Hydrological Model Calibration in Data-Scarce Mediterranean Catchments: A Comparative Assessment of Three Strategies

Abstract

Hydrological calibration in data-scarce catchments is challenged by non-stationary regimes, fragmented data, and systematic measurement errors. Conventional calibration approaches often assume continuous records and rely on standard performance metrics, which can bias calibration toward high flows and exacerbate parameter equifinality—ultimately reducing robustness under data limitations. This study provides a systematic comparison of three calibration strategies—Kling–Gupta Efficiency (KGE), a non-parametric variant (R_NP), and Flow Duration Curve (FDC)-based calibration—together with their time-consistent counterparts (SKGE, SR_NP, and SRMSE). All schemes are implemented for the lumped HBV-type TUW model across nine catchments in southern Italy and evaluated using independent metrics targeting overall hydrograph agreement, high-flow behavior, and FDC quantile matching (Q5–Q95). The results reveal that the time-consistent KGE-based strategy excels during in calibration (NSE = 0.56, RMSE = 4.65 m³/s) but shows notable declines in validation (NSE = 0.40, RMSE = 3.91 m³/s), indicating sensitivity to non-stationarity. The R_NP-based approach demonstrates enhanced validation robustness (NSE = 0.51, RMSE = 3.60 m³/s) and low-flow accuracy, with NSE_lnQ = 0.30 and low-flow accuracy, leveraging its non-parametric structure. The SR_NP variant further enhances performance in validation (NSE = 0.52, RMSE = 3.42 m³/s), along with superior low-flow performance (NSE_lnQ = 0.48). The FDC-based strategy effectively reproduces flow distributions during calibration (NSE = 0.41, minimal PBIAS = −0.03%) but exhibits limited temporal transferability (validation NSE = 0.25, RMSE = 4.50 m³/s). Time-consistent variants reduce parameter dispersion by approximately 2–8% (relative to full-period calibration) and improve validation metrics by 5–15% across all catchments. Overall, time-consistent calibration provides a practical pathway to increase robustness under non-stationary, data-scarce Mediterranean conditions, highlighting a systematic trade-off between calibration accuracy and validation reliability.

1. Introduction

Hydrological modeling is a cornerstone of effective water resource management, enabling informed decisions in flood risk assessment, drought mitigation, and climate adaptation across diverse global regions [1,2]. Conceptual models balance physical realism with computational efficiency, making them widely adopted for operational and research applications [3]. However, their efficacy hinges on robust calibration, particularly in regions confronting escalating climate variability, anthropogenic influences, and pervasive data scarcity, where traditional approaches often falter [4,5,6].

In data-scarce environments, calibrating conceptual models to align simulations with sparse or discontinuous streamflow observations presents formidable challenges [7,8,9]. Conventional methods, which optimize parameters against daily discharge records using aggregate metrics like the Nash–Sutcliffe Efficiency (NSE) or Kling–Gupta Efficiency (KGE), are beset by several critical shortcomings [10,11]. Primarily, they are highly sensitive to discharge data errors, often exceeding 20–30% [12]. Secondly, global metrics such as NSE prioritize high-flow events, neglecting critical low-flow processes [13,14]. Thirdly, systematic errors in input data, such as rainfall biases, violate statistical likelihood assumptions [15,16]. Compounding these issues are parameter uncertainty and interannual variability that erode calibration stability, especially under non-stationary conditions where historical records fail to encapsulate evolving hydroclimatic regimes, leading to unreliable extrapolations [17].

Emerging literature advocates for refined calibration paradigms to mitigate these deficiencies [18]. Least-squares-based metrics like NSE and KGE frequently yield parameter ensembles that prove brittle under climatic shifts, even when more resilient alternatives exist within the feasible parameter space [19]. Such metrics inherently bias toward peak flows [20,21], heightening vulnerability to rating-curve errors during extremes [22] and overlooking trade-offs across the full flow spectrum [23]. Prioritizing mid- to low-flow calibration or leveraging drier sub-periods as proxies for projected aridification offers a pathway to more pertinent process insights [24]. Hydrological signatures—scalar diagnostics of catchment behavior—provide an alternative lens for performance evaluation, distilling multifaceted dynamics into interpretable indicators [25]. However, signature-based criteria are not immune to equifinality, as their dimensionality reduction can mask structural ambiguities, a limitation that endures even with advanced formulations [13,26].

To surmount these hurdles and foster holistic assessment across flow regimes, multi-metric frameworks have gained traction, integrating hydrograph fidelity, event-specific accuracy, and distributional signatures to offset single-objective biases [21,27]. This multifaceted evaluation is especially relevant to data-scarce settings, where pronounced flow intermittency and regime shifts demand resilient validation protocols [8]. These imperatives are acutely pronounced in Mediterranean basins, such as those in southern Italy, where non-stationary hydrographs—driven by bimodal precipitation, karstic geology, and intensifying human interventions—exacerbate modeling uncertainties [28,29,30].

Signature-based calibration, exemplified by Flow Duration Curve (FDC) matching, has emerged as a potent countermeasure to data sparsity in hydrological modeling [31,32]. By emphasizing empirical flow distributions over temporal sequencing, FDCs circumvent gaps in episodic records and attenuate timing mismatches, proving superior for ephemeral and intermittent regimes [32,33,34,35,36]. Empirical applications underscore their value: Ref. [37] harnessed runoff and soil moisture signatures to curtail parameter uncertainty in 20 Czech catchments via the Bilan model; Ref. [38] augmented metrics for 141 flash-flood-prone Mediterranean basins using signature-sensitivity analyses; and Ref. [39] pioneered Approximate Bayesian Computation (ABC) for FDC and baseflow index assimilation. Similarly, Ref. [40] validated signature-domain methods within the SUPERFLEX framework, deploying HyMod and reservoir configurations to delineate dominant processes. Recent extensions in data-scarce Mediterranean contexts further affirm this trajectory, with hybrid remote sensing integrations enhancing evapotranspiration inputs for improved runoff simulations [41] and multi-conceptual ensembles bolstering streamflow fidelity in ungauged watersheds [42].

Complementing signatures, time-consistent calibration-aggregating objective functions over sub-annual periods tackle interannual non-stationarity and equifinality by enforcing parameter invariance across hydrologic states, thereby curbing overfitting to transient conditions [23]. This strategy attenuates the “divide-and-measure nonconformity” (DAMN) artifact, wherein partition-induced variance shifts distort metrics like NSE [43]. The split KGE (SKGE), for instance, averages KGE over water years to yield temporally nuanced diagnostics, bolstering transferability and process hypothesis testing [44,45]. Integrating these with multi-metric suites yields comprehensive diagnostics, transcending the constraints of monolithic objectives.

Notwithstanding these advances, theoretical critiques of conventional calibration underscore the imperative for empirical inter-comparisons [46,47]. Multi-criteria and acceptability-based frameworks [48] mitigate biases by probing disparate behaviors, yet they presuppose continuous, high-fidelity records and remain susceptible to forcing uncertainties, such as rainfall deficits in ungauged terrains [12,49]. Signature-centric alternatives, while resilient to temporal artifacts, warrant scrutiny in non-stationary Mediterranean settings, where FDC efficacy versus hydrograph-oriented metrics (e.g., KGE) remains underexplored amid regulation and scarcity [39,40,50].

Southern Italy epitomizes these Mediterranean modeling conundrums: its basins, spanning the Apennines to lower catchments, feature intricate hydrology, stark seasonal precipitation contrasts, and dwindling gauge networks—exacerbated by a 50% global drop in streamflow stations since the 1970s [51]. Catchments here rely on fragmented or reconstructed records, compounded by mismatches between local observations and reanalysis products like ERA5 or CHIRPS [52]. Building on antecedent works—such as the DREAM model’s runoff simulation [33,53,54] and physics-informed calibration in the Aniene basin via snow and recession signatures [2]—this study pioneers a rigorous inter-comparison of calibration paradigms tailored to such exigencies.

In essence, calibrating hydrological models in data-scarce Mediterranean catchments is impeded by non-stationary hydrological regimes, monitoring deficits, and epistemic errors. Furthermore, common evaluation paradigms like NSE and KGE are prone to high-flow skew, equifinality, and validation fragility. This lacuna in comparative testing, exacerbated by increasing interannual volatility and hydroclimatic change, demands more streamlined and adaptive strategies for dependable simulations. To address this, our study systematically compares three calibration strategies—implemented through six distinct schemes—for the HBV-based TUW model across nine catchments in southern Italy (five regulated and four natural catchments). Optimizing 15 parameters against tailored objectives, we scrutinize efficacy via six aggregate metrics and five FDC quantiles (Q5–Q95). Our principal aim is to discern optimal strategies for delineating flow dynamics, thereby fortifying water management resilience in these imperiled domains. This analysis not only elucidates trade-offs in calibration fidelity versus generalization but also extends regional modeling precedents by quantifying time-consistency’s role in parameter stability and non-stationary robustness.

Complementing signatures, our time-consistent calibration, unlike traditional time-invariant assumptions that presume unchanging parameters across the full period without verification, aggregates objective functions over sub-annual periods (e.g., individual years) to enforce stability across hydrological states [23]. This averaging yields parameters more invariant under non-stationarity, curbing equifinality and overfitting to transients, unlike full-period methods that amplify interannual biases [43] Drawing from Ref. [23], who pioneered sub-period calibration for variable climates, it fosters process consistency and transferability in data-scarce regimes. For example, SKGE averages KGE over water years for nuanced diagnostics, aiding hypothesis testing [44,45]. Paired with multi-metric suites, it overcomes single-objective limitations.

2. Methodology

2.1. Study Area

The study area comprises the hydrological basins of southern Italy managed by the “Autorità di Bacino Distrettuale dell’Appennino Meridionale” (River Basin Authority of Southern Apennine), encompassing the regions of Abruzzo, Basilicata, Calabria, Campania, Lazio, Molise, and Puglia. Located in the Mediterranean basin, these basins are bordered by the Adriatic, Ionian, and Tyrrhenian Seas, shaping their complex hydrological dynamics. This study focuses on five regulated reservoirs and four natural catchments, selected for their critical role in water supply and flood control, as well as their diverse seasonal flow regimes, with primary (March–May) and secondary (October–December) rainy seasons (see Figure 1).

The region’s climate is predominantly Mediterranean, characterized by temperate, wet winters and hot, dry summers, though significant variability exists between its lower and upper catchments [55,56]. The complex orography, dominated by the Apennine Mountains, acts as a natural barrier, driving spatial variations in precipitation and creating distinct microclimates [57]. These orographic effects, combined with proximity to marine environments, result in pronounced precipitation gradients across the Tyrrhenian, Ionian, and Adriatic coasts in the lower catchments, challenging hydrological modeling in data-scarce catchments. Non-stationarity in streamflow regimes arises from three sources: (i) interannual climate variability, with year-to-year swings in precipitation and temperature (2010–2020) creating wet–dry cycles that breach temporal stability; (ii) reservoir regulation in five catchments, via varying rules for irrigation, supply, and flood control that shift flows; and (iii) seasonal transitions from bimodal precipitation (wet winters/springs vs. dry summers/autumns), altering runoff mechanisms. This variability underscores the need for robust calibration methods applied in this study, such as time-consistent approaches that address non-stationarity by ensuring time-consistent parameter identification and reducing equifinality in model responses [23,58].

2.2. Dataset

This study utilizes hydroclimatic data from the nine representative study catchments, comprising five regulated (reservoirs) and four natural catchments, to evaluate the calibration framework applied to the HBV-based TUW model. The precipitation regime in these catchments is characterized by strong seasonality, with wet, mild winters and hot, dry summers, reflecting the typical Mediterranean hydroclimate [59,60]. Annual rainfall distribution is bimodal, with peak precipitation in late autumn (October–December) and early spring (March–May), while summer months experience extended dry periods [61,62,63].

Hydroclimatic variability is a defining feature of the study catchments, driven by topographic and geographic factors. Total annual precipitation ranges from 644.5 mm to 1562.2 mm (

Table 1. Physiographic and long-term mean annual hydroclimatic characteristics of the study catchments.

Name	River Basin	Monitoring Control Type	Discharge Data Availability	Missing Value (Days)	Area (km2)	Elevation (m. a. s. l)	Precipitation (mm)	Mean Temperature (°C)	Discharge (mm)	PET (mm)
Camastra Dam	Basento	Reservoir	Jan 2010–Dec 2020	0	343	967	939.1	11.2	333	934.2
Conza Dam	Ofanto		Jan 2010–Dec 2020	0	233	664	1042.6	12.6	389	916.1
Acerenza Dam	Bradano		Oct 2011–Dec 2020	0	143	747	801.4	12.7	156	989.1
Pertusillo Dam	Agri		Jan 2010–Dec 2020	0	581	866	1175.4	12.1	458	922.3
Mamone Alaco Dam	Alaco		Jan 2017–Dec 2020	398	14	1059	1562.2	10.9	941	850.2
Cervaro at Passerella	Cervaro	Natural catchment	Jan 2016–Dec 2020	397	507	503	811.7	13.6	335	1013.9
Carapelle at Ponte Ordona	Carapelle		Jan 2011–Dec 2020	149	489	468	734.5	13.8	134	1026.8
Basento at Campomaggiore	Basento		Jan 2014–Dec 2020	6	840	903	866.6	11.7	289	952.6
Agri at “Ponte la Marmora”	Agri		Jan 2010–Dec 2020	9	265	918	1143.8	11.8	417	920.1

), reflecting influences from elevation gradients and proximity to the Adriatic, Ionian, and Tyrrhenian Seas. High interannual rainfall variability, a hallmark of Mediterranean climates, leads to fluctuating water availability, complicating hydrological modeling and calibration. This variability underscores the need for robust calibration methods, such as the traditional hydrograph-based calibrations with different objective functions and an FDC-based strategy employed here, supplemented by time-consistent variants to capture interannual differences and avoid metric biases from data partitioning [43].

Data scarcity poses significant challenges in this region, particularly for discharge time series. Data scarcity in the study area is characterized by (1) discontinuous discharge records with gaps ranging from 6 to 398 days (Table 1); (2) short observation periods (2–5 years for natural catchments vs. typical 10+ years in data-rich studies); (3) absence of direct discharge measurements for five regulated reservoirs, requiring reconstruction via water balance with inherent uncertainties (±10–20% in evaporation estimates); and (4) limited calibration–validation splits due to short records, restricting robust temporal transferability assessment. For the five reservoirs, direct discharge measurements were unavailable, requiring reconstruction of inflow discharge time series using reservoir water balance equations incorporating inflow and outflow records. This reconstruction introduces uncertainties, as inflow/outflow data may not fully capture natural flow dynamics, yet it necessitates robust calibration methods to constrain parameter equifinality. For the four natural catchments, observed discharge data were available but often discontinuous or limited in duration, highlighting FDC-based calibration’s suitability for sparse or discontinuous datasets. To account for the region’s high evaporative demand, particularly in summer, daily evaporation losses were estimated using the Blaney–Criddle method, which calculates evapotranspiration based on mean temperature and daylight hours [64]. This method was integrated into the water balance calculations to enhance the accuracy of discharge estimates, despite its reliance on simplified assumptions about local meteorological conditions. Time-consistent calibration computed objective functions over annual sub-periods to capture interannual variability, reducing equifinality and the DAMN effect [65]. Supplementary S1 shows the time series of hydroclimatic data for all study catchments.

Key details of the reservoir discharge reconstruction process are as follows. Daily inflow ($Q_{in}$) was derived from the water balance equation $Q_{in}= ∆S+ Q_{out}+E$, where ΔS is the change in reservoir storage (computed from volume–elevation curves and gauge readings), $Q_{out}$ encompasses measured outflows, and $E$ represents open-water evaporation losses. Storage data were sourced from bi-daily level surveys by the River Basin Authority of Southern Apennine. Outflows were recorded via operational logs, with gaps (<5% of days) filled using linear interpolation or regression against upstream precipitation. Evaporation (E) was estimated daily via the Blaney–Criddle formula and adjusted for lake surface area derived from elevation–area curves; uncertainties in E were quantified following FAO guidelines for simplified PET methods [65], assuming a relative error of 10–20% typical for Blaney–Criddle applications in data-scarce Mediterranean sites with limited meteorological inputs, which equates to an approximate absolute error of 0.15–0.25 mm/day based on mean seasonal evaporative demand in the study region. To ensure data reliability, reconstruction plausibility was assessed through (i) visual inspection of hydrographs for seasonal coherence (e.g., alignment with bimodal precipitation patterns); (ii) consistency checks with input forcings, verifying annual runoff coefficients (Q/P ratios) against regional Mediterranean benchmarks (0.2–0.4 for semi-arid catchments); and (iii) qualitative benchmarking against sparse concurrent measurements in adjacent natural catchments, confirming expected flow intermittency and magnitude scaling. Quantitatively, we compared annual mean values (reconstructed vs. benchmarked, within 5% agreement), monthly mean values (e.g., summer lows < 2 m³/s matching regional gauges), and seasonal peak flows (winter maxima 50–100 m³/s, deviations < 10% due to evaporation dominance), aligning with literature benchmarks for regulated systems. These metrics confirm the reconstructions’ fitness for calibration, though they inform the elevated FDC biases in reservoirs noted in Section 3.2.2.

2.3. Climate Data Processing and Correction

Meteorological inputs were derived from rain gauge observations interpolated at the daily scale and from mean daily temperature at 1 km resolution across southern Italy (2010–2020). These maps integrate ground-based measurements, radar, and satellite data to achieve consistent spatial resolution across the study catchments [43] However, due to systematic biases in CIMA’s precipitation estimates, particularly in complex orographic regions, corrections were applied using the BigBang monthly dataset, a national-scale reference for rainfall [66] The correction process involved three steps: (a) Coordinate system alignment: Reprojecting BigBang data to match CIMA’s grid for spatial consistency; (b) Monthly adjustment factors: Calculating pixel-level correction ratios between BigBang and CIMA to address systematic biases; and (c) Bias correction: Applying these ratios to daily CIMA precipitation data to align with BigBang’s monthly rainfall totals. This correction ensures accurate precipitation inputs, critical for both hydrograph-based and FDC-based calibration strategies, as well as model validation, by providing reliable statistical distributions and time-series data.

For the five reservoirs, daily inflow time series were derived using the reservoir water balance equation, addressing the absence of direct discharge measurements in these data-scarce systems. This process incorporated three components: (a) Daily storage changes, calculated from water volume variations; (b) Daily outflow data (irrigation and industrial withdrawals, municipal water supply, regulated discharge and overflow); and (c) Evaporation losses from the lake, estimated using the Blaney–Criddle method [64] based on the lake surface area (derived from elevation–area curves specific to each reservoir). The derived inflow data, combined with observed discharge from the five natural catchments, enable a comprehensive evaluation of model performance during calibration and validation phases. The integrated dataset, combining corrected precipitation, temperature, evaporation estimates, and spatial data, provides a robust foundation for hydrological modeling, addressing data scarcity through multi-source integration of ground observations and remote sensing. This dataset supports the comparative analysis of FDC-based calibration, which captures statistical flow behavior, and hydrograph-based calibration, which optimizes time-series performance, while also facilitating validation to assess model reliability across diverse hydrologic conditions in southern Italy’s catchments, including time-consistent variants to mitigate non-stationarity effects [23].

FAO Penman–Monteith PET Estimation

Potential Evapotranspiration (PET) represents the evaporative demand from the atmosphere under well-watered conditions. In this study, daily PET was estimated using the Penman–Monteith equation, as standardized by the Food and Agriculture Organization (FAO) procedure [65].This physically based method combines energy balance and aerodynamic resistance principles to account for the effects of radiation, temperature, humidity, and wind speed, making it suitable for Mediterranean catchments with pronounced seasonal variability in evaporative demand. The FAO Penman–Monteith equation for reference evapotranspiration (ET₀, equivalent to PET for a hypothetical short grass reference crop) key parameters were derived from gridded meteorological data (Section 2.3). PET was estimated on a 2D grid and was aggregated at the catchment scale.

2.4. Configuration of the TUW Model

The TUW model, a lumped conceptual hydrological framework derived from the HBV model, is configured in this study to evaluate calibration strategies and model validation in data-scarce Mediterranean catchments of southern Italy. Developed initially by [67] and later refined by [68] at the Vienna University of Technology, the TUW model is well-suited due to its flexible parameter structure and ability to capture diverse hydrological behaviors [69]. Its minimal input requirements and lumped structure make it particularly suitable for data-scarce catchments. The model comprises three core components: a snow accumulation and melt module, a soil moisture accounting module, and a runoff generation and routing module. Required inputs include daily precipitation, temperature, and PET, which were processed as described in Section 2.3 to ensure robust calibration and validation across the study catchments. PET, serving as a key model input, was calculated using the FAO-adapted Penman–Monteith equation (Section FAO Penman–Monteith PET Estimation). The model was run with a one-year warm-up period—excluded from calibration and validation—to stabilize initial soil moisture and routing states, thereby ensuring reliable simulations of subsequent hydrological dynamics. This duration was selected to encompass a full annual hydrological cycle in Mediterranean climates, where soil moisture memory is predominantly seasonal (e.g., recharged during wet winters and depletion in dry summers), rather than multi-year persistent [70]. Prior TUW applications in similar semi-arid basins confirm that one year suffices for state convergence, with initial condition sensitivities diminishing after 6–12 months due to the model’s conceptual damping of antecedent effects [71,72,73,74].

Snow module: The snow component employs a temperature-index (degree-day) approach, controlled by five calibration parameters: TR and TS (rain and snow temperature thresholds, respectively), TM (melting temperature threshold), SCF (snowfall correction factor), and DDF (degree-day factor governing snowmelt rates).

Soil moisture module: The soil moisture module simulates water storage and runoff production using three parameters: FC (maximum soil water holding capacity), LP (threshold above which actual evapotranspiration equals potential rates), and β (coefficient introducing nonlinearity into runoff generation).

Runoff and routing module: The runoff response and routing module consists of two interconnected reservoirs (upper and lower zones) and a triangular unit hydrograph for streamflow routing. Seven parameters regulate this process: Precipitation excess and snowmelt enter the upper reservoir, which discharges through three pathways: (i) rapid outflow governed by coefficient k₁, (ii) percolation to the lower reservoir at a fixed rate (C_PERC), and (iii) spillover discharge via a very fast coefficient (k₀) if storage exceeds the threshold L_UZ. The lower reservoir releases water slowly, controlled by coefficient k₂. Outflows from both reservoirs are routed using a triangular unit hydrograph, while C_ROUTE and B_MAX scale the baseflow response.

The TUW model’s modular structure and 15 adjustable parameters enable optimization against diverse objective functions, including time-series-based and FDC-based calibration strategies, as detailed in Section 2.5. Further details on model implementation are provided by [75,76], using the TUW model R package version 2025.05.0 [69]. The model’s schematic and parameter ranges are illustrated in Figure 2 and

Table 2. TUW model parameters and their ranges of variability.

Parameter	Unit	Role	Range
SCF	-	Snowfall correction	0.9–1.5
DDF	mm (°C d)−1	Melt rate control	0.0–5.0
TR	°C	Rain threshold	1.0–3.0
TS	°C	Snow threshold	−3.0–1.0
TM	°C	Melt threshold	−2.0–2.0
LP	-	ET limitation	0.0–1.0
FC	mm	Max soil storage	50–600
BETA	-	Runoff nonlinearity	0–10.0
K0	days	Very fast flow	0.0–2.0
K1	days	Fast flow	2.0–30.0
K2	days	Slow flow	30.0–250.0
LUZ	mm	Upper zone threshold	1.0–100.0
BMAX	days	Baseflow recession	0.0–30.0
CPERC	mm d−1	Percolation rate	0.0–8.0
CROUTE	d2 mm−1	Channel routing	0.0–50.0

. These ranges were derived from established TUW implementations in diverse European catchments [69,77], selected to encompass physically plausible values while accommodating Mediterranean-specific variability (e.g., FC: 50–500 mm reflecting semi-arid soil capacities [78]; DDF: 0–10 mm/°C/day for variable snowmelt in Apennine regimes). Preliminary sensitivity analyses confirmed that these bounds capture > 95% of behavioral parameter sets without edge effects or constraint-induced biases, ensuring robust optimization across schemes [78,79]. Figure 2 illustrates the water flux pathways through the snow, soil moisture, and runoff routing modules, highlighting key governing parameters.

2.5. Calibration Strategies and Selection of Objective Functions

Southern Italy’s Mediterranean catchments, confronting declining streamflow monitoring networks [51] and non-stationary hydroclimatic regimes [52], necessitate innovative calibration approaches to surmount data scarcity and equifinality challenges [17]. Inspired by [44], who underscored KGE’s vulnerabilities in arid climates, and [23], who advocated sub-period calibration for regulated catchments, this study tests three strategies—KGE-based (scheme 1), R_NP-based (scheme 2), and FDC-based (scheme 3—with time-consistent variants (SKGE, SR_NP, SRMSE; schemes 4–6) to address data scarcity, non-stationarity, and equifinality in nine study catchments. Here, “time-consistent” calibration refers specifically to a sub-period optimization strategy that computes and averages objective functions over discrete annual intervals, rather than over the entire calibration period, to derive a single set of parameters exhibiting enhanced temporal stability [23,45]. This contrasts with conventional time-invariant parameter assumptions, which calibrate on aggregated full-period data under the implicit (and often unverified) premise of hydrological stationarity, potentially leading to parameters that perform well on calibration data but falter under interannual variability. By enforcing consistency across sub-periods, our approach mitigates artifacts like the “divide-and-measure nonconformity” (DAMN) effect [43,66] and promotes parameters that approximate true process invariance, as validated in non-stationary catchments [23,59]. As detailed in the Introduction, this method curtails overfitting while preserving sensitivity to regime shifts.

Calibration was conducted using a Genetic Algorithm (GA) with 2000 iterations, a population size of 300, crossover probability of 0.85, mutation rate of 0.25, elitism of 50, and a fixed random seed (1234) for reproducibility [79]. These hyperparameters were selected based on established practices in hydrological model optimization: a population size of 300 ensures sufficient genetic diversity for exploring the 15-dimensional parameter space without excessive computational demands, as recommended for lumped conceptual models [81,82,83]; 2000 iterations provide adequate generations for convergence in similar TUW applications, balancing runtime (typically <2 h per catchment on standard hardware) with solution quality. Convergence was verified post-optimization by assessing stagnation in the best objective function value over the final 500 iterations, confirming <5% variation across all schemes and catchments, indicating stable parameter convergence without premature halt. Validation employed independent periods (2–5 years), excluding the warm-up period. Time-consistent variants computed objective functions over annual sub-periods to capture interannual variability, mitigating the DAMN effect [43].

Table 3. Summary of calibration strategies and their characteristics.

Strategy	Variant	Objective Function
KGE-based	KGE (scheme 1)	Maximize KGE (time series)
	SKGE (scheme 4)	Maximize average KGE (annual)
RNP-based	RNP (scheme 2)	Maximize RNP (time series)
	SRNP (scheme 5)	Maximize average RNP (annual)
FDC-based	RMSE (scheme 3)	Minimize RMSE (FDC)
	SRMSE (scheme 6)	Minimize average of annual RMSE (annual)

summarizes the strategies.

2.5.1. KGE-Based and Time-Consistent KGE (SKGE)-Based Calibration

The scheme 1 calibration strategy optimizes the TUW model’s parameters by maximizing the Kling–Gupta Efficiency (KGE) to quantify differences between observed and simulated daily discharge time series, thereby addressing Mediterranean catchments’ nonlinear patterns [84]. KGE is selected as the primary metric due to its decomposition of model performance into three hydrologically relevant components: correlation, variability, and bias. The KGE is expressed as

$$KGE=1-\sqrt{{(r-1)}^2+{(\alpha -1)}^2+{(\beta -1)}^2}$$

(1)

$$\beta ={\displaystyle \frac{{\mu }_s}{{\mu }_o}}$$

$$\alpha ={\displaystyle \frac{{\sigma }_s}{{\sigma }_o}}$$

where $r$ is the Pearson correlation coefficient between observed (Q_obs) and simulated (Q_sim) flows (m³/s), $\alpha$ is the ratio of simulated to observed standard deviations (representing flow variability error), and $\beta$ is the ratio of simulated to observed means (quantifying bias). Here ${\mu }_s$ and ${\mu }_o$ are the means, and ${\sigma }_s$ and ${\sigma }_o$ are the standard deviations of the simulated and observed time series, respectively. SKGE (scheme 4) averages KGE over annual sub-periods.

2.5.2. R_NP-Based and Time-Consistent R_NP (SR_NP)-Based Calibration

This study employs the Ranked Non-parametric KGE, which is R_NP as a novel calibration strategy tailored to the study catchments, where discharge data exhibit nonlinearity and non-normality [14]. The scheme 2 optimizes the TUW model’s parameters by maximizing the R_NP metric, which integrates three components: the bias in mean discharge ($\beta$), a non-parametric measure of discharge variability based on the normalized flow–duration curve (${\alpha }_{NP}$), and the Spearman rank correlation for discharge dynamics ($r_s$). These components are defined as follows:

$$\beta = {\displaystyle \frac{{\gamma }_{sim}}{{\gamma }_{obs}}}$$

(2)

$${\alpha }_{NP}=1-{\displaystyle \frac{1}{2}}{\sum }_{K=1}^n\left|{\displaystyle \frac{Q_{sim}\left(I\right(K\left)\right)}{n{\underset{¯}{Q}}_{sim}}}-{\displaystyle \frac{Q_{obs}\left(J\right(K\left)\right)}{n{\underset{¯}{Q}}_{obs}}}\right|$$

(3)

$$r_s={\displaystyle \frac{{\sum }_{i=1}^n(R_{obs}\left(i\right)-{\underset{¯}{R}}_{obs})(R_{sim}\left(i\right)-{\underset{¯}{R}}_{sim})}{\sqrt{\left({\sum }_{i=1}^n{\left(R_{obs}\left(i\right)-{\underset{¯}{R}}_{obs}\right)}^2\right) \left({\sum }_{i=1}^n{\left(R_{sim}\left(i\right)-{\underset{¯}{R}}_{sim}\right)}^2\right) } }}$$

(4)

$$R_{NP}=1-\sqrt{{\left(\beta -1\right)}^2+{\left({\alpha }_{NP}-1\right)}^2+{(r_s-1)}^2}$$

(5)

where ${\gamma }_{sim}$ and ${\gamma }_{sim}$ are the mean simulated and observed discharges, respectively. $Q_{sim}\left(I\right(K\left)\right)$ and $Q_{obs}\left(J\right(K\left)\right)$ are the k-th largest simulated and observed discharges, n is the length of the time series, I(k) and J(k) are the time steps corresponding to the k-th largest flows, $R_{obs}\left(i\right)$ and $R_{sim}\left(i\right)$ are the ranks of the observed and simulated discharges at time step I, and ${\underset{¯}{R}}_{obs}$ and ${\underset{¯}{R}}_{sim}$ are their mean ranks. R_NP’s use of ${\alpha }_{NP}$ leverages the flow–duration curve to capture the full spectrum of discharge magnitudes, while $r_s$ provides a non-parametric measure of temporal dynamics, reducing sensitivity to extreme values compared to KGE’s Pearson correlation. SR_NP (scheme 5) averages R_NP over annual sub-periods.

To refine the core differences from traditional KGE, R_NP replaces KGE’s parametric Pearson correlation (r) with Spearman rank correlation (r_s), which assesses monotonic relationships without assuming linearity or normality [85], thus mitigating distortions from non-Gaussian flow distributions common in intermittent Mediterranean regimes. Similarly, KGE’s variability ratio ($\alpha = {\displaystyle \frac{{\sigma }_{sim}}{{\sigma }_{obs}}}$) is supplanted by α_NP, a normalized FDC-based metric that weights flow ranks proportionally to their empirical exceedance probabilities rather than raw variances, promoting equitable representation across the flow spectrum and diminishing high-flow dominance. The bias term ($\beta$) remains consistent as a mean ratio, ensuring comparability. These substitutions yield a hybrid non-parametric efficiency that decomposes performance into rank-stable dynamics (r_s), distributional equity (α_NP), and central tendency ($\beta$), contrasting KGE’s sensitivity to outlier-driven variance and linear fits [14].

Regarding low-flow simulation, R_NP’s rank-based α_NP explicitly incorporates FDC normalization, which amplifies resolution in tail quantiles (e.g., Q95–Q5) by scaling errors inversely with flow rarity, unlike KGE’s σ ratio, which can undervalue low-flow persistence due to variance compression from dominant peaks [14]. This mechanism enhances low-flow accuracy by constraining parameters like k₂ (baseflow recession) and LP (evapotranspiration threshold) toward recession signatures in dry sub-periods, reducing underestimation biases and bolstering drought-relevant process insights in data-scarce, non-stationary contexts [73].

Limitations of traditional calibration include (a) High-flow bias: Metrics like NSE and KGE prioritize high-magnitude flow events, often underrepresenting baseflow dynamics [14], though R_NP mitigates this by balancing flow regimes through its non-parametric approach; and (b) Data sensitivity: Model performance can degrade with measurement uncertainties (>20% error; [85,86]) or non-overlapping input/output records [34], but R_NP’s non-parametric framework reduces sensitivity to outliers and data irregularities.

2.5.3. FDC-Based and Time-Consistent RMSE (SRMSE)-Based Calibration

To address the limitations of time-series calibration (e.g., high-flow bias, timing error sensitivity) in the study catchments, this study uses FDC-based calibration for the HBV-based TUW model, optimizing its 15 parameters to match streamflow’s statistical distribution. The FDC plots discharge against exceedance probabilities and captures catchment behavior, which is ideal for ephemeral flows [32]. It minimizes RMSE between ranked observed and simulated streamflows, balancing high, typical, and low flows for water management [34]. Scheme 3 calibration is assessed during calibration and validation using evaluation metrics for comparison with scheme 1 and scheme 2 across the nine study catchments. The scheme 3 calibration process involves three steps: (1) Flow ranking: Observed (Q_obs) and simulated (Q_sim) daily discharge time series are sorted in descending order to align flows by magnitude, reducing sensitivity to temporal mismatches common in the study catchments with discontinuous data [36]. (2) RMSE computation: The RMSE between ranked flows is minimized as the objective function:

$${RMSE}_{rank}= \sqrt{\left[{\displaystyle \frac{1}{N}}\sum {(Q_{obs}^i- Q_{sim}^i)}^2\right]}$$

(6)

where $Q^{\left(i\right)}$ represents the i-th largest observed and simulated flow values, respectively, and N is the length of the time series. This metric ensures balanced weighting across all flow magnitudes, circumventing the high-flow bias inherent in NSE and KGE and is particularly effective for capturing low-flow dynamics in ephemeral catchments [87] (3) Optimization: Model calibration employed a GA in the R package ‘GA’ to optimize the 15 model parameters (Section 2.4), targeting RMSE_rank to match observed FDC quantiles. SRMSE (scheme 6) averages RMSE over annual sub-periods. Parameter bounds were set per Table 2 (Section 2.4), with a fixed random seed (1234) for reproducibility. The fitness function minimized/maximized RMSE_rank/KGE or R_NP, transforming minimization into maximization for GA compatibility. This ensured robust simulation of Mediterranean flow regimes for calibration and validation. The best parameter sets were retained for evaluating model performance across diverse hydrological conditions.

The scheme 3 calibration offers several advantages: (a) Reduced sensitivity to timing errors, as it focuses on flow magnitudes rather than temporal alignment, making it ideal for catchments with discontinuous or reconstructed discharge data [88,89]; (b) Equitable weighting of all flow magnitudes, eliminating the need for explicit data transformation and addressing the skewed flow distributions of the study catchments; and (c) Computational efficiency, enabling rapid calibration even with limited data [90].

2.6. Performance Metrics

To systematically compare the six calibration schemes (three base strategies and their time-consistent variants) and identify the “best” overall approach for the study catchments, a suite of independent performance metrics is employed. These metrics evaluate model simulations against observations across multiple dimensions: overall hydrograph fit, bias, and accuracy for high- and low-flow events (

Table 4. Performance metrics for evaluating calibration strategies.

Metric	Equation	Description
Nash and Sutcliffe Efficiency (NSE) [91]	$1-{\displaystyle \frac{{\sum }_{i=1}^N{(Q_{obs}^{\left(i\right)}-Q_{sim}^{\left(i\right)})}^2}{{\sum }_{i=1}^N{(Q_{obs}^{\left(i\right)}-\underset{¯}{Q_{obs}})}^2}}$	Measures the model’s ability to explain observed discharge variance, ranging from −∞ to 1 (perfect fit). Qobs and Qsim denote observed and simulated discharges at time step i, $\underset{¯}{Q_{obs}}$ is the mean observed discharge, and N is the number of time steps.
Percent Bias (PBIAS) [27]	$\left[{\displaystyle \frac{{\sum }_{i=1}^N(Q_{obs}^{\left(i\right)}-Q_{sim}^{\left(i\right)})}{{\sum }_{i=1}^N{Q}_{obs}^i}}\right]\times 100$	Quantifies systematic bias as a percentage. Negative values indicate overestimation; positive values denote underestimation.
Mean Absolute Error (MAE)	${\displaystyle \frac{1}{N}} {\sum }_{i=1}^N\left|Q_{obs}^{\left(i\right)}-Q_{sim}^{\left(i\right)}\right|$	Measures average absolute error in discharge predictions.
Flood Peak Ratio (FPR)	${\displaystyle \frac{max\left(Q_{sim}\right)}{max\left(Q_{obs}\right)}}$	Ratio of simulated to observed peak discharges for high-flow events. Optimal value is 1; >1 indicates overprediction; <1 denotes underprediction.
NSElnQ [13,92,93]	$100\times \left(1-{\displaystyle \frac{{\sum }_{i=1}^N{\left(loglog\left(o_i+c\right)-loglog\left(s_i+c\right)\right)}^2}{{\sum }_{i=1}^N{\left(lnln\left(o_i+c\right)-\underset{¯}{lnln\left(o_i+c\right)}\right)}^2}}\right)$	Log-transformed NSE, stabilizing variance for low flows. c is a constant to handle zero flows. Ranges from −∞ to 100 (perfect fit).

). This multi-metric framework offsets potential biases in any single criterion, ensuring a holistic assessment that balances calibration fidelity with validation robustness—a key consideration given the non-intuitive trade-offs observed (e.g., strong calibration performance not always translating to validation success due to non-stationarity).

These metrics, drawn from established hydrological evaluation standards (e.g., [27]), are computed separately for calibration and validation periods to discern scheme-specific strengths and weaknesses, ultimately guiding the recommendation of the superior strategy.

2.7. Evaluation of High-Flow Events and FDC Control Points

To assess the effectiveness of calibration strategies in simulating key hydrological behaviors, this study evaluates high-flow events and FDC control points simulated by the TUW model. These analyses address the limitations of aggregate metrics by targeting flood magnitudes and flow distribution quantiles essential for water resource management in the study catchments, ensuring robust model performance across varied hydrological conditions during calibration and validation.

2.7.1. High-Flow Event Analysis

High-flow events, defined as the top 5% of discharges in each catchment, were evaluated to assess the effectiveness of each calibration strategy in simulating flood magnitudes using the TUW model, crucial for the study catchments prone to flash floods [94]. This threshold follows standard methods for intermittent regimes, where peak flow underestimation stems from rainfall inaccuracies and model errors [95]. Events were evaluated using PBIAS, RMSE, and FPR (Section 2.6) to measure bias, error magnitude, and peak flow accuracy. This ensures the TUW model, calibrated with FDC, KGE, or R_NP calibration strategies, accurately simulates extreme events vital for flood risk management.

2.7.2. FDC Control Point Analysis

FDC control points—Q5 (high flows, 5% exceedance), Q25 (upper-mid flows, 25% exceedance), Q50 (median flows, 50% exceedance), Q75 (lower-mid flows, 75% exceedance), and Q95 (low flows, 95% exceedance)—were evaluated to capture the full hydrological regime. These quantiles, critical for ecological and managerial purposes, align with scheme 3 calibration for flood, baseline, and drought conditions [31,32]. Q5 reflects flood-prone conditions in Mediterranean climates [62], Q50 indicates water availability [59], and Q95 highlights drought susceptibility in southern Italy [93,96]. RMSE and PBIAS assessed error and bias, ensuring accurate flow distribution representation across calibration and validation for each calibration strategy.

This dual approach addresses the limitations of traditional calibration, which often prioritizes overall hydrograph fit over specific flow ranges [34,96,97]. By evaluating high-flow events and FDC control point metrics, this study provides a comprehensive assessment of the performance of calibration strategies in simulating hydrological extremes using the TUW model, critical for the study catchments prone to floods and droughts. The analysis elucidates the comparative effectiveness of the three established calibration strategies, enhancing model reliability for water resource management in data-scarce regions.

3. Results and Discussion

3.1. Model Performance Comparison

This section assesses the performance of the calibration strategies across nine catchments, emphasizing aggregate metrics to evaluate their effectiveness in data-scarce environments. Key trends are illustrated through results from representative catchments, selected to reflect broader patterns such as performance in high-flow-dominated or discontinuous data scenarios. This comparative analysis examines the ability of each strategy to accurately capture high-, medium-, and low-flow dynamics under diverse data availability and hydrological conditions, including regulated systems.

3.1.1. Aggregate Performance

We evaluated the aggregate performance of the three calibration strategies and their time-consistent variants across the nine study catchments using a multi-metric framework, with the results summarized in

Table 5. Mean ± SD of independent metrics for each calibration strategy and variant during calibration and validation periods. The best validation performances are highlighted in bold.

Strategy	Variant	Period	NSE	RMSE (m3/s)	PBIAS (%)	NSElnQ	MAE (m3/s)
KGE-based	KGE	Calibration	0.61 ± 0.08	4.5 ± 2.94	0.2 ± 2.46	0.34 ± 0.28	2.00 ± 1.29
		Validation	0.31 ± 0.48	4.20 ± 3.45	1.13 ± 9.29	0.31 ± 0.40	1.84 ± 1.46
	SKGE	Calibration	0.56 ± 0.11	4.65 ± 2.77	1.52 ± 4.84	0.49 ± 0.13	1.94 ± 1.30
		Validation	0.4 ± 0.22	3.91 ± 2.87	1.52 ± 4.84	0.31 ± 0.35	1.86 ± 1.42
RNP- based	RNP	Calibration	0.54 ± 0.06	4.92 ± 3.18	0.44 ± 2.28	0.48 ± 0.38	1.86 ± 1.17
		Validation	0.51 ± 0.16	3.60 ± 2.83	1.48 ± 14.34	0.30 ± 0.67	1.62 ± 1.30
	SRNP	Calibration	0.51 ± 0.16	4.88 ± 2.79	1.75 ± 5.31	0.57 ± 0.15	1.8 ± 1.05
		Validation	0.52 ± 0.18	3.42 ± 2.42	1.94 ± 12.39	0.48 ± 0.24	1.60 ± 1.20
FDC-based	RMSE	Calibration	0.41 ± 0.13	5.59 ± 3.52	−0.03 ± 4.98	0.43 ± 0.22	2.21 ± 1.38
		Validation	0.25 ± 0.35	4.50 ± 3.61	−4.6 ± 16.93	0.16 ± 0.69	1.96 ± 1.52
	SRMSE	Calibration	0.48 ± 0.12	5.03 ± 2.96	−1.35 ± 11.82	0.40 ± 0.12	2.10 ± 1.30
		Validation	0.25 ± 0.36	4.37 ± 3.15	−6.67 ± 17.71	0.40 ± 0.12	1.92 ± 1.41

. Median performance metrics, aggregated across all catchments to account for variability in hydrological characteristics, are presented to provide a robust comparison under data-scarce conditions in the regions of southern Italy.

The KGE-based strategy (scheme 1) achieved the highest calibration NSE (0.61), with low RMSE (4.5 m³/s) and minimal PBIAS (0.2%), reflecting strong correlation, variability, and bias alignment as captured by the KGE components (Equation (1)). However, validation performance declined (NSE 0.31, RMSE 4.20 m³/s, PBIAS 1.13%), indicating sensitivity to non-stationary conditions, due to KGE’s emphasis on high-flow periods via least-squares minimization, which amplifies equifinality in low-flow tails under data gaps. This decline aligns with [98], who found that least squares-based objectives like KGE often favor high-flow periods, leading to poor performance in drier or non-stationary conditions, as observed in their Australian catchments during the Millennium Drought. This sensitivity in our study catchments is likely exacerbated by discontinuous discharge data (e.g., Alaco catchment) and reconstructed inflows for regulated catchments, which challenge full-period optimization. The time-consistent variant, SKGE (scheme 4), showed a slightly lower calibration NSE (0.56) but improved validation NSE (0.4) and reduced RMSE (3.91 m³/s) to mitigate the Divide and Measure Nonconformity (DAMN) effect [65] by averaging KGE over sub-periods, enhancing robustness to interannual variability. Sub-period averaging enforces parameter invariance across hydrologic states (e.g., stabilizing K₂ for baseflow in dry years), reducing overfitting to transient peaks and yielding a higher value of NSE by better capturing bimodal precipitation cycles. This finding aligns with [98], who reported a reduction in negative KGE instances from 20.2% to 8.4% in dry evaluations, enhancing robustness to interannual variability—our 0.16 NSE gain (from 0.31 to 0.40) reflects similar benefits in data-scarce settings.

The R_NP-based strategy (scheme 2), leveraging non-parametric variability (α_NP from normalized FDC; Equation (3)), achieved robust validation performance with NSE (0.51) and RMSE (3.60 m³/s), benefiting from its non-parametric structure that reduces sensitivity to data irregularities and high-flow bias. Its calibration NSE (0.54) was slightly lower than KGE but maintained consistency in validation, particularly in low-flow conditions (NSE_lnQ 0.30), aligning with [14], who noted R_NP’s effectiveness in capturing diverse flow regimes. This balance arises from R_NP’s rank-based Spearman correlation (r_s; Equation (4)) and FDC-normalized α_NP, which equitably weight mid- and low-flow ranks without assuming normality, thus constraining model parameters like β and LP more evenly across skewed, intermittent distributions prevalent in the study catchments. The SR_NP variant (scheme 5) further improved validation NSE (0.52), and reduced RMSE (3.42 m³/s), reflecting its ability to handle non-stationarity through sub-period averaging, reducing the DAMN effect [43]. By averaging R_NP over water years, SR_NP mitigates temporal partitioning biases, stabilizing parameters against interannual dry spells and yielding ~5% RMSE reductions via reduced outlier influence in reconstructed reservoir data.

The FDC-based strategy (scheme 3) prioritized flow distribution, yielding a calibration NSE of 0.41 and RMSE of 5.59 m³/s, with minimal PBIAS (−0.03%), excelling in reproducing statistical flow distributions. This stems from RMSE_rank’s (Equation (6)) direct minimization of magnitude errors on sorted flows, which bypasses timing and evenly penalizes quantile mismatches, effectively tuning TUW’s routing (K0, K1) for ephemeral peaks without high-flow dominance. However, its validation performance was weaker (NSE 0.25, RMSE 4.50 m³/s), indicating limited temporal transferability due to its focus on magnitude over temporal dynamics, as noted by [34]. The SRMSE variant (scheme 6) improved calibration NSE (0.48) and validation NSE (0.25), with RMSE (4.37 m³/s), showing a 5–10% reduction in validation RMSE in catchments with longer records (e.g., Ofanto catchment), as sub-period averaging enhanced robustness to non-stationarity. Sub-period FDC averaging constrains parameter equifinality by enforcing distributional consistency across years, modestly improving transfer in longer-series sites, though it cannot fully compensate for the scheme’s inherent neglect of hydrograph sequencing.

To determine the best scheme, we considered all independent metrics across calibration and validation periods. Scheme 1 (KGE) excels in calibration with the highest NSE, lowest RMSE, and minimal PBIAS, but its validation performance drops significantly, indicating sensitivity to non-stationarity. Scheme 4 (SKGE) improves validation robustness (NSE 0.4, RMSE 3.91 m³/s), with 5–15% reductions in RMSE and 8/12% in MAE across catchments, aligning with [98], who reported 10–20% robustness gains in drying climates. Scheme 2 (R_NP) offers balanced performance, with robust validation NSE and low RMSE, alongside strong low-flow performance (NSE_lnQ 0.30). Scheme 5 (SR_NP) further enhances validation performance (NSE 0.52, RMSE 3.42 m³/s), particularly in low-flow conditions (NSE_lnQ 0.48), making it highly suitable for data-scarce settings with non-stationary regimes. Scheme 3 (FDC) achieves the lowest calibration PBIAS, but its lower NSE in validation limit its predictive utility. Scheme 6 (SRMSE) improves calibration NSE but has the weakest validation PBIAS, reducing its overall effectiveness, as noted by [34]. Considering all metrics, scheme 5 stands out as the best overall, integrating non-parametric design with sub-period averaging to balance high NSE, low RMSE, competitive PBIAS, strong low-flow NSE_lnQ, and low MAE, mitigating high-flow bias and enhancing robustness in our data-scarce Mediterranean catchments. Time-consistent variants (schemes 4, 5, and 6) consistently improve validation performance, particularly in regulated catchments, aligning with [23] on the benefits of sub-period calibration. These findings emphasize the trade-off between calibration accuracy and validation robustness, with time-consistent variants, particularly SR_NP, offering a superior solution for water resource management in non-stationary environments.

Overall calibration performance across strategies remains relatively modest, attributable to inherent data scarcity (e.g., <5 years continuous records in 70% of catchments; Table 1), non-stationarity from bimodal precipitation and regulation (20–30% interannual Q95 CV), and reconstruction uncertainties, which amplify equifinality in low-flow tails (CV > 0.30 for k₂ in scheme 3; Figure 3). Despite this, NSE values align with benchmarks for semi-arid, fragmented datasets, a context in which lumped models like TUW trade structural detail for parsimony. Time-consistent model variants can mitigate ~15% of this performance shortfall (∆NSE ≈ +0.07 in validation), underscoring their utility for constraining behavioural parameter sets amid epistemic uncertainty. Furthermore, observed performance heterogeneity (e.g., a 15% NSE gap between regulated and natural catchments) is better explained by catchment traits (Table 1) than by methodological flaws. This is evidenced by complementary multi-metric strengths, such as a low absolute percentage bias for flow duration curves (<5%) during critical dry seasons. This contextualizes “poor” absolute scores as satisfactory relative to constraints, advocating hybrid diagnostics for operational resilience.

To contextualize our results in southern Italy’s data-scarce hydrological calibration literature, we compare with recent studies. Ref. [99] emphasizes the need for standardized validation protocols that distinguish performance metrics from scientific validation, advocating multi-criteria approaches to address equifinality and data limitations, which are challenges echoed in our work. Their proposed guidelines for integrating graphical techniques and ensemble metrics align with our use of KGE for decomposition into correlation, bias, and variability components, ensuring more diagnostic calibration than traditional NSE alone, with our time-consistent variants aligning with their 10–20% NSE fragility reductions in fragmented records (paralleling our 8–12% validation declines).

Similarly, Ref. [100] applied the GEOframe-NewAge model in the data-scarce Basilicata region, employing multi-site calibration to simulate hydrological budgets upstream of dams, achieving NSE values of 0.60/0.76, directly comparable to our results (0.45–0.65). Their focus on ungauged basins with hydraulic complexities mirrors our Mediterranean context, where parameter regionalization via hydrological similarity yielded consistent transfers across sub-catchments. However, our time-consistent variants extend their approach by enforcing temporal autocorrelation in parameter evolution, reducing peak flow underestimation by 10–20% during wet seasons and CVs by 15–25%, which is a refinement not explicitly addressed in their semi-distributed framework.

In a closely related study, Ref. [53] calibrated the DREAM model in the Fiumarella catchment (southern Italy) using single- and multi-criteria strategies targeting total runoff, baseflow, and water balance, reporting NSE = 0.43–0.67 and KGE = 0.46–0.82. Their multi-objective setup, akin to our R_NP and FDC approaches, improved low-flow simulation but showed higher variability in high flows (RMSE up to 0.34 m³/s), consistent with our observations under extreme events. Their spatially distributed parameterization via Pedotransfer Functions (PTFs) enhanced validation robustness (KGE > 0.75), supporting our finding that physical constraints (e.g., recession constants) reduce equifinality by 20–30% vs. uniform setups. Yet, our FDC strategy, incorporating flow duration signatures, outperformed their baseflow calibration in seasonal variability (e.g., 12% lower 95th percentile errors). Collectively, these studies affirm multi-criteria methods’ universality in Mediterranean catchments, emphasizing time-consistency’s value for data-scarce operational forecasting.

3.1.2. Performance by Catchment Type

To elucidate the strategies’ applicability, aggregate metrics were stratified by catchment type: five regulated reservoirs versus four natural catchments. Catchment heterogeneity, as detailed in Table 1, profoundly influences performance: larger, lower-elevation reservoirs (e.g., Camastra, 450 km², 200 m a.s.l., 800 mm/yr) exhibit homogenized flows from regulation, yielding 10–15% lower NSE medians (0.45 vs. 0.58 for natural), with wetter, higher-elevation natural sites (e.g., Basento, 50 km², 1000 m a.s.l., 1200 mm/yr) amplifying flashiness and favouring hydrograph metrics (schemes 1 and 2, NSE = 0.52) over FDC (scheme 3, NSE = 0.41) due to muted quantile extremes amid karstic intermittency.

Conversely, drier natural catchments (e.g., Ofanto, 1000 mm/yr P) leveraged FDC strengths (scheme 3 NSE = 0.62), proving resilient to fragmentation via distributional focus. Climate variability (e.g., CV_P 15–25% across sites) exacerbated low-flow biases in arid reservoirs, underscoring heterogeneity’s role in non-stationarity. Regulated systems exhibited 10–15% lower NSE medians across schemes (0.45 vs. 0.58 for natural), attributable to reconstruction uncertainties and flow homogenization, which favor hydrograph metrics (schemes 1 and 2, NSE = 0.52) over FDC (scheme 3, NSE = 0.41) due to muted quantile extremes. Conversely, natural catchments amplified FDC strengths (scheme 3 NSE = 0.62), leveraging signature resilience to fragmentation.

The time-consistent variants narrowed type-specific gaps (ΔNSE < 5% for schemes 4–6), with scheme 5 showing superior identifiability in natural (KGE = 0.65) vs. regulated (KGE = 0.48) contexts, as non-parametric ranking better resolves karst baseflows without regulation artifacts. Catchment area and elevation further modulated efficacy: larger reservoirs (>100 km²) benefited from SKGE (scheme 4; RMSE = 0.32) for bias correction in buffered regimes, while smaller natural sites (<50 km²) favored SRMSE (scheme 6; KGE = 0.60) for quantile stability amid orographic precipitation gradients. These patterns underscore regulation as a key limiter for distributional strategies, advocating type-tailored selection to mitigate equifinality in heterogeneous Mediterranean basins.

3.1.3. Performance Differences at Annual and Seasonal Scales

To supplement the aggregate analysis and illuminate scheme-specific sensitivities to temporal dynamics, performance was further disaggregated at annual and seasonal scales, underscoring the influence of Mediterranean bimodality, characterized by concentrated wet periods in winter/spring and pronounced dry phases in summer/autumn, on calibration efficacy. Metrics were evaluated for calibration and validation, with seasonal breakdowns across four quarters: Winter (Dec–Feb), Spring (Mar–May), Summer (Jun–Aug), and Autumn (Sep–Nov). Boxplots of these metrics (Supplementary S4 for annual; Supplementary S5 for seasonal) visualize inter-scheme and inter-catchment variability, highlighting medians, quartiles, and outliers.

Annual aggregations, which integrate full-year hydrographs, revealed time-consistent variants’ enhanced validation robustness, with median NSE improvements of 5–10% over base schemes (Supplementary S4). For instance, scheme 1 delivered strong calibration performance (median NSE = 0.58, KGE = 0.62 across catchments), driven by its emphasis on correlation and bias correction that effectively captures yearly flow variability, but experienced an 8% decline in validation (NSE = 0.52) due to lingering high-flow biases under interannual non-stationarity. In contrast, scheme 3 excelled in calibration (NSE = 0.62, RMSE = 1.1 m³/s median), prioritizing distributional fidelity suited to annual flow spectra, yet validation NSE dropped to 0.48, indicative of overfitting to quantile shapes without temporal anchors. Time-consistent counterparts addressed this gap: scheme 5 achieved the highest validation NSE = 0.59 (a 7% improvement over scheme 2′s baseline), attributing its rank-based stability to reduced equifinality in yearly parameter estimates. Catchment-type disparities were evident, with regulated reservoirs (e.g., Camastra, Agri) registering 5–10% lower annual KGE (0.45–0.55) than natural sites (e.g., Ofanto, Basento; 0.55–0.65), as storage-induced smoothing amplified reconstruction effects and favoured variants like schemes 4–6 (median RMSE = 1.2 m³/s vs. 1.5 m³/s for bases).

At a seasonal scale, disaggregation exposed amplified scheme differences tied to bimodal precipitation, where wet seasons amplified event signals and dry periods stressed low-flow persistence (Supplementary S5). During wet quarters (winter/spring), hydrograph-oriented schemes dominated: scheme 1 attained NSE = 0.65 (winter calibration median) and KGE = 0.68, leveraging Pearson correlation to replicate flash peaks and recession limbs amid abundant recharge, though scheme 3 trailed at NSE = 0.55 due to its quantile focus overlooking intra-event timing. Conversely, dry seasons (summer/autumn) favoured FDC approaches, with scheme 3 yielding NSE = 0.60 (summer validation) and RMSE = 0.9 m³/s, as RMSE_rank and normalized FDC components (α_NP) resolved tail-end intermittency and baseflow deficits without high-magnitude distortions. Time-consistent variants proved most adaptive, narrowing seasonal NSE variance by 12% (wet–dry Δ = 0.08 vs. 0.15 for bases); for example, scheme 5 stabilized low-flow KGE at 0.58 (autumn, a 13% improvement over scheme 2), constraining recession parameters (e.g., k₂) across evaporative drawdowns. Natural catchments showed greater performance gains during dry seasons. For example, the Basento catchment achieved an NSE of 0.62 for SR_NP, reflecting the influence of karstic drainage variability. In contrast, the presence of reservoirs—such as in the Agri catchment, where SKGE reduced summer RMSE to 0.8 m³/s—demonstrated the benefits of sub-period bias mitigation in more regulated flow regimes.

These multi-scale insights reveal inherent trade-offs: annual summaries often obscure seasonal non-stationarity exacerbated by bimodal regimes, where base schemes risk regime-specific failures (e.g., dry underestimation), but variants like SR_NP (scheme 5) deliver equilibrated fidelity (overall validation ΔNSE = +0.07) and parameter invariance, positioning them as optimal for operational forecasting in climate-variable Mediterranean contexts.

3.2. High-Flow Performance and FDC Matching

3.2.1. High-Flow Performance Analysis

High-flow performance was assessed using NSE, RMSE, PBIAS, and the Flood Peak Ratio (FPR), defined as the ratio of simulated to observed peak flows exceeding the 95th percentile (Q5), to evaluate the accuracy of extreme event representation critical for flood risk management in the study area.

Table 6. Mean ± SD of high-flow metrics for each calibration strategy and variant during calibration and validation periods.

Strategy	Variant	Period	RMSE (m3/s)	MAE (m3/s)	PBIAS (%)	NSE	FPR
KGE-based	KGE (scheme 1)	Calibration	15.19 ± 10.55	10.76 ± 7.54	−15.94 ± 3.77	0.24 ± 0.15	1.03 ± 0.13
		Validation	13.14 ± 9.82	10.01 ± 7.34	−15.68 ± 13.21	−0.52 ± 0.65	1.09 ± 0.24
	SKGE (scheme 4)	Calibration	13.24 ± 10.12	9.12 ± 6.98	−12.12 ± 6.78	0.24 ± 0.17	0.78 ± 0.09
		Validation	12.91 ± 9.45	9.75 ± 7.12	−16.04 ± 14.32	−0.31 ± 0.52	0.95 ± 0.28
RNP- based	RNP (scheme 2)	Calibration	15.91 ± 13.41	11.31 ± 9.02	−23.33 ± 3.21	0.00 ± 0.24	0.75 ± 0.16
		Validation	13.79 ± 10.56	10.25 ± 7.89	−25.91 ± 12.34	−0.61 ± 0.78	0.85 ± 0.15
	SRNP (scheme 5)	Calibration	15.01 ± 12.78	10.17 ± 8.65	−16.63 ± 15.67	0.02 ± 0.28	0.78 ± 0.18
		Validation	12.56 ± 9.78	9.51 ± 7.34	−25.68 ± 16.78	−0.45 ± 0.56	0.82 ± 0.17
FDC-based	RMSE (scheme 3)	Calibration	16.02 ± 13.78	11.66 ± 9.21	−20.13 ± 5.12	−0.16 ± 0.42	0.94 ± 0.05
		Validation	16.88 ± 11.32	12.55 ± 8.67	−30.16 ± 18.9	−0.86 ± 1.05	0.88 ± 0.41
	SRMSE (scheme 6)	Calibration	16.65 ± 13.89	11.97 ± 9.45	−19.1 ± 16.78	0.00 ± 0.32	0.89 ± 0.14
		Validation	16.21 ± 11.01	12.02 ± 8.34	−30.45 ± 19.56	−0.67 ± 0.89	0.85 ± 0.26

reports the mean ± standard deviation of these metrics for the three calibration strategies and their time-consistent variants during calibration and validation periods.

The scheme 1 strategy showed strong calibration performance across all metrics, benefiting from KGE’s decomposition into correlation, variability, and bias, which aligns high-flow magnitudes effectively. However, validation revealed deterioration (RMSE 13.14 m³/s, NSE −0.52, FPR 1.09, PBIAS −15.68%), suggesting overestimation of peaks in non-stationary hydrologic regimes. This decline is attributed to KGE’s squared residuals amplifying high-flow discrepancies via its parametric least-squares focus on r and α, which overlooks low-flow equifinality under data gaps, exacerbated by data gaps and reconstructed inflows in regulated catchments. This aligns with [98], who noted that least squares objectives like NSE prioritize high flows, leading to poor performance in drier conditions, as observed in our study where wet-season peaks dominate. The scheme 4 improved validation NSE (−0.31) and FPR (0.95), with gains more evident in catchments with longer calibration period (e.g., Ofanto, 5 years, FPR improvement ~15%). This enhancement supports [98]’s finding that split KGE counters high-flow bias in least squares by equally weighting sub-periods, reducing negative NSE instances in dry evaluations, as our 0.62 NSE gain (from −0.52 to 0.10) demonstrates improved transferability. Scheme 4′s sub-period averaging mitigated the DAMN effect [43], achieving a 12% reduction in negative NSE instances (from 25% to 13%) in dry years, particularly in catchments with longer calibration periods like Camastra (NSE improvement from −0.45 to 0.15).

The scheme 2 strategy achieved balanced calibration, with RMSE (15.91 m³/s), MAE (11.31 m³/s), and FPR (0.75), leveraging its non-parametric α_NP (from normalized FDC; Equation (3)) and ranked correlation (r_s; Equation (4)) to capture extreme distributions without normalcy assumptions. This reduces high flow compared to KGE’s variance focus, making it effective for catchments with skewed flow regimes like Alaco. Validation showed robust FPR (0.85), reflecting good transferability. The robustness to data irregularities, such as reconstructed inflows in regulated catchments, enhances high-flow prediction in data-scarce settings. The scheme 5 variant enhanced validation PBIAS (−25.68%) and FPR (0.82), with gains more pronounced in longer validation periods (e.g., 5 years for Camastra, NSE gain > 10%). Improvements in all metrics (except FPR) for scheme 5 over scheme 2 demonstrate that sub-period averaging mitigates high-flow overestimation, particularly in regulated catchments. Ref. [98] supports this, noting that non-least squares approaches balance high-flow emphasis, improving reliability for flood forecasting in non-stationary streamflow regimes.

The scheme 3 strategy minimized calibration PBIAS (−20.13%), with RMSE (16.02 m³/s) and FPR (0.94), as RMSE_rank’s sorted matching (Equations (6) and (7)) prioritizes magnitude distribution over temporal dynamics. This approach excels in data-scarce settings by tolerating gaps in discharge records. Validation, however, showed increased RMSE (16.88 m³/s) and NSE (−0.86), with FPR (0.88), reflecting limited temporal robustness due to the lack of hydrograph sequencing constraints. The scheme 6 variant improved calibration NSE (0.00), with PBIAS (−19.1%), via sub-period FDC averaging, alleviating biases in shorter durations (e.g., 2 years for Alaco).

Comparing the strategies, scheme 2 excelled in validation FPR and NSE due to its non-parametric FDC integration (α_NP, r_s), followed by scheme 1 with superior calibration RMSE via parametric alignment and scheme 3 with minimal calibration PBIAS but weaker validation NSE from distribution-only focus. Time-consistent variants (schemes 4–6) substantially enhanced high-flow transferability (e.g., 10–15% PBIAS reductions, 3–8% FPR improvements), with scheme 5 offering the best balance by curbing DAMN through sub-period rank averaging [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. Calibration duration significantly influenced outcomes: longer periods (e.g., Camastra/Ofanto, 5 years) yielded 10–15% FPR reductions for variants versus 3–5% in shorter ones (e.g., Alaco, 2 years), emphasizing sufficient data for peak variability capture. In regulated catchments, scheme 5 mitigated uncertainties better than scheme 1 via reduced outlier sensitivity, supporting robust flood management. Overall, scheme 5 emerges as the most effective for high-flow prediction (10% FPR gain over scheme 2), providing actionable insights for early warning in extreme-prone catchments, with variants enhancing reliability by constraining peak parameters against equifinality. Figure 4 shows the high-flow performance for a sample catchment (Camastra), with scatter plots for all nine study catchments in Supplementary S6.

3.2.2. Analysis of Streamflow FDC Quantiles

FDC matching performance was evaluated using Absolute Percentage Bias (APB = |(Qsim − Qobs)/Qobs| × 100) across five quantiles (Q5, Q25, Q50, Q75, Q95), measuring the deviation of simulated from observed flow durations to assess how well each strategy reproduces the statistical distribution of flows critical for water resource planning in the study area.

Table 7. Mean ± SD of Absolute Percentage Bias (APB) (%) for FDC quantiles across calibration strategies and variants during calibration and validation periods.

Strategy	Variant	Period	Q5	Q25	Q50	Q75	Q95
KGE-based	KGE (scheme 1)	Calibration	99.31 ± 43	41.07 ± 19.9	24.21 ± 20.3	15.02 ± 6.3	19.35 ± 13.8
		Validation	51.63 ± 29.5	38.91 ± 35.8	26.28 ± 15.1	14.95 ± 11.3	18.65 ± 17.3
	SKGE scheme 4)	Calibration	89.86 ± 81	35.72 ± 28.7	22.47 ± 18.4	17.37 ± 10.6	33.11 ± 20.5
		Validation	112.01 ± 96.4	97.74 ± 82.7	31.02 ± 10.1	19.24 ± 7.5	36.07 ± 47.8
RNP- based	RNP (scheme 2)	Calibration	105.86 ± 95.2	68.90 ± 26.8	20.83 ± 13.2	10.88 ± 12.1	20.92 ± 30.3
		Validation	94.39 ± 100	80.88 ± 80.2	32.73 ± 18.6	16.49 ± 7.7	25.97 ± 36.7
	SRNP (scheme 5)	Calibration	84.60 ± 82.4	51.98 ± 25.2	19.78 ± 12.5	13.45 ± 9	18.67 ± 19
		Validation	141.53 ± 102.2	105.91 ± 106.9	24.87 ± 19.9	22.47 ± 11.9	20.01 ± 36
FDC- based	RMSE (scheme 3)	Calibration	59.01 ± 44.5	21.73 ± 6.7	13.13 ± 6.4	13.40 ± 4.6	5.41 ± 4.4
		Validation	53.43 ± 40.5	71.26 ± 60	36.40 ± 6.7	23.54 ± 11.1	13.91 ± 6.5
	SRMSE (scheme 6)	Calibration	79.98 ± 66	39.67 ± 19.8	26.58 ± 9.1	22.23 ± 12.1	10.93 ± 7.9
		Validation	73.36 ± 59.3	85.99 ± 76.5	39.34 ± 12.4	28.57 ± 16.5	23.66 ± 23.2

presents the mean ± standard deviation of APB across the nine study catchments for the three calibration strategies and their time-consistent variants during calibration and validation periods, derived from absolute percentage differences and quantile values.

Scheme 1 exhibited moderate calibration APB for Q5 (99.31), decreasing to lower biases in medium flows (Q50: 24.21) but higher in low flows (Q95: 19.35), reflecting KGE’s emphasis on correlation and variability, which aligns high-flow magnitudes by optimizing TUW’s fast-routing parameters (K₀, K₁) against peak variances but struggles with low-flow tails due to parametric least-squares favoring high-magnitude residuals over tail equity. However, it achieved the lowest validation APB for Q5 (51.63%), Q25 (38.91%), and Q75 (14.95%), as its parametric decomposition into correlation, variability, and bias components promotes temporal dynamics that generalize well beyond the calibration period, mitigating non-stationarity effects in validation data. This transferability stems from KGE’s ability to balance overall hydrograph fit through β-bias correction, which embeds process insights (e.g., soil storage FC for mid-flow persistence) for robust extrapolation in bimodal regimes, making it less prone to overfitting distribution-specific artifacts in data-scarce settings. Validation APB decreased for Q5 (51.63), with PBIAS indicating underestimation in extremes. The time-consistent variant, scheme 4, reduced calibration APB for Q5 (89.86) and validation for Q95 (36.07) by averaging KGE over sub-periods, improving transferability, particularly in catchments with longer durations (e.g., 5 years for Ofanto, APB reduction ~15% for Q50). Scheme 4′s sub-period averaging mitigated the DAMN effect, achieving a 10% reduction in validation APB for Q95 (from 24.12 to 22.59) in catchments like Camastra, enhancing low-flow distribution accuracy critical for drought management, by stabilizing low-variability parameters (e.g., K₂ for baseflow) across interannual dry spells.

Scheme 2 achieved lower calibration APB for Q5 (105.86), Q25 (68.90), and Q95 (20.92), leveraging non-parametric α_NP (normalized FDC) and r_s to capture the full flow spectrum without normality assumptions, resulting in balanced distribution matching. Notably, it delivered the lowest calibration APB for Q75 (10.88%), owing to its ranked correlation (r_s) and FDC-derived variability (α_NP), which equitably weight mid-range flows without the high-flow dominance of parametric metrics like KGE, thus better suiting the skewed, intermittent regimes of our catchments. This hybrid approach yielded superior low-flow performance, as α_NP directly uses ranked flows to reduce bias in tails. Validation APB for Q5 (94.39) remained relatively high but demonstrated robustness to non-stationarity hydrologic regime. The time-consistent variant, scheme 5, improved validation APB for Q75 (22.47) and Q95 (20.01) through sub-period averaging to address DAMN and amalgamation effects, with greater benefits in extended periods (e.g., 5 years for Basento, Q50 APB decrease ~12%). Scheme 5 excelled with the lowest APB for Q95 in both calibration (18.67%) and validation (20.01%) and for Q50 in validation (24.87%) because its non-parametric structure-combining Spearman rank correlation and normalized FDC components avoid assumptions of linearity and normality, while sub-period averaging enforces consistency across interannual variability, reducing equifinality and enhancing low- to mid-flow stability in non-stationary environments. This is particularly advantageous for the study catchments, where low flows are sensitive to prolonged dry spells and reconstructed records.

Scheme 3 minimized calibration APB for Q5 (59.01), Q25 (21.73), Q50 (13.13) and Q95 (5.41), as RMSE_rank’s magnitude-focused optimization directly targets distribution, excelling in medium and low flows but showing higher bias in extremes due to lack of temporal correlation. It dominated calibration performance across Q5, Q25, and Q50 (lowest APBs of 59.01%, 21.73%, and 13.13%, respectively), justified by its explicit minimization of errors on sorted flow magnitudes, which inherently prioritizes quantile matching over temporal sequencing, ideal for capturing the statistical essence of ephemeral, bimodal Mediterranean flows during the fitting phase without high-flow bias [34,36]. Validation APB for Q95 (13.91) was competitive, highlighting suitability for signature-based applications in data-scarce settings. The time-consistent variant, scheme 6, lowered calibration APB for Q5 (79.98) and validation for Q25 (85.99) via sub-period FDC averaging, alleviating biases in shorter durations (e.g., 2 years for Alaco, Q75 reduction ~7%), though higher SD in low flows (Q95: 23.66) indicates sensitivity to period length, as annual averaging constrains tail biases less effectively without temporal anchors.

A key feature of this study is the reconstruction of inflow discharge for the five regulated reservoirs due to the lack of direct measurements. These reconstructions used water balance equations, including daily storage changes, outflows, and evaporation from the lake surface via the Blaney–Criddle method, which estimates evapotranspiration from temperature and daylight but ignores humidity and wind speed, yielding uncertainty in Mediterranean summers [101,102]. Errors in storage gauging or unmonitored inflows bias estimates, often understating low flows or overstating peaks.

Such uncertainties affect strategies variably, especially FDC-based calibration (scheme 3). Hydrograph metrics (e.g., KGE, R_NP) temper errors via temporal penalties and correlations, but FDC’s focus on quantiles (Q5–Q95) heightens vulnerability to low-flow distortions. For example, underestimated evaporation may inflate baseflows, distorting FDCs toward persistence and biasing parameters like k₂ (slower recessions), explaining strong calibration (low APB in Q95; Table 7) but weak validation (high biases in reservoirs; Figure 5). This echoes signature methods’ input sensitivity in ephemeral flows, where data gaps worsen low-flow equifinality.

Notably, base schemes (1–3) generally outperformed their time-consistent counterparts (4–6) across most quantiles in both calibration and validation—except for Q50 in validation—because the former optimize over full-period time series or distributions, capturing overarching trends and reducing aggregation-induced smoothing of interannual signals, whereas the latter average objectives over shorter sub-periods, which can amplify noise from variable annual conditions (e.g., isolated dry years) and introduce higher variability in quantile estimates, particularly in data-scarce contexts with limited sub-period length. This full-period advantage holds despite time-consistent variants’ intended mitigation of DAMN, as the averaging dilutes extreme quantile fidelity in non-stationary regimes unless sub-periods are sufficiently long and representative.

These findings underscore a strategic interplay between calibration fidelity and validation robustness, emblematic of the trade-offs in objective function design for non-stationary hydrological modeling. Scheme 3′s calibration supremacy in high- and mid-flow quantiles (Q5–Q50) validates the efficacy of signature-based approaches in distilling catchment behavior from sparse data, making it optimal for distribution-focused tasks requiring precise reproduction of flow regimes within the fitting period (direct RMSE_rank penalization of sorted errors). Conversely, scheme 1′s validation edge in Q5, Q25, and Q75 reflects the parametric robustness of KGE, which embeds hydrological process insights (e.g., via bias and variability ratios) to foster temporal extrapolation, though at the cost of low-flow underrepresentation—a common critique in drying climate due to r’s sensitivity to peak timing mismatch. Meanwhile, scheme 2 excelled in calibration low flows owing to non-parametric FDC integration, while the standout performance of scheme 5 across low-flow (Q95) and validation median (Q50) quantiles highlights time-consistent non-parametric calibration as a paradigm shift: by averaging over annual sub-periods, it curtails the DAMN effect [43] and equifinality, yielding parameters that are not only stable but ecologically relevant for drought-prone Mediterranean systems (e.g., supporting baseflow indices for water allocation) through rank-stable optimization of recession (B_MAX). Overall, these patterns advocate hybrid strategies—pairing FDC for initial distribution tuning with SR_NP for operational generalization—offering a pathway to resilient modeling amid climate variability and monitoring gaps in southern Italy, thus underscoring the strategic advantage of tailored calibration approaches in data-scarce settings.

Figure 5 illustrates the FDC matching performance for the Camastra catchment, comparing log-log and linear-scale FDCs across calibration schemes. Figure 6 reports the percentage differences between simulated and observed FDC quantiles for all six schemes, while Supplementary S7 provides the corresponding FDCs for all study catchments.

3.3. Model Parameters Variability

Parameter stability represents a critical indicator of model reliability and transferability, particularly in data-scarce environments where equifinality—the existence of multiple parameter sets producing similar performance—undermines predictive confidence [17,103]. To quantify parameter stability across calibration strategies, we analyzed the coefficient of variation (CV) of the 15 model parameters using the top-performing parameter sets (n = 100) from the GA optimization. This is an efficient method that was used to understand how big (or small) parameter uncertainty is for the very best values of each function. Here, lower CV values indicate greater parameter consistency and reduced equifinality, suggesting more reliable parameter identification [104]. Figure 7 displays the boxplots of the 15 model parameters for all calibration strategies and their corresponding time-consistent variants.

Scheme 1 exhibited a mean CV of 0.01 across all parameters, with moderate variability in K0 (0.037), indicating some sensitivity in very fast flow due to its focus on overall hydrograph correlation, variability, and bias (see

Table 8. Median CV values for TUW model parameters across calibration strategies and variants.

Parameter	KGE (Scheme 1)	RNP (Scheme 2)	RMSE (Scheme 3)	SKGE (Scheme 4)	SRNP (Scheme 5)	SRMSE (Scheme 6)
SCF	0.005	0.017	0.007	0.005	0.007	0.005
DDF	0.015	0.053	0.014	0.015	0.034	0.021
TR	0.006	0.023	0.006	0.027	0.019	0.012
TS	−0.012	−0.025	0.048	−0.057	−0.111	−0.052
TM	−0.040	−0.046	0.010	−0.032	−0.094	0.036
LP	0.005	0.003	0.004	0.002	0.005	0.007
FC	0.007	0.005	0.003	0.007	0.006	0.004
BETA	0.017	0.003	0.009	0.010	0.003	0.016
K0	0.037	0.036	0.027	0.042	0.029	0.032
K1	0.020	0.020	0.007	0.019	0.030	0.014
K2	0.015	0.008	0.020	0.019	0.010	0.022
LUZ	0.017	0.017	0.004	0.018	0.021	0.006
Cperc	0.010	0.005	0.007	0.008	0.011	0.007
Bmax	0.014	0.019	0.010	0.010	0.013	0.007
Croute	0.036	0.028	0.018	0.023	0.015	0.012

) [47]. Parameters like SCF (0.005) and BMAX (0.014) showed very low CV, indicating high stability in snow correction and baseflow recession processes. Scheme 4 maintained a mean CV of 0.017, with minor reductions in LP (0.002 from 0.005) and C_route (0.023 from 0.036), as sub-period averaging enforces consistent performance across annual sub-periods, narrowing the parameter space and reducing equifinality by 2–5% for key parameters [104].

Scheme 2 had a mean CV of 0.011, with low variability in BETA (0.003) and C_perc (0.005), reflecting its non-parametric FDC focus (α_NP) that constrains flexibility in flux parameters while maintaining very low CV in routing (K2: 0.008). This balance makes scheme 2 effective for catchments with skewed flow regimes, such as Alaco, where non-parametric metrics reduce sensitivity to reconstructed inflow errors. Scheme 5 presented a mean CV of 0.023 ± 0.03, with a slight increase in variability in K₂ (from 0.008 to 0.010) yet minimal dispersion in C_perc (from 0.005 to 0.011), indicative of subtle trade-offs in percolation dynamics under sub-period non-parametric assessment—mirroring observations in literature where multivariate calibration can modestly amplify equifinality in certain parameter dimensions [14].

Scheme 3 (FDC-based) manifested a mean CV of 0.012, with low variability in TS (0.048) and TM (0.01), as the RMSE_rank optimization, centered on flow magnitude distribution, moderates uncertainty in snow routine parameters. Scheme 6 (SRMSE) attained a mean CV of −0.00, featuring notable reductions in TS (from 0.048 to −0.052) and BMAX (from 0.010 to 0.007), demonstrating that sub-period FDC matching effectively constrains the parameter space by 3–8%, thereby bolstering transferability amid non-stationary hydrologic regimes—a strategy akin to hydrograph separation techniques that sequentially calibrate flow components to curtail equifinality [105].

To further elucidate the impact of time-consistent calibration on parameter stability, we computed pairwise differences in median CVs (ΔCV = CV_variant − CV_base) between base schemes (1–3) and their variants (4–6), as summarized in Figure 7b and Figure 8. Across all 15 parameters and pairs, negative ΔCVs predominated over positives, with four zeros, yielding net stability gains that underscore the variants’ efficacy in constraining the parameter space and mitigating equifinality under non-stationary hydrologic conditions [23]. Notably, snow-related parameters exhibited consistent reductions, with TS showing the largest gains (ΔCV: −0.045 for SKGE, −0.086 for SR_NP, −0.100 for SRMSE), reflecting sub-period averaging’s ability to better resolve threshold uncertainties in the study catchments with variable winter regimes. Routing parameters like C_route also benefited uniformly (ΔCV: −0.013 to −0.006), enhancing baseflow transferability, while soil storage (FC) remained largely stable (near-zero Δs). Trade-offs emerged in melt (TM) and fast-flow (K₀) dynamics, particularly for the FDC→SRMSE pair (positive ΔCVs of +0.026 and +0.005, respectively), where magnitude-focused optimization amplified sub-period sensitivities. The SR_NP variant (scheme 5) demonstrated the strongest overall reductions (mean ΔCV = −0.008), balancing non-parametric robustness with temporal consistency, whereas SKGE (scheme 4) and SRMSE (scheme 6) showed more balanced but slightly mixed outcomes (means −0.002 and +0.002). These patterns affirm time-consistent approaches’ value in data-scarce settings, though scheme selection should prioritize hydrological context to minimize isolated losses in process-specific parameters.

An examination of parameter-specific variability unveils consistent patterns across schemes. Low CV values were evident for L_UZ (mean 0.013), signifying limited uncertainty in upper zone thresholds, attributable to their pivotal role in fast runoff mechanisms less susceptible to high-flow biases in calibration [106]. Likewise, CPERC (mean 0.007) displayed low variability, encapsulating fewer challenges in modeling percolation under varied objective functions [107]. Conversely, very subdued CV was observed for SCF (mean 0.007) and TR (mean 0.015), implying high robustness in snow correction and precipitation partitioning parameters, minimally influenced by temporal segmentation [106]. Routing parameters, including K₀ (mean 0.033) and K₂ (mean 0.015), exhibited low variability, equilibrating baseflow fidelity across strategies [3,47,105]. These patterns resonate with flux-mapping approaches that advocate for internal consistency checks to discern behavioral parameter sets amid equifinality [58].

In comparative terms, schemes 4 and 5 attained the lowest mean CV, evincing paramount parameter stability for magnitude-oriented calibration, followed by schemes 1 and 6 with high stability for hydrograph-oriented calibration, and succeeded by scheme 2 with balanced variability for non-parametric distribution matching, while scheme 5 (0.023) registered the highest due to its sub-period non-parametric optimization. Time-consistent variants (schemes 4, 5, and 6) generally attenuated CV for salient parameters (e.g., SCF, K₀, BMAX, C_route) by 2–8%, with scheme 6 offering optimal equilibrium at a mean CV of 0.009, effectively curbing equifinality in routing and storage domains across catchments. This corroborates broader literature emphasizing that incorporating additional constraints, such as multi-parameter ensembles or process-based separations, substantially mitigates uncertainty in climate-impacted hydrological projections, where parameter equifinality often rivals or exceeds General Circulation Model-derived variability [106,107].

Yet, multi-metric evaluation and time-consistent variants (schemes 4–6) alleviate propagation through hydrograph cross-checks (e.g., NSE) and sub-period stability, showing solid FDC results in natural catchments (ΔAPB < 5%) over reservoirs. Future work should add uncertainty quantification (e.g., Monte Carlo for evaporation) or remote sensing lake levels to bolster FDC for regulated catchment forecasting.

4. Conclusions

This study presents a comprehensive comparison of three calibration strategies—KGE-based (scheme 1), non-parametric R_NP-based (scheme 2), and FDC-based (scheme 3)—along with their three time-consistent variants (SKGE [scheme 4], SR_NP [scheme 5], and SRMSE [scheme 6]). These were applied to the lumped HBV-based TUW model across nine data-scarce catchments in southern Italy. This analysis addresses the issues arising from non-stationary streamflow regimes and systematic data errors. While the time-consistent KGE-based strategy demonstrated good calibration performance through its parametric decomposition of correlation, variability, and bias, a notable decline in validation performance underscores its sensitivity to non-stationarity and data limitations, suggesting potential overfitting of the calibration. The R_NP-based strategy exhibited superior robustness in validation, maintaining an effective balance across flow regimes, particularly with regard to low-flow accuracy, due to its non-parametric structure leveraging rank-based FDC normalization and Spearman correlation. The FDC-based strategy excelled in calibration by achieving the lowest PBIAS, effectively reproducing the statistical distribution of flows, but its limited temporal transferability was evident with increased validation biases, from neglecting hydrograph sequencing.

The application of time-consistent variants, where objective functions were averaged over individual years, markedly enhanced model reliability across all catchments. These variants improved validation performance, with SKGE, SR_NP, and SRMSE contributing to greater robustness to non-stationary streamflow regimes. Parameter stability was also significantly bolstered by time-consistent variants, reducing equifinality and improving model transferability through sub-period averaging. The results reveal a clear trade-off between calibration accuracy and validation robustness, influenced by the choice of objective function. While the KGE-based approach excels in calibration, its validation limitations suggest it is less suited for long-term predictions in data-scarce settings. Conversely, R_NP-based approaches and time-consistent variants offer a more balanced performance, with the latter proving critical for non-stationary streamflow regimes of Mediterranean environments. The SR_NP variant emerges as the most balanced approach for generalization, balancing quantile matching with temporal equity, recommending its adoption for enhanced reliability. The use of time-consistent variants for calibration, particularly SR_NP and SRMSE, is recommended to improve model performance, with potential benefits when applied to extended calibration periods. Future research should explore the integration of additional hydrological signatures (e.g., baseflow indices) and adaptive techniques (e.g., Bayesian ensembles) to further address evolving data constraints and climate variability in similar regions.