All models were run on daily time step and calibrated with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm by as implemented in the MARRMoT Toolbox. We used a 10-year time period from 2004 to 2014 for calibration and a 10-year time period from 1993 to 2003 for evaluation with a one-year warm-up period each. The evaluation period of the catchment AUS6 had to be shortened to eight years (1981–1988) because of data gaps; the calibration period covers 1990–1999. We conducted 18 800 (5×47×8×10) calibration runs to calibrate each of the 47 models on all eight metrics in each of the ten catchments. To consider parameter uncertainty we calibrated each combination on five different seeds and retained the best 500 parameter sets across all seeds.

For all analysis, we focus on the calibration period only, because it provides the closest connection between objective function choice and resulting model behaviour. If objective functions cannot produce accurate signatures during calibration, it is unlikely that they will systematically do so during evaluation. We provide additional plots showing model and signature performance during the evaluation period in the Supplement (Figs. S13/S14).

We establish a baseline performance benchmark to remove poorly performing models from further analysis. Based on earlier arguments and examples , we use an ensemble of benchmark models that can be used to establish the minimum performance a model should exceed. The HydroBM package , provides 22 benchmark models that can easily be used. They cover three broad categories: benchmarks derived from streamflow data, such as the daily mean flow timeseries, which accounts for seasonality; benchmarks derived from rainfall-runoff ratios; and very simple empirical models that approximate aggregated catchment behaviour. For each catchment, we compute the performance of the timeseries these benchmark models create by comparing it to the observed discharge data in the calibration period. By calculating all eight performance metrics we can identify which benchmark model yields the highest performance for each metric and catchment. This performance will be used as the benchmark to beat. Model runs that fail to outperform this highest benchmark are excluded from further analysis, ensuring that only sufficiently reliable models are carried forward to the analysis of signature performance. For catchments with a snow fraction larger than 30 % we additionally remove all models without a snow module from the analysis should they manage to beat the benchmark.

We selected 15 streamflow signatures to investigate the extent to which objective function choice influences a model's ability to replicate streamflow signatures. Our goal with this selection is to cover different aspects of the flow regime, as well as a range of hydrological processes . The selected signatures are shown in Table  and were all calculated using the TOSSH toolbox , a more detailed description of each signature can be found in Sect. S2.5. Most of the considered signatures describe streamflow properties such as the slope of the flow duration curve (FDC Slope, 33rd–66th exceedance percentiles), the 5th and 95th streamflow percentiles (Q5 and Q95), the high and low flow duration (HFD & LFD) and frequency (HFF & LFF) as well as the mean half flow date (MHFD). The slope of the FDC describes the variability of the streamflow regime, indicating how quickly a river responds to rainfall events and how sustained the flows are during dry periods. Representing it correctly therefore indicates a good representation of in-catchment storage and flashiness behaviour. The 5th and 95th streamflow percentile describe the magnitude of low and high flows. Representing these signatures well indicates a good representation of extreme flow behaviour, while representing the high and low flow duration and frequency well ensures that also these important characteristics of extreme flow can be met. The MHFD helps to determine if the general timing and seasonality of streamflow is represented well. Additionally, we evaluate the impact of the objective function on the total runoff ratio (Total RR), event runoff ratio (Event RR), baseflow index (BFI), baseflow recession coefficient (BFRC), flashiness index (FI), variability index (VI) and rising limb density (RLD). These are intended to deliver information on the different catchment processes such as the general water balance (Total RR), individual storm responses (Event RR), the baseflow processes (BFI, BFRC) or general water storage behaviour and runoff dynamics (flashiness index, variability index, rising limb density).

Figure  shows the performance of all 47 calibrated models with their 500 best parameter sets (violins) compared to the highest calculated benchmark (red dash) as described in Sect. .

The number of models that beat the benchmark varies considerably across catchments and objective functions (number shown below each violin). In three catchments (C12, HYS, LAM) the number of models is comparatively low. The explanation is a strong snow influence, which produces seasonality that only the 12 of the 47 MARRMoT models that include a snow module can accurately reproduce. In other catchments, most models beat the benchmark, and the models that fail may be missing important process controls (e.g., groundwater representation) though this is more difficult to diagnose than the snow cases. In a handful of cases all models can beat the benchmark (e.g. GB2 for the KGE objective function), and for every combination of catchment and OF, there are at least 3 models exceeding the benchmark ensemble. As may be expected, more complex models (more parameters and stores), tend to outperform the benchmark more often and were retained more frequently (result not shown).

To begin the analysis of how objective functions affect hydrological adequacy, we compare the simulated signature values with the observed signature values for all eight objective functions. Figure  shows the distribution of absolute errors (y-axis) over all catchments (x-axis) for each metric (subplots) for one of the 15 signatures, the Total Runoff Ratio. The plots for all other signatures can be found in Sect. S2.9 (Figs. S16 through S29).

In Fig. , there are three things of note. First, the location of the violin plots shows whether the signature values are underestimated (negative values), overestimated (positive values) or relatively unbiased (centered around zero). Second, the size of the violins indicates whether the signature predictions are well-constrained (short violin) or not (long violin). Third, the catchments are ordered from driest (left) to wettest (right) indicating if signature error correlates with climate.

There is no clear pattern in Runoff Ratio errors related to the catchments' aridity values. Instead, there appear to be two categories of results: objective functions that return mostly unbiased models in all catchments (KGE and KGE-NP), and objective functions where the signature representation of the resulting models varies strongly per catchment (e.g. NSE: relatively unbiased in some basins, large variability in signature errors in others). The KGE-NP constrains the variability within the models much better and is therefore assessed as the best available objective function for the general water balance as represented through the Total RR signature. For the remaining six objective functions, the Runoff Ratio tends to be underestimated and positive errors are relatively rare. This means that generally the models tend to put too much water into storage and/or evaporation or other sink terms, which may become relevant when modelling climate change impacts.

To show the results for more signatures in an aggregated way, Fig.  shows the median simulated signature value over all models above the benchmark (underlying data can be seen in Figs. S16–S29). The median was chosen to achieve the most representable summary of the model ensemble, which is not susceptible to outliers. This gives an overall impression on the capability of the different models to represent the hydrological signatures of interest. It also allows a first impression of the impact different objective functions have on signature representation. In Fig. , the coloured dots indicate the median modelled signature value for each objective function, while the black line shows the signature values calculated from observations. The grey violins indicate the variability in the modelled signature value if all individual model results with their 500 best parameter sets are considered (every model that beats the benchmark for any objective function). The plot therefore allows insights on how well a signature value can generally be represented through the different tested models and gives a first impression on the influence the objective function has on these representations. The x-axis denotes the 10 selected catchments and the y-axis gives the signature value in its native unit (see Table ).

Initially, we can use this plot to compare the violin ranges to the observed values of signatures. For the vast majority of cases, the observed value is always within the boundaries of the model ensemble, which indicates that the tested conceptual models are able to capture the hydrologic variability across diverse catchments. The spread of the coloured dots around the observed values indicates different degrees of accuracy in the signature representation depending on the calibration metric used. For some signatures, the range of signature values is notably smaller (e.g. Total RR) than for others (e.g. Rising Limb Density). There are signatures (e.g. Q95, BFI) where the objective functions differ strongly from each other and signatures where different objective functions lead to similar modelled values (e.g. MHFD, HFD). To move beyond these very broad conclusions, the next section will use the previously introduced error metric (Eq.  from Sect. ) to assess the relative skill of each objective function in more detail.

In this section we use Eq. () to normalize the signature errors using the observed signature value. Figure  shows the normalized error in signature representation for all objective functions. Generally, we can see that the performance varies largely depending both on the signature (each violin in a plot) and catchments/models (within the violins).

The KGE in Fig.  has good performance for the Total Runoff Ratio and the high flow percentile Q95 (violin has a smaller spread around the zero error line). This does not only apply to the median performance (white dot in the violin) but also has a high consistency among catchments and parameter sets (violin spread). However, particularly for the low flow percentile Q5, LFF, FDC slope, and Variability Index the representation obtained from calibrating to KGE relative to the other objective functions is often worse.

The NSE performs mediocre on almost all of the evaluated signatures: the range within catchments and runs (spread of each violin) is often large. This indicates that the suitability of the NSE metric can be very catchment- and model-dependent. HFF, FI, RLD and Q95 are usually underestimated by models calibrated on the NSE. Compared to the KGE, the performance on Q5, and FDC slope is typically better.

For KGE0.2 and log NSE, we see similar patterns in signature error. Both (KGE0.2 and log NSE) underestimate the runoff generation and high flows as well as the reactivity of the catchment (Flashiness Index). The log NSE is often the worst objective function among the eight investigated, indicated by high or low values. Both metrics show improvements compared to the KGE for FDC Slope and Q5, but not necessarily for low flow duration (LFD) and frequency (LFF). It is important to notice that the FDC Slope can also be met well if the runoff is systematically biased, which is the case with underestimation here. In many of the evaluated 15 signatures, the KGE0.2 shows a better performance than the log NSE (violin closer to 0).

The diagnostic efficiency generally performs similarly to the KGE0.2. It mainly improves representation of the BFI but has comparable issues for Total RR and Q95. Compared to the KGE, the errors are constrained better across catchments (smaller violins). In conclusion, the diagnostic efficiency proves to be a viable alternative for low-flow calibration, while offering benefits on additional signatures (such as BFI and VI).

The non-parametric version of the KGE performs worse than the KGE on high flows, but improves other signatures strongly, such as the BFI, FDC Slope, Q5 and LFF. The KGE-NP is among the objective functions that perform best overall. The expectations (general improvement due to more information being included) for KGE-NP are thus largely met, with the main benefit being better incorporation of flow variability for a larger fraction of flow percentiles.

KGE-Split performs similar to the regular KGE, though shows a tendency towards larger errors. Like the NSE, it has no signature that is represented both more accurately and consistently than alternative objective functions. Compared to the regular KGE, there are slight improvements on selected signatures (FDC Slope, BFI, Variability Index).

Lastly, the SHE is one of the objective functions with the largest range in signature representation. The general patterns are similar to the KGE (as expected due to their similar formulation), except for selected signatures like FDC Slope. This indicates that a change from value-based correlation to rank-based can be influential for signature representation.

The violin plots also show that some signatures are affected very little by the choice of objective function such as the Rising Limb Density and the Mean Half Flow Date, which is indicated by a similar distribution among objective functions. This suggests that either the models or the catchment mainly influence the results. As the signature value cannot be simulated well from any of the models, this shows the limits of objective function influence.

The Supplement (Figs. S30 and S31) includes plots on the analysis with 25 and 100 parameter sets in comparison to the 500 used here. Since the results remain comparable, we assume that parameter uncertainty plays only a minor role here. Additionally, the SM also provides an example of the error metric collapsed to one value per catchment as it is being used in the assessment of overall skill (Fig. S32), which emphasizes the differences more, but does not account for model- and run-level uncertainty.

This previous section showed the skills and shortcomings of the individual objective functions regarding signature representation. However, it is not easy to assess whether the observed influences that were described can be considered significant for the process representation. To investigate this, we apply statistical testing in this section. Figure  shows the distributions of p-values when testing the significance of signature values calculated with different OFs against each other.

All signatures show a large range in p-values, which implies that there are both objective functions which have similar and different representation for each signature. Some OFs typically behave similar, e.g. the distributions of KGE0.2 and log NSE are often comparable for low flow signatures. Figure  shows that the choice of objective function strongly affects the following signatures: the Total RR, Event RR, Q5, Q95, LFF, BFI, BFRC, and the Flashiness Index. For the remaining 7 signatures (Low and High Flow Duration, HFF, Mean Half Flow Date, FDC Slope, Variability Index, Rising Limb Density) a change of objective function does not lead to a clear shift in signature representation for most of the combinations of objective functions. Table S3, Sect. S2.11 shows the frequency of objective function pairs reaching p-values of below 0.10 or 0.05 respectively.

By comparing Fig.  to Fig.  we can conclude that there can be considerable spread in the representation of the signatures that do not show a significant difference. This is because the spread for signatures like Low Flow Duration, Variability Index, or Rising Limb Density is often not consistent, meaning that when comparing the distribution of signature values of two objective functions with each other, there is variation as to which one has higher or lower values. Therefore, the significance often shows no significant impact because the signal is not clear. The significance test indicates that the variation is not driven by the objective function and we speculate that in these cases other influences such as catchment characteristics or models drive the spread seen in the signature representation.

Figure  shows the random forest feature importance for catchment, model, and OF (parameter-set variability is considered as a median value across the 500 parameter ensemble).

Reading the value and error panels together clarifies the role of each factor. Catchment dominates the absolute signature values which is expected, since the basins were deliberately chosen to be hydroclimatically diverse. However, its importance for the signature error is markedly lower and roughly equal across the eight signatures. Objective function has comparatively limited control over the value, yet its importance rises for the error, most strongly for Total RR, Event RR and Q95, and typically exceeds that of model choice. Model structure contributes throughout and gains relevance for low-flow and baseflow signatures (BFI, BFRC, Q5), where together with OF choice it challenges the catchment as the leading predictor. The pattern is consistent across signatures: the catchment largely controls the order of magnitude of the simulated signatures, but the choice of objective function and model structure play a large role in how closely those magnitudes match the observations.

Our results suggest that all objective functions can represent some signatures well while having shortcomings in others. This implies that, when selecting an objective function, there is not a single choice that will ensure realistic values across the spectrum of streamflow signatures we investigated. Yet, we can identify objective functions that generally have good process representation across several signatures by investigating the accumulated errors of all significantly influenced signatures as shown in Fig. . For this, we use Eq. () to get one median error value per signature and objective function. Figure  shows this accumulated error for the eight tested objective functions.

The modeled overall error in signature representation varies strongly depending on the objective function chosen. Considering the entire set of signatures with significant metric influence, the KGE-NP, NSE, and DE show the best overall performance. Conversely, this study identifies the log NSE as having the overall largest errors. This, however, does not immediately imply that certain OFs should not be used as each has its strengths and weaknesses. As shown before, the KGE is the best metric for high flow conditions (small errors for Q95) and works well for Total RR, while it has considerable weaknesses for low flow representation (e.g. BFI, BFRC and Q5). And while the log NSE performs decently on low flow conditions (Q5) it is considerably worse for most other significant signatures. Similarly, despite the KGE-NP showing the best overall performance, it still comes with weaknesses in Q5 and FI representation.

As a robustness check, we repeated the central signature-error and objective-function ranking analysis for the evaluation period. The evaluation-period results broadly confirm the calibration-period patterns. As expected, signature errors generally increase during evaluation, but the relative strengths and weaknesses of the objective functions remain largely similar. In particular, the ranking of objective functions for the OF-sensitive signatures is comparable between calibration and evaluation, suggesting that the main conclusions are not an artefact of calibration-period performance alone. Detailed evaluation period results are provided in the Supplement (Fig. S33).

Across 47 model structures and 10 hydro-climatically diverse basins, OF choice exerts a systematic but selective influence on simulated streamflow signatures. A paired significance test indicated that 8 of 15 signatures vary significantly with OF choice (Fig. ), whereas timing descriptors such as MHFD and RLD are largely OF-insensitive. This may in part be due to the selection of OFs, as objective functions that specifically target time offset (e.g Mean Absolute Peak Time Error; MAPTE) are less frequently used than the OFs we did select. Generally, no single OF excels at all tested signatures. Considering the cumulative error across OF-sensitive signatures (Fig. ), KGE-NP yields the lowest overall error, with NSE and DE performing competitively in some basins but less consistently across signatures. The DE and the selected transformed OFs (log NSE, KGE0.2) reproduce low flow metrics better (Q5, LFF), but particularly the latter come with considerable tradeoffs in the representation of other signatures such as Total RR, baseflow related signatures, or HF signatures.

Our analysis hence contributes to the available information of specific strengths and weaknesses of individual OFs. KGE, for example, most reliably reproduces Q95 , and KGE-NP is one of the best OFs for total runoff ratio and for the baseflow index (BFI), while sharing the best representation of baseflow recession (BFRC) with DE. Log NSE, in comparison, showed few strengths for representing hydrological signatures in our experiments, performing well only on Q5. However, DE reproduces Q5 comparably while carrying a smaller overall error, which is why we recommend DE for that signature and DE or KGE0.2 for low-flow frequency rather than the transformed NSE. The KGE-Split, NSE, and SHE show a balanced error field with individual differences in cumulative errors (Fig. ); within this group, NSE is the most reliable for Event RR, where it ranks alongside KGE-NP, and KGE-Split is otherwise unremarkable but reproduces the Flashiness Index best of all tested OFs.

We also compared the influence of OF choice on signature representation with other influencing factors such as catchment characteristics or model structure choice. Our random-forest analysis showed that catchment characteristics are the dominant control of signature representation, with OF choice typically more influential than model choice (Fig. ). Model choice does, however, gain relevance for signatures connected to low flow or baseflow representation, while OF choice seemed especially relevant for baseflow related signatures.

When reducing the impact of the conducted catchment selection by training the random forest on signature errors instead of signature values, the importance of the objective functions and model selection increased considerably for most signatures. This indicates the importance of appropriate objective function and model choice across hydro-climatic differences, which may be an overlooked aspect in large sample studies, potentially indicating a path for more detailed evaluation using signatures and their deviations. The broader analysis also contextualizes for which characteristics objective function choice can be influential, while others are predefined by catchment (MHFD) or a combination of catchment and model (RLD), which is shown in Fig. S34. In summary, our results support the argument for a purpose-based model calibration, that considers specific aspects of the flow regime, rather than defaulting to a familiar single metric .

For the signatures that were found to be significantly impacted by OF choice, we used our results to develop guidelines for which OF will perform well in reproducing a given signature as shown in Table . We can conclude that most OF lead to the best representation for at least one signature, highlighting the need for appropriate selection. However, if the goal is a balanced representation of the water-balance and variability across hydrologic regimes, KGE-NP is a strong option. If low flows are central (ecological flows, drought assessment), preference should be given to DE or KGE0.2. If peak flows are the priority (flood risk, infrastructure design), KGE generally performs best for Q95 and related high-flow signatures. Reflecting back on our review of metric choice justification (Fig. ), we strongly recommend to document the trade-offs one is willing to accept explicitly (e.g., low-flow degradation under KGE) and, where possible, to verify unaffected signatures (e.g., MHFD, RLD) since OF changes have limited influence there.

Signatures are not independent from each other. When investigating correlations among observed signatures (Fig. ) we noticed three clusters with similar patterns. First, a runoff/high-flow cluster (Total RR, Event RR, and Q95) shows strong positive association, linking long-term water partitioning to the reaction to events. This aligns with aridity being a primary control on mean runoff . Second, a baseflow/storage cluster, including BFI, BFRC and FI, exhibits tight coupling (higher BFI ↔ lower BFRC and FI) and a strong relationship to low-flow frequency, reflecting how sustained baseflow suppresses low-flow events. Similar to the first cluster, this group was also sensitive to objective-function (OF) choice. Third, a variability/threshold cluster (FDC slope, HFF/LFF, low-flow duration, VI) captures distributional shape and threshold exceedance. These signatures, derived from the hydrograph, partly encode duplicate information and were mostly OF-insensitive. Several other signatures showed weak or inconsistent ties to these clusters, such as High-Flow Duration, Mean Half-Flow Date, Rising Limb Density.

These clusters help explain why improving one signature typically also improves the other signatures in the cluster, yet they do not imply that different OFs are needed for each cluster. For example, KGE-NP performed best for many signatures in the first two clusters (e.g., Total/Event RR, BFI).

We identified some overlap between signatures that are strongly/weakly affected by OF choice and those that were identified as more/less predictable from hydrologic drivers by : some signatures (e.g., FDC slope, durations) tend to be OF-insensitive with low spatial predictability, whereas water-balance and high-flow signatures were more OF-sensitive and spatially predictable. A notable exception is Mean Half-Flow Date, which was well predicted in but showed little OF sensitivity in our study suggesting a stronger climatic control.

If we consider the structural differences among OFs some of these patterns become clearer. For bias/mean terms, KGE's mean component directly constrains volumes, explaining its systematic advantage for Total RR and Q95. OFs that deviate from this approach (NSE, DE, log NSE; Table ) typically perform worse for these metrics . Across objective functions, Total RR tends to be underestimated (Fig. ), reflecting systematic water-balance biases related to excessive storage or evapotranspiration. This pattern underscores the importance of bias terms in objective functions, which directly constrain mean flow and promote a more realistic overall water balance . This underestimation is strongest for low-flow-focused objectives, as also noted by . Our results do not support the claim that KGE resolves NSE's low-flow insensitivity or performs well simultaneously for high and low flows ; note, however, that investigate more basins (albeit in a specific biome), while we test a larger number of models.

For variability terms, replacing variance ratios with FDC-based components (as done for the KGE-NP) or integrating relative errors along the FDC (as done for the DE) re-targets calibration toward distributional shape and mid/low flows, improving BFI, Q5, and Event RR in our results (Fig. ).

For correlation terms, moving from Pearson to Spearman (KGE-NP, SHE) reduces sensitivity to extremes and stabilizes correlation. A direct comparison of KGE and SHE, where the dependence component is the only structural change, suggests improved representation for FDC slope, VI, and baseflow metrics, with similar or slightly worse performance for high-flow signatures . Annual weighting using the KGE-Split yielded mixed, context-dependent benefits and no systematic improvement of low-flow characteristics over baseline KGE in our experiments (Fig. ; ).

Overall, each objective function emphasizes the hydrograph component it encodes, and no single OF performs best across all signatures. Within this picture, the variability term emerges as a particularly influential lever: changes to it propagated to more signatures than changes to the correlation term, an effect most pronounced for low- and mid-flow signatures, while bias terms remain essential for water-balance and event signatures. This component-specific behaviour is consistent with evidence that signature performance depends strongly on which aspect of the hydrograph a metric targets , and reinforces that OF selection should be guided by the signatures of interest rather than by a search for a universally optimal metric.

Streamflow transformations act as a further handle on signature representation, operating not on a single component but on the flow values entering all three. By compressing the dynamic range, the power and log transformations (KGE0.2, log NSE) shift calibration emphasis toward low and mid flows, which is reflected in their improved Q5 and LFF representation at the expense of high-flow and water-balance signatures (Fig. ). The choice and strength of transformation is therefore itself a design decision shaping which signatures a calibration favours, complementing the component-level differences discussed above .

Our study aimed to fill a specific research gap in the current understanding of the impact of objective function choice on signature representation; using a larger number of models across diverse hydrological regimes (in comparison to Table ). To enable a thorough investigation of the results we necessarily had to impose certain limits in other parts of the experimental design (i.e., having to “balance depth with breadth”, ).

First, compared to most studies in Table  we use a limited number of catchments. This keeps computational cost manageable and allows more detailed analysis into individual modelling results than would otherwise be possible. We selected these basins to ensure a hydro-climatic spread, as is common practice in these scenarios (see for example the 12 MOPEX basins that have been used for a large number of studies e.g.. Compared to existing studies, our selected number of objective functions and signatures is fairly typical, while our number of models is clearly higher. The presented study found relevant differences in signature representation depending on the model structure, which might indicate a limitation in generalising signature influence from single-model studies. Conversely, our broader model sample implies that conclusions drawn from the many-basin, single-model studies in Table  may themselves be difficult to transfer to other model structures, given that we find model choice to be a non-negligible, signature-dependent control.

Second, we focus on single-objective calibration because of its prevalence in the current literature. When multiple aspects of the flow regime matter simultaneously, multi-objective calibration has been shown to provide considerable benefits . Multi-objective formulations can expose the trade-offs explicitly via a Pareto front and allow practitioners to choose solutions that best satisfy competing goals . If a single composite metric must be used, a transparent weighting that reflects decision priorities can be helpful. , for instance, argue for directly incorporating multiple ecological-flow characteristics in the OF to improve the relevance of the model for management applications. Similarly, signature values have directly been used in calibration, either as additional objectives or as constraints, to target process realism , and our component-level insights into individual metric strengths and weaknesses can help identify which signatures or complementary metrics to add when a particular aspect of the flow regime is the target. This can potentially improve baseflow behaviour, low-flow frequency, or water-balance partitioning when those aspects are central. However, incorporating signatures does not guarantee a better hindcast/forecast skill in all settings, and can even degrade time-series fit if misapplied .

Third, we note the following three methodological limitations in our study design: (1) The application of the median to calculate representative values within the error metric is an important choice, as this does not capture information on the spread of the signature representation. We accounted for that by visually inspecting the underlying violins, but did not explicitly quantify the spread within the applied metrics. (2) The random-forest importance scores should be read as a relative diagnostic within this specific design rather than a universal attribution of variance. The three predictors differ in cardinality (47 models, 10 catchments, 8 objective functions), which can affect permutation-based importance, and benchmark filtering removes poorly performing combinations beforehand. The scores therefore reflect experiment-specific influence rather than general rankings of hydrological controls. (3) Finally, we did not perform any sensitivity analysis before calibrating the models, and simply calibrated all model parameters. Across all calibration runs, approximately 10 % of parameters reached one of their bounds. We found no indication that these boundary hits were systematically concentrated in a specific catchment, model, or objective function. Still, boundary hits can indicate parameter insensitivity, missing processes, data issues, or overly restrictive parameter ranges. They are therefore difficult to interpret in large multi-model calibration experiments and should be considered as an additional diagnostic of calibration reliability in future benchmarking studies.

Going forward, we see four priorities to build on the individual strengths of existing work (Table ). First, broaden external validity with a larger, stratified basin sample (including ephemeral and groundwater-dominated systems) and potentially a wider model palette spanning physically-based and machine-learning models. Second, test cluster-aware multi-objective calibration that deliberately pairs complementary OFs, e.g., a water-balance/high-flow metric (KGE or KGE-NP) with a low-flow/storage metric (DE or KGE0.2), optionally adding signature-based components. Third, make component-level experiments less ambiguous by swapping KGE-type components one-by-one in a controlled setup, and test weighted KGE-type variants. Finally, propagate forcing/observation and signature-method uncertainty (e.g., baseflow separation) and explore information-rich objectives that go beyond the bias-variability-correlation trio, such as distributional divergences along the flow-duration curve to link calibration more directly to hydrologic processes . Designs like KGE-NP already go in this direction and offer a principled path to retain low-flow sensitivity without relying solely on log transforms.