.e. that need to be calibrated) and the least important parameters (i.e. that can be fixed as constants) (Reusser et al., 2011; Wang and Solomatine, 2019). GSA, which ranks the relative influence of model parameters on model output (Sun et al., 2022), is generally recommended for hydrological models due to its advantages over local sensitivity analysis methods. Indeed, GSA can consider the influence of input parameters over their entire range of variation and is suitable for non-linear and non-monotonic models, providing results that are independent of modeller bias and a particular site (Song et al., 2015). Among the GSA methods widely applied to hydrological models, we chose a variance-based method as it can provide the most accurate and robust sensitivity indices for complex non-linear models (Reusser et al., 2011; Song et al., 2015; Wang and Solomatine, 2019). Variance-based methods assume that a parameter's influence can be measured by the contribution of the parameter itself or its interactions with two or more other parameters to the variance of the output. The main advantage of variance-based methods is that they can calculate the main and higher-order effects of parameters, which identifies which ones strongly influence the output on their own and which ones strongly influence the output due to their interactions with other parameters (Wang and Solomatine, 2019). We used the Fourier amplitude sensitivity test (FAST) (Saltelli et al., 1999) from the SPOTPY Python framework (Houska et al., 2015) to calculate variance-based sensitivity indices that ranged from 0–1. FAST calculates a first-order sensitivity index (Si), which measures the effect of each parameter on the output, and a total sensitivity index (STi), which measures the effect of each parameter and its interactions with the other parameters on the output (Shin and Kim, 2017). Because STi provides more reliable results than Si when investigating the overall influence of each parameter on the output (Saltelli et al., 2009), we used it to investigate parameter sensitivity, as defined by Saltelli and Annoni (2010): 6STi=EX∼i⋅VXiY|X∼iV(Y), where Xi is the ith parameter, and X∼i is the vector of all parameters except Xi.

The variance between parentheses in the numerator denotes that the variance of Y, the value of the scalar objective function, is considered over all possible values of Xi while keeping X∼i fixed. The expectation operator outside the parentheses is considered over all possible values of X∼i, while the variance V(Y) in the denominator is the total (unconditioned) variance (Shin and Kim, 2017). The numerator represents the expected variance if all parameters except Xi are fixed (Saltelli and Annoni, 2010).

Calculating STi for a single parameter requires n×(p+2) model runs, where n is the sample size and p is the number of parameters (Saltelli, 2002). To determine an appropriate sample size for this GSA, we relied on the experiment of Nossent et al. (2011), in which the sensitivity index did not converge until n=12000; thus, with 14 hydrological parameters, we performed 192 000 model runs. In this GSA, the Nash–Sutcliffe model efficiency coefficient (Nash and Sutcliffe, 1970) was used to assess daily streamflow output, as suggested by Nossent et al. (2011).

To limit adverse effects of equifinality and ensure robust posterior parameter distributions to represent processes meaningfully, extensive multi-objective and multi-variable calibration was performed by calibrating hydrological and biogeochemical model predictions simultaneously. When using multi-objective optimization to calibrate a model, the goal is to find a set of solutions that simultaneously optimize several, potentially conflicting, objective functions that measure individual processes. The interaction of multiple objectives leads to a set of compromised solutions known as Pareto-optimal front (Mostafaie et al., 2018). As none of the solutions can be considered superior when there is more than one objective to optimize, Pareto-optimal solutions (hereafter “Pareto front”) are also called non-dominated solutions (Yeste et al., 2023) with equally good parameter sets, which provides an uncertainty boundary of the predictive model. The caRamel algorithm (Monteil et al., 2020) used in this approach combines the multi-objective evolutionary annealing-simplex algorithm (Efstratiadis and Koutsoyiannis, 2008) and the non-dominated sorting genetic algorithm II (Reed and Devireddy, 2004). The caRamel algorithm produces an ensemble of parameter sets (i.e. a “generation”) to run the model, downscales the generation to the parameter sets that optimize the objective functions, and generates a new parameter set that produces more accurate results.

The research hypotheses of this study were tested using a stepwise strategy with four model calibration scenarios based on different combinations of model-performance metrics (Table 3):

scenario 1 (S1) – only data on streamflow used for calibration, with six metrics used to describe the predicted streamflow signatures;

Up to 70 000 model runs were used for each calibration scenario, with several successive optimizations to confirm reproducibility of the results, as recommended by Monteil et al. (2020). All parameter sets that belonged to the final Pareto fronts (hereafter, “envelope”) were retained as feasible solutions for each calibration scenario (Table 3). To illustrate the results for the predicted discharges and solute concentrations, a “best-compromise” set was selected from the Pareto front that minimized the Euclidean distance to the optimal point in the multi-objective space of each calibration scenario. All simulated discharges and concentrations using all parameter sets of the Pareto front provided information about the uncertainty in the model's output.

In the later evaluation step, observed soil water content and groundwater level measurements were used as independent data to assess the consistency of internal processes of the best-compromise model for each scenario.

Soil moisture is a key variable for the energy and water balance at the land surface. It affects the partitioning of solar radiation into latent and sensible heat as well as the partitioning of precipitation into direct runoff and catchment storage (Duethmann et al., 2022). Accurate prediction of soil moisture is thus essential for simulating streamflow, evapotranspiration, and percolation (Rajat and Athira, 2021; Rajib et al., 2016) and for constraining the parameters of hydrological models. The role of groundwater in the seasonal and multi-year dynamics of streamflow is also essential: in many temperate catchments, groundwater stores water during wet periods and releases it throughout the year, thus contributing greatly to low flows (Pelletier and Andréassian, 2022). These variables are important for characterizing the internal hydrological dynamics of a catchment and are therefore relevant for assessing the internal consistency of the model.

The data observed for soil water content at Toullo and PG2 were normalized (from 0–1) as a function of their minimum and maximum values over all of the periods studied. All normalized data observed at Toullo station and point PG2 were compared to the normalized simulated water content in the hillslope reservoir (SU) and riparian reservoir (SUR), respectively. To compare to the observed groundwater level, the simulated groundwater level was estimated from simulated water storage in the groundwater reservoir (SS) (Seibert, 2000) using the exponential function z=-eA⋅SS+B, where SS is water storage in the slow reservoir, and z is the groundwater level. Coefficients A and B were determined by linear regression between the simulated water storage and the observed groundwater level. The non-parametric Mann–Whitney U test was used to test whether model predictions of calibration scenarios S2, S3, and S4 differed significantly (p<0.05) from those of the baseline scenario S1.

The hydrological parameters that influenced predicted streamflow the most were related to recharge (CP; ST=0.59), deep-infiltration losses (QL; ST=0.25), percolation capacity (Pmax; ST=0.18), storage capacity of the hillslope unsaturated zone (SU_max; ST=0.15), and storage coefficient of the fast-responding reservoir in the riparian-zone reservoir (kR; ST=0.14) (Fig. 3). The strong influence of CP was logical, as it determines the recharge from SU to SS and SUR to SR (i.e. how water from runoff is redistributed between the riparian zone and groundwater). Parameters related to the area of the riparian zone (f) and the transpiration threshold (LP) had less influence.

Overall, the model reproduced the main features of the observed hydrological response (Fig. 4) in both the calibration (NSE_Q, NSE_log⁡Q, and KGEQ>0.8) and evaluation (NSE_Q, NSE_log⁡Q, and KGEQ>0.7) periods for all scenarios. The predicted streamflow reproduced the seasonal dynamics observed during the wetting-up (rising limb of the hydrograph), wet, and recession periods. The high flow variations associated with storm events were usually represented relatively well (NSEQ>0.75) in calibration and evaluation periods, with good synchronicity, particularly in winter 2010 and 2014. Overall, model performances for the evaluation period were only slightly lower than those for the calibration period for all four scenarios (Figs. 4 and A1). Performance of the best-compromise model was slightly higher for S1 than for the other scenarios, for both calibration and evaluation periods (Fig. 4). The difference in performance between S1 and S2 was smaller. The uncertainty in predicted streamflow estimated from the envelope was low for the calibration and evaluation periods but appeared to peak during low flow periods. The calibrated model provided similarly reasonable representations of DOC (Fig. 5) and NO3- (Fig. 6) concentrations. Predicted DOC concentrations for the calibration period were slightly more accurate for S2 (Fig. 5a) than for S4 (Fig. 5b). Predicted NO3-concentrations for the calibration period were slightly more accurate for S3 (Fig. 6a) than for S4 (Fig. 6b). The model reproduced the contrasting dynamics of stream DOC and NO3- (Aubert et al., 2013; Strohmenger et al., 2020), with maximum DOC and minimum NO3- concentrations occurring in autumn. During this period, the median simulated DOC concentration was ca. 8.7 mg L⁻¹, while that of NO3- concentration was ca. 11 mg N–NO₃ L⁻¹. During the wetting-up period, DOC concentrations decreased to a median of 2.5–3.5 mg L⁻¹, while NO3- concentrations increased to a median of 14–16 mg N–NO₃ L⁻¹. These concentrations remained relatively stable during the wet and recession periods. At the end of the recession period, DOC concentration increased slightly to a median of ca. 5.5–6 mg L⁻¹, while NO3- concentration decreased to a median of ca. 12 mg N–NO₃ L⁻¹. The model simulated high NO3- concentrations in summer, when streamflow and NO3- concentrations had not been observed. During summer dry periods, the stream effectively dries up, and no water flows at the outlet, which made it more difficult to calibrate the model to predict their solute concentrations. The model simulated near-zero water flow during dry periods but occasionally simulated flow on certain days when zero flow had been observed, which yielded relatively high simulated NO3- concentrations. The lack of observed NO3- concentrations during dry periods also provided no constraints that could help the model represent NO3- concentrations realistically.

The simulated hydrological signatures for all solutions on the Pareto front provide evidence that including solute data in the calibration improves the ability of the model to reproduce certain streamflow characteristics. While the performance based on median hydrological metrics (NSE_Q, NSE_log⁡Q, KGE_Q, VE_Q, NSE_FDC) was lower overall for S2 and S4 than for S1 for both calibration and evaluation periods (Fig. 7), the median NSE runoff ratio (NSE_RUNOFF) was significantly higher for S4 than for S1 for the evaluation period (Fig. 7b). In contrast, the performance was significantly higher for S3 than for S1 based on median NSE_log⁡Q and VE_Q metrics for the calibration period and on median NSE_Q, NSE_log⁡Q, VE_Q, and NSE_RUNOFF metrics for the evaluation period. These results suggest that simultaneously evaluating model predictions of streamflow and NO3- concentration improves the model's ability to reproduce streamflow, especially low flows, due to the improvement in NSE_log⁡Q. Compared to S1, the model's hydrological performance decreased the most for S2 and the least for S3. The hydrological metrics for S2 also had wider ranges than those for the other scenarios.

Including DOC concentration with streamflow in the calibration showed lower performance for S4 than for S2, while that using NO3- concentration showed lower performance for S4 than for S3 (Fig. 7). These results, consistent for both calibration and evaluation periods, supported the observations (Figs. 5 and 6), which suggests that calibrating the model with each solute individually with streamflow better reproduced solute concentrations than calibrating the model with all solutes and streamflow simultaneously.

Overall, the posterior distribution of hydrological parameters differed among the four calibration scenarios (Fig. 8), except for fSUR and kR, which were less sensitive to the calibration method (i.e. similar optimal values and distributions), indicating that they had been identified well (Fig. 8i and n). For some parameters, the distributions differed only for one scenario, such as SU_max for S3 (Fig. 8a) and Pmax for S3 (i.e. smaller values and a narrower range of uncertainties compared to other scenarios, considering both the interquartile range and the total whisker range) (Fig. 8d). The latter suggests that calibration using NO3- concentration strongly influenced soil parameters, decreasing percolation of water from SU to SS. Similarly, the distribution of SUR_max for S2 differed from other scenarios and had a narrower range of uncertainties, considering both the interquartile range and the total whisker range. This suggests that calibration using DOC concentration improved identification of SUR_max (Fig. 8l) and that reservoir SUR needs a lower capacity to reproduce both streamflow and DOC concentrations. In addition, for S4, distributions of the most influential hydrological parameters (i.e. CP and QL) (Fig. 8b and j), as well as of groundwater parameters kS and SS_mix, differed from those of the other scenarios. Comparing distributions of the groundwater mixing volume in the slow reservoir (SS_mix) for S2 and S3 showed that its size could be decreased by a factor of ca. 3 when calibrating using NO3- concentrations instead of DOC concentrations (Fig. 8h).

Overall, all parameters except for kF and kS had lower uncertainty when the model was calibrated using solute concentrations, whether simultaneously or separately (Fig. 8). More specifically, the uncertainty in βH, fSUR, SS_mix, and kR decreased for S2, S3, and S4. The uncertainty in CP, βR, and SUR_max decreased for S2 and S3, while that in Pmax and Lp decreased for S3 and S4. The uncertainty in SU_max decreased only for S2, while that in f decreased only for S3. For deep-infiltration losses (QL), only calibration using DOC and NO3- concentrations simultaneously (S4) decreased its uncertainty compared to those for other scenarios (Fig. 8j).

Calibrating the model with DOC and NO3- concentrations along with streamflow data influenced water-balance components and changed the storage in reservoirs SU, SS, and SUR. The median simulated total evaporative flow (EU and EUR) was highest for S1 (470 mm yr⁻¹) and lowest for S4 (372 mm yr⁻¹) (Fig. 11a). Median deep-infiltration losses (QL) were highest for S4 (128 mm yr⁻¹) and lowest for S3 (54 mm yr⁻¹). The median contribution of SR to discharge (QR) was slightly but significantly higher for S3 and S4 (108 and 109 mm yr⁻¹, respectively) than for S1 (100 mm yr⁻¹). The median contribution of SS to discharge (QS) was significantly higher for S2 (293 mm yr⁻¹) than for S1 (242 mm yr⁻¹). SS and SUR stored water during the simulation, while SU lost water. SS tended store significantly more water for S4 (2.7 mm yr⁻¹) than it did for S1 (1.2 mm yr⁻¹) (Fig. 11b). SU lost significantly more water for S3 (-21 mm yr⁻¹) than for S1 (-12 mm yr-1) and lost the least for S4 (-10.6 mm yr⁻¹).

The parsimonious solute-transport model reasonably reproduced simultaneously the dynamics of discharge, DOC and NO3- concentrations in the stream of the Kervidy–Naizin catchment for all scenarios. Model predictions based on independent data indicated that the model generally reproduced the dynamics of groundwater level and soil moisture in upslope and riparian zones for all scenarios. Including solute (DOC and NO3-) data along with streamflow data in a multi-objective calibration strategy improved the representation of groundwater storage and soil moisture in the upslope zone (Figs. 9 and 10b). The improvement in the representation of groundwater level was significant and relatively large for scenarios S2, S3, and S4 compared to S1 (Fig. 9). In contrast, the improvement in the representation of soil moisture in the upslope zone was significant but relatively small only for scenario S2 compared to S1 (Fig. 10b). Thus, only scenario S2 improved the representation of both groundwater and soil moisture in the upslope zone.

Studies have shown that using additional information to constrain hydrological models usually improves spatial and/or temporal patterns of internal state variables and flows but does not necessarily improve the accuracy of predicted runoff (López López et al., 2017; Tong et al., 2021). Woodward et al. (2013) developed a catchment simulation model that predicted streamflow and water chemistry by connecting a model of soil water balance to two groundwater reservoirs. They found that calibrating the model using daily streamflow and monthly NO3- data simultaneously from a small lowland milk-production-oriented catchment improved hydrological understanding and estimated catchment NO3- flows relatively well. In particular, they were able to infer daily contributions of near-surface water; fast shallow groundwater; and slower, deeper groundwater to water and NO3- discharge. However, including NO3- data in the calibration overpredicted low flows compared to calibration using streamflow data alone. Yen et al. (2014) used regional estimates of annual denitrification mass and the percentage of NO3- load at the catchment outlet that had come from groundwater as soft data to constrain water-flow partitioning, which yielded realistic internal catchment behaviour but decreased the accuracy of predicted streamflow. In this study, when considering only the best-compromise model for each scenario, the use of solute data improved the representation of groundwater storage (S2, S3 and S4, Fig. 9) and soil moisture in the upslope zone (S2, Fig. 10b) but slightly decreased the accuracy of predicted streamflow in both calibration and evaluation periods (Fig. 4). In contrast, considering all hydrological signatures for discharge obtained from the envelope, S3 improved the model's ability to reproduce streamflow characteristics, especially low flows (Fig. 7) and groundwater level (Fig. 9).

We included solutes (DOC and NO3-) that have opposite dynamics and whose conceptual models had been successfully tested in the literature (Birkel et al., 2014; Fovet et al., 2015b), with the aim of adding useful constraints to the hydrological modelling. However, none of the scenarios that included DOC and/or NO3- improved both the model's representation of streamflow dynamics and internal consistency in representing groundwater level and soil moisture in the riparian and upslope zones. Given the limits of this study, it remains uncertain whether including solutes with streamflow in calibration only improved the representation of hydrological states and flows of specific reservoirs or also improved the model's overall internal consistency. The first limit came from comparing point-scale in situ observations to simulated soil moisture and groundwater levels that represented catchment-scale storage, as these observations may not have represented the actual dynamics of groundwater and soil storage. Furthermore, although the dynamics of DOC and NO3- concentrations in the stream were represented well, the conceptualization of biogeochemical processes and transport of these solutes may remain too simple to represent internal state variables and flows of solutes. The model represents the hydrological and biogeochemical processes that are assumed to dominate, and these assumptions are limited by incomplete knowledge. In addition, the representation of reactive solutes increased the number of parameters and the complexity of the model. Consequently, it would be interesting to compare this approach to the use of non-reactive solutes in calibration, such as natural tracers that are assumed to be conservative, including chloride (Cl⁻) and stable isotopes of water (¹⁸O and ²H) (Kirchner et al., 2010), to assess whether the model can reproduce the dynamics of both soil moisture and groundwater better.

The factors that improve internal hydrological consistency when solute data are included are not well understood. Streamflow aggregates information from many catchment-scale processes, but this information is too ambiguous to determine the exact catchment configuration (Kuppel et al., 2018b) or flow pathways that produced the observed signal (Woodward et al., 2017). This is because streamflow aggregates downstream along a convergent network towards a single outlet, but the divergent nature of an upstream network makes it impossible to uniquely backtrack the locations where the flow was generated (Kirchner et al., 2001). Thus, streamflow can be simulated well with many alternative model parameterizations, whether or not they are physically consistent (Kirchner, 2006). Results of the present study thus suggest that if streamflow alone is used for calibration, the model predicts discharge correctly for the wrong reason, as internal consistency, especially the representation of groundwater level, is not guaranteed. The model thus simulates water pathways and storage dynamics that do not represent those in the actual catchment. Consequently, it appears that the hydrological behaviour of the catchment required to reproduce the observed DOC and NO3- concentrations in the stream is different from that required to reproduce only the observed discharge. This hypothesis is supported by the fact that the calibration scenarios influenced the main components of the water balance differently. For example, S3 yielded better representation of the groundwater reservoir, with good reproduction of the groundwater level (Fig. 9) but lower evapotranspiration and higher water loss from the SU reservoir than S1 (Fig. 11b). In comparison, S2 yielded better representation of upslope soil water storage (Fig. 10b) and a higher contribution of SS to discharge than S1 (Fig. 11a). The large amount of information in the solute time series thus constrained internal reservoirs and water flows more than a streamflow-only approach, which increased internal consistency of the hydrological model. This occurs because a hydrological model only needs to represent an input–output response, whereas when biogeochemistry is included, a model needs to represent both residence-time distributions and biogeochemical processing to reproduce the observed stream concentrations (Medici et al., 2012) and the decrease in solute-input signals. The use of solute time series, which mitigates the equifinality problem, thus excluded infeasible model configurations that would have also yielded high performance (Dimitrova-Petrova et al., 2020; Kuppel et al., 2018b; Yen et al., 2014).

An additional step is needed to understand the benefits of including solute data for internal hydrological consistency by analysing effects of including DOC and NO3- concentration data on the storage dynamics (state and flows) of model components. For example, the simulations showed that including NO3- data decreased kS and SS_mix (Fig. 8g and h), suggesting that simulations of NO3- dynamics were optimized at a lower groundwater mixing volume and lower flow rate in SS. However, it is important to go further to understand why including NO3- concentration data improved simulation of groundwater level (Fig. 9) and low flow (Fig. 7). In this landscape, most of the NO3- leached from the unsaturated reservoir accumulates in the shallow groundwater (Aubert et al., 2013; Strohmenger et al., 2020). The groundwater, with a legacy mass storage of NO3- (Basu et al., 2010; Molenat et al., 2008), thus contributes water to the stream that sustains the base flow and export of NO3- (Aubert et al., 2013; Molenat et al., 2008). Given these characteristics, good reproduction of NO3- concentrations and flows in the stream, mainly supplied by groundwater, can be assumed to constrain the model sufficiently to yield good reproduction of water flows from the groundwater to the stream and thus good representation of groundwater level.

Using a parsimonious hydrochemical model without explicit biogeochemical processes, Strohmenger et al. (2021) found that overall parameter uncertainties were higher when calibrating using solute data (DOC, NO3-) along with streamflow data than when calibrating using streamflow data alone. They assumed that DOC and NO3- sources behave as infinite pools with a fixed concentration in each reservoir contributing to the stream. The modelling approach in the present study was relatively similar but explicitly represented biochemical processes related to DOC and NO3-. This approach resulted in decreased parameter uncertainty when solute concentrations were included in calibration, except for storage coefficients of the fast (kF) and slow reservoirs (kS) (Fig. 8). Comparing the results of these two studies suggests that the infinite-solute-pool assumption is sufficient to reproduce annual and storm-event dynamics of discharge and DOC and NO3- concentrations in the stream but is insufficient in calibration to constrain the model to adequately reproduce water storage dynamics and flow paths and to reduce uncertainties in hydrological parameters. In the infinite-solute-pool assumption, hydrological parameters are indeed less sensitive to solute concentrations than they are in models that explicitly represent biogeochemical processes and dynamic solute concentrations in reservoirs. Notably, the results of this study highlight that S4, which considered all constraints (i.e. streamflow and DOC and NO3- concentrations), greatly influenced the distributions of the most influential hydrological parameters, specifically QL and CP, whose values were among the highest or lowest, respectively (Fig. 8b and j), and reproduced groundwater levels the best (Fig. 9). This highlights the importance of parameters QL and CP, which determine inter-catchment groundwater flows and the recharge from SU to SS and SUR to SR, respectively, in ensuring that the model reproduced the observed groundwater dynamics. Based on these results, for the model to best reproduce the dynamics of streamflow, concentrations (DOC, NO3-), and groundwater, recharge should be decreased and inter-catchment groundwater flow should be increased to ca. 0.35 mm d⁻¹ (best-compromise parameter value for S4, Fig. 8j). This value is consistent with the values found in modelling studies of a similar physiographic headwater catchment in Brittany (Fovet et al., 2015a; Hrachowitz et al., 2014).

The model conceptualizes biogeochemical processes for DOC and NO3- in a relatively simple way but has reduced the uncertainties of the parameters. An additional step in future studies will be to analyse whether more complex representation of biogeochemical processes in the model can further reduce uncertainties in hydrological parameters. Results of the present study are consistent with those of other studies, in which inclusion of additional variables in multiple-objective calibration generally reduced parameter uncertainty (Tong et al., 2021). For example, Yen et al. (2014) found that including data related to water quality yielded lower parameter uncertainties than calibration using streamflow alone, especially for hydrological parameters that strongly influence denitrification. Silvestro et al. (2015) demonstrated that the equifinality of soil parameters was reduced by including satellite-derived soil moisture when calibrating a process-based, spatially distributed hydrological model. Similarly, Rajib et al. (2016) found that including satellite-derived soil moisture, especially that in the rooting zone, reduced parameter uncertainties, particularly for parameters related to subsurface hydrological processes.

A remaining issue is the limited comparability of point-scale in situ measurements and simulated soil moisture and groundwater level to catchment-scale storage. In situ volumetric soil moisture was calculated as the mean of several TDR probes, which reduces uncertainty at the point scale, but upscaling these point measurements to a reservoir that represents a hillslope or riparian zone is associated with uncertainties. Consequently, we considered normalized soil moisture as a proxy for dynamics of unsaturated storage in hillslope and riparian zones. Similarly, we used the daily mean normalized water level at point PG5 as a proxy for groundwater storage dynamics. An additional step in future studies will be to determine how point measurements can be upscaled to areal-mean point-scale soil moisture and groundwater measurements compatible with catchment-scale storage. A complementary approach is to include other promising methods, such as remote sensing, to estimate the spatial distribution of storage in catchments, especially of soil moisture (Duethmann et al., 2022; Tong et al., 2021). The high spatial resolution, worldwide spatial coverage, and increasing availability of remotely sensed data may provide ample opportunities to further constrain hydrological models and their parameters (Bouaziz et al., 2021; Duethmann et al., 2022; Gomis-Cebolla et al., 2022; Nijzink et al., 2018; Tong et al., 2021). Recent soil moisture data from satellite-derived soil-moisture products (e.g. SMAPL3E, SCATSAR, ASCAT DIREX SWI) with high spatial and temporal resolutions (e.g. 0.5–9.0 km and 1–3 d, respectively) (Duethmann et al., 2022) would help constrain the model of the Kervidy–Naizin catchment. Other promising methods include cosmic-ray neutron-sensor probes to estimate dynamics of near-surface soil water storage (Dimitrova-Petrova et al., 2020) and geodesy and geophysical methods (Fovet et al., 2015a). Additional data can be used to assess the internal representation of evapotranspiration, which has a wide spatial and temporal distribution at the catchment scale, to provide more confidence in simulation of the partitioning of water between soil storage and groundwater recharge (Moazenzadeh and Izady, 2022). For example, using spatially and temporally gridded remotely sensed evapotranspiration data to calibrate the Soil and Water Assessment Tool (SWAT) hydrological model decreased the equifinality of the calibrated parameters compared to calibration using only streamflow data (Shah et al., 2021). These results demonstrate the benefit of using increasingly available open-access remotely sensed evapotranspiration data to improve calibration of hydrological models. These methods provide a spatially aggregated overview of catchment water content and go beyond traditional methods of direct storage observations at the point scale that are limited to a single reservoir (Dimitrova-Petrova et al., 2020).

This study's results indicate that solute data are important for improving the internal consistency of hydrological models, which can help guide collection of field data and modelling (Stadnyk and Holmes, 2023). When collecting field data for model calibration, it may be important to collect solute data along with streamflow data. These data can then be used in a hydrological model to which simple representations of biogeochemical processes are added to improve the representation of internal behaviour of the catchment by calibrating streamflow and solutes simultaneously. The type of solute measured is also important, as calibration using NO3- improved the internal consistency of the groundwater reservoir, while that using DOC improved the internal consistency of soil water storage in the upslope zone. With the increasing availability of solute data from catchment monitoring, this approach provides an objective way to improve representation of complex hydrological systems when information about their internal functioning is insufficient. A catchment model that represents observed behaviour of the system more accurately can then be used with confidence when assessing scenarios, such as those of nutrient remediation or climate change. If the internal behaviour of the hydrological system is not represented correctly, predicting streamflow acceptably is pointless and perhaps counter-productive, leading to erroneous conclusions and potential mismanagement of catchment resources. For example, Yen et al. (2014) showed that a lack of constraints to realistically represent the internal functioning of a catchment can lead to misleading assessments of pollution-control scenarios, even when typical streamflow performance criteria are satisfied.

The ability to apply this modelling approach to other catchments with different physiography will depend on the model's ability to represent dominant sources and pathways of DOC and NO3- concentrations that differ from those of Kervidy–Naizin. To address this question, we analysed the response of stream water chemistry to changes in discharge observed in this catchment and how the model represents it. Changes in solute concentrations as a function of discharge (i.e. concentration–discharge (CQ) relationships) (Appendix B) provide insight into how catchments store and release water and solutes and can therefore be considered a “fingerprint” of catchment transport, mixing, and reaction processes (Godsey et al., 2009; Knapp et al., 2020). Long-term seasonal CQ slopes for NO3- in Kervidy–Naizin generally indicated a chemostatic NO3- export regime (Fig. B1a). Indeed, this pattern often emerges in catchments with a spatially uniform distribution of abundant solute sources, such as NO3- in agricultural areas, which leads to a relatively constant release of solutes to the stream network (Bieroza et al., 2018). In contrast, in the winter of a few years (2010, 2012 and 2014), the CQ slope indicates instead a slightly more chemodynamic export regime with a dilution pattern. Long-term seasonal CQ slopes for DOC indicate a chemodynamic export regime with an accretion pattern that changes to a chemostatic export regime in autumn (Fig. B1b). The model reproduced the differing export regime of each solute from 2008–2016 relatively well (Fig. B1). Model performance was slightly lower for DOC (RMSE = 0.13–0.27) than for NO3- (RMSE = 0.08–0.21). For a few years, the model did not represent the export regime accurately. The export regime for NO3- observed in winter 2008 and 2009 was chemostatic, but the model simulated a chemodynamic export regime with a dilution pattern. The export regime for DOC observed in autumn 2011 and 2014 and summer 2012 and 2014 was an chemostatic export regime, but the model simulated a more chemodynamic export regime with an accretion pattern. As the model simulated hydrological dynamics relatively well during these periods (Fig. 4), it was likely overpredicting DOC. Analysis of the CQ relationships observed and simulated in Kervidy–Naizin highlighted two important points: (i) each solute in this catchment did not have a single pattern but instead seasonal and interannual differences in export regimes, and (ii) the parsimonious solute-transport model was able to reproduce different export regimes. Thus, this modelling approach may be applicable, in particular due to its flexible structure, to headwater catchments, whose characteristics and export regimes differ from those of Kervidy–Naizin. Applying the model to catchments whose streams can be intermittent would first require solving the methodological issue of high NO3- concentrations in summer, when no observed data are available, to prevent overpredicting concentrations and risk overestimating NO3- flows in summer. The model can also be adapted to represent catchments whose hydrological and biochemical patterns differ from those of Kervidy–Naizin, where most DOC accumulates in the soils of the riparian zone and NO3- accumulates in the groundwater. For example, the reservoirs in which DOC is produced or lost can be modified easily. In addition, more complex models of biogeochemical processes can also be considered. While we represented heterotrophic denitrification as a constant, dynamic equations (Heinen, 2006) could easily be incorporated to represent the seasonality of this process.