The Han River is the largest tributary of the Yangtze River and flows through Shaanxi and Hubei provinces in China. Its main channel stretches 1577 km, draining a basin of approximately 159 000 km², with average annual water resources of 56.6 billion m³ (Fig. 1a). More than 2700 reservoirs have been constructed along the river, including Shiquan, Ankang, and Danjiangkou reservoirs (Zhao et al., 2021). In order to minimize the influence of anthropogenic activities, this study focuses on the Upper Han River Basin (UHRB) above Shiquan Hydrological Station (Sun et al., 2013), located between 105°59^′–108°38^′ E and 32°20^′–34°16^′ N (Fig. 1b). To illustrate, land use in the UHRB was analysed using the 2008 data from the China multi-period land use remote sensing monitoring dataset (CNLUCC; Xu et al., 2018) and the Global Dam Watch (GDW; Lehner et al., 2024) dataset, as shown in Fig. S1. The land use pattern in the basin is clearly dominated by forest, grassland, and cropland. Forested areas are mainly distributed along the northern and southern mountain slopes, whereas irrigated paddy fields are concentrated in the low-lying central plains along the Han River. Overall, natural land use types dominate the UHRB (∼ 75 %), while anthropogenic components account for only ∼ 25 %. Anthropogenic hydraulic structures are generally scarce: Shimen and Nanshahe reservoirs, located in the upper and mid-reaches, have maximum storage capacities of only 110 and 43 MCM (million cubic meters), respectively, which are negligible for hydrological modelling. The Shiquan Reservoir, with a maximum storage of 412 MCM, located upstream of the Shiquan hydrological station, represents the only potential source of uncertainty in the simulations. Nevertheless, it operates on a daily regulation scheme and is primarily used for hydropower generation and flood control. As the model aims to simulate daily streamflow, its operational effects are expected to be minimal. This is further supported by the large annual runoff at the station (∼ 10.8 billion cubic meters), which far exceeds the reservoir storage capacity. In light of these considerations, the reservoir is not explicitly represented in the model, and its influence is assumed to be negligible.

The basin is characterized by a predominantly mountainous landscape, with hills, plains, and platforms comprising the remainder. Spatially, the elevation distribution defines a saddle-shaped topography that exerts a controlling influence on the river network, giving rise to a well-developed dendritic drainage pattern throughout the region. A monitoring network comprising five stations was deployed (Fig. 1b): three along the main channel (Hanzhong, Yangxian, Shiquan), and two on the headwater tributaries (Youshui, Lianghekou). This configuration establishes a well-monitored nested basin (five sub-basins, Fig. 1c), which provides the basis for this study to evaluate the impacts of spatially explicit parameterization and multi-gauge calibration on hydrological modelling. Furthermore, the UHRB experiences a subtropical monsoon climate, with annual precipitation of 800–1200 mm largely concentrated from July to September, which yields abundant runoff and rendering it highly suitable for the VIC model predicated on the Xinanjiang formula (Li et al., 2022; Lehmann et al., 2022).

The modelling exercises of this study require a wide variety of data products, which fall into three categories: meteorological forcings, land surface characteristics, and in-situ streamflow observations. The meteorological forcings were sourced from the China Meteorological Forcing Dataset (CMFD), selected for its 3-hourly temporal resolution, which satisfies the VIC-5 image driver (hereinafter VIC-5) time-stepping scheme requirement of at least four steps per day. This dataset offers seven key meteorological variables across China at a 0.1° × 0.1° spatial resolution (1979–2018), has been widely adopted in various hydrological modelling applications (He, 2020; Sun et al., 2023).

In addition, several datasets were collected to describe the land surface characteristics (i.e., soil, topography, land cover type, and vegetation). Specifically, the soil texture (i.e., the proportions of sand, loam, and clay) and the bulk density of six soil layers at depths between 0 and 200 cm were obtained from the SoilGrids1km dataset (Poggio et al., 2021). Topography was characterized using the Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) V4.1 (90 m resolution) (Jarvis et al., 2008) and land cover (14 classes) was derived from the University of Maryland's 1 km global dataset (UMD Land Cover; Hansen et al., 2021). Furthermore, monthly vegetation information – including the leaf area index (LAI), albedo, and partial vegetation cover fraction (fcanopy) – was calculated from multi-year data of several Moderate Resolution Imaging Spectroradiometer (MODIS) products (MCD43D51.061, MOD13A3.061, and MOD15A2H.061). Following established methodologies, fcanopy can be derived from the Normalized Difference Vegetation Index (NDVI) using the formula provided by Bohn and Vivoni (2019): 1fcanopy=NDVI-NDVImin(NDVImax-NDVImin)2 Then, the four-layer soil temperature from the ERA5 Land product is extracted and averaged to serve as the bottom boundary condition for the soil heat flux in the VIC model (Muñoz Sabater et al., 2021). Collectively, the land surface characteristics are integrated into a standalone parameter file for VIC-5 model execution. This parameterization entails the conversion of land surface variables into model-specific parameters, as detailed in the following section.

Finally, for model calibration and evaluation, we retrieved the observed daily streamflow records from the five hydrological stations (Fig. 1b), as published in the China Hydrological Yearbooks, and stored them in units of m³ s⁻¹. The datasets utilized in this study have varying temporal coverages; a common overlap period from 2003 to 2018 was therefore defined to ensure consistency in the modeling exercises, spanning the time during which all required model input data and streamflow records were available. Table 1 lists all the datasets used for deploying the VIC-5 model in this study.

The VIC model used for the hydrological simulation in this study was originally developed by Liang et al. (1994) as a land surface scheme within general circulation models (GCMs). As a physically based, spatially distributed hydrological model, it represents one of the most archetypal implementations of the FH69 blueprint (Freeze and Harlan, 1969), capable of simulating water and energy balances while accounting for the physical exchanges among the atmosphere, vegetation, and soil. The model is extensively used worldwide in studies of floods (Brunner et al., 2021), droughts (Lin et al., 2022), and broader water resource management (Nanditha and Mishra, 2022). For brevity, a concise overview of the VIC model is presented here, highlighting the components most pertinent to the spatially distributed parameters considered in this study, with full details available elsewhere (Melsen et al., 2016; Hamman et al., 2018; Gou et al., 2020).

The VIC model employs a structured rectangular grid for spatial discretization, with each grid cell treated as an independent runoff generation unit without lateral interactions and assigned a distinct set of parameters to reflect land surface characteristics (i.e., land cover and soil). To represent sub-grid heterogeneity, the fractional coverage of each land cover type within a cell is modelled as a separate tile and the grid-scale response is derived by aggregating the contributions of all tiles using an area-weighted average. This stochastic, non-distributed modelling approach is sometimes referred to in the literature as the variability approach (Wen et al., 2012). Through the designed structure, the parameters in the VIC model possess a naturally capacity to represent spatial variability, allowing them to be physically linked to pre-compiled information such as topography, vegetation, and soil properties. As an illustration, the saturated hydrologic conductivity can be estimated from soil texture, following the empirical formulations proposed by Cosby et al. (1984), as given below: 2log⁡Ks=0.0126x-0.0064y-0.6 where x denotes the sand content and y denotes the clay content. Overall, such transfer functions provide the conceptual foundation for regionalization approaches such as MPR.

In the VIC model, total runoff (Qt) is partitioned into surface runoff (R) and baseflow (Qb). Under the standard three-layer vertical soil structure (VIC-3L), surface runoff is generated from the thin top layer and the upper layer according to the variable infiltration capacity curve, as shown below (Liang et al., 1994): 3R=PE-Wm-W0,PE+i0≥imPE-Wm-W0+Wm1-PE+i0im1+b,PE+i0<im where PE denotes the effective precipitation; Wm represents the mean infiltration capacity of the grid cell; im is the maximum infiltration capacity at a point within the grid cell; W0 is the initial soil moisture and i0 is the corresponding initial infiltration capacity; and b is the shape parameter of the variable infiltration capacity curve. All of these quantities refer to the upper two soil layers. The VIC model does not explicitly represent soil drainage processes, such as interflow, or groundwater storage above the water table. Instead, these components are treated in a conceptual lumped manner and represented as baseflow from the bottom soil layer by a single term, Qb, which is parameterized using the Arno baseflow scheme, as follows (Liang et al., 1994): 4Qb=DsDmWsθbs⋅θb,0≤θb<WsθbsDsDmWsθbs⋅θb+(Dm-DsDmWs)(θb-Wsθbsθbs-Wsθbs)c,θb≥Wsθbs where θbs is the maximum soil moisture of the bottom layer; Dm is the maximum baseflow; Ds is the fraction of Dm at which nonlinear baseflow begins; Ws is the fraction of θbs at which nonlinear baseflow begins; and c is the exponent of the nonlinear part of the Arno baseflow curve, which is usually set to 2. All of these quantities refer to the bottom soil layer. The Arno baseflow equation can be equivalently reformulated as a coupled linear reservoir and a nonlinear reservoir, and can thus be expressed in the following form, thereby alleviating parameter interactions (Nijssen et al., 2001): 5Qb=D1θb,0≤θb<D3D1θb+D2(θb-D3)D4,θb≥D3 where D1 is the linear reservoir coefficient; D2 is the nonlinear reservoir coefficient; D3 denotes soil moisture at which baseflow transition occurs from linear to nonlinear; and D4 has the same conceptual meaning as c. This formulation is also known as the Nijssen form of the Arno model, has been incorporated into the official VIC model and can be specified through the global parameter file.

The complete rainfall-runoff process comprises both runoff generation and routing stages. The RVIC model was proposed as a post-processor of the VIC model, designed to trace river channel flow by a pre-defined Unit Hydrograph (UH) and generate hydrographs at specified outlet points (Lohmann et al., 1996). The principle of RVIC can be briefly described as the solution of the linear Saint-Venant equations within a linear time-invariant system. Its primary parameters, flow velocity and diffusion coefficient, are generally treated either as spatially uniform free parameters to be calibrated or as fixed constants in the absence of observations. To date, RVIC remains the official extension of the VIC-5 and its earlier version, and has seen broad application (Shrestha et al., 2025).

Here, the VIC-5 image driver version and RVIC are consistently deployed at 6 km × 6 km spatial resolution (Fig. 1c) with a 3-hourly timestep, and the simulated output are aggregated to the daily timestep for calibration and evaluation. For the parameter estimation and calibration procedures, detailed descriptions are provided in the following sections.

Samaniego et al. (2010) introduced a hierarchy of spatial scales to distinguish information across different resolution, which provides a basis for MPR implementation. Following this concept, we define the observational resolution describing land-surface characteristics as the level-0 scale (i.e., 1 km), while modelling resolution is represented by the level-1 scale (i.e., 6 km), reflecting the principal process scale resolved by the model. As introduced before, the MPR technique is model-independent, and its application to the VIC model requires specific refinement. Specifically, for each VIC parameter, we identify applicable prior transfer functions from literature and generalize them into a scale-independent form by incorporating the g-parameters. Using Eq. (2) as an example, we generalize it into the following form: 6Ks=10g1x+g2y+g3 where gi constitutes a set of g-parameters to be calibrated. For clarity and tractability, refinement is applied exclusively to several sensitive parameters (Gou et al., 2020), while the coefficients in the transfer functions of all other parameters are retained at their prior values (Mizukami et al., 2017), thus mitigating the issues arising from the curse of dimensionality. Table 2 summarizes the VIC-specific refinement of MPR. It is worth noting that VIC supports two equivalent baseflow parameterizations. Following Mizukami et al. (2017), we adopt the Nijssen formulation (i.e., D1, D2 and D3) to avoid the parameter interactions present in the original Arno formulation (Eq. 5). Namely, calibration of D1, D2 and D3 is equivalent to calibrating Ds, Dm and Ws, which have been identified as sensitive parameters in previous studies (Wen et al., 2012; Gou et al., 2021).

Besides the spatially explicit parameterization of soil hydraulic-related parameters (b, D1, D2, and D3), two additional refinements were made to parameters that exert strong control on runoff generation and concentration. First, it is widely recognized among the VIC users that the vertically discretized soil depth is a key determinant of runoff generation. In the classic VIC-3L (i.e., VIC three-layer) configuration, the upper two soil layers respond rapidly to precipitation, generating surface flow according to the Xinanjiang formulation, whereas the bottom layer governs baseflow, resulting in a slower runoff response (Eqs. 3 and 5). Different soil layer thicknesses produce significantly different runoff responses; consequently, these thicknesses (h1, h2, and h3) are typically treated as free parameters during calibration to fine-tune the VIC behavior (Gou et al., 2020). In addition, the original soil dataset (i.e., SoilGrids1km) provides six soil layers, each characterized by distinct properties (e.g., soil texture), whereas VIC-3L adopts a three-layer soil structure. In order to feed original soil data into the transfer function, it is necessary to reconcile its soil-layer structure with the VIC vertical structure. As shown in Fig. 2, a two-step mechanism is applied here, involving aggregation and scaling. In the first step, the original soil data are aggregated into a standard three-layer structure defined by the layering numbers z1 and z2, with the corresponding layer thicknesses summed and the soil properties averaged within each standard layer. In the second step, the original thickness (h0) is scaled by g10 to allow flexible adjustment of the final computational layer thickness. This mechanism is applicable to most soil-column-based hydrological models and has been validated in Mizukami et al. (2017). However, previous implementations used domain-wide uniform values of z1, z2, and g10, a simplification that diminished the representation of spatial heterogeneity in soil layer depths and reflected the limited availability of spatially grounded information on vertical soil structure. In this study, we compare simulations using uniform depths with those employing subbasin-unique depths (i.e., subbasin-specific values of z1, z2, and g10), analogous to a semi-distributed scheme, to examine how spatially explicit parameterization alter model behavior.

Second, the refinement is applied to the RVIC parameters, velocity (v) and diffusion (D), respectively. In previous studies, these two parameters were generally considered constant or spatially uniform free parameters to be calibrated (Shrestha et al., 2025; Yousefi Sohi et al., 2024). The official VIC documentation also recommends a diffusivity of 800 m² s⁻¹ and a velocity of 1.5 m s⁻¹ as acceptable values (https://vic.readthedocs.io/en/vic.4.2.d/Documentation/Calibration, last access: 25 April 2026). Nonetheless, we use the MPR technique here to enhance the spatial representation of these two parameters by linking them to topography (Fig. S2). This enhancement is then assessed for its impact on model behavior, which is particularly relevant for applications with limited prior information on channel routing, such as Manning's coefficients or channel morphology. Additionally, RVIC relies on UH as the impulse response function to convert runoff into streamflow, requiring them to be predefined. While various types of UH exist, such as the dimensionless SCS UH and the Nash UH (Roy and Thomas, 2016), the general UH (GUH) has drawn our attention due to its analytical formulation (Guo, 2022), with its expression presented as follows: 7ut=dgdt=μtpx(1+mx)-(1+1/m)8gt=1-(1+mx)-1/m9xt=exp⁡μttp-1 where tp is the peak flow time; m is a dimensionless recessing coefficient that is determined by the downstream water surface condition; and μ is the rising coefficient related to the basin characteristics. By calibrating the three parameters, the shape of the GUH can be freely adjusted, thereby providing flexibility in model representation when prior knowledge is limited. The GUH also demonstrate several advantages, including a solid theoretical and mathematical foundation (i.e., the solution of Chow's linear hydrologic systems equations), the ability to reproduce typical flood responses with high accuracy, and, under certain conditions, the capacity to closely approximate traditional unit hydrographs. Based on this, we select it as the engine for RVIC, which acts as grid UH over the domain.

For this study, we design an Experiment Framework to evaluate the effect of Spatially explicit Parameterization and Multi-gauge calibration, termed EF-SPM. The eight calibration cases, differing in their configurations of parameterization and calibration objectives, are summarized in Table 3. By grouping and comparing these cases, we can derive seven experiments with clearly defined objectives (Table 4), and can organize them into the following four main experimental setups. The EF-SPM experimental framework is illustrated in Fig. 3. For clarity and ease of understanding, the terms “distributed” and “spatially explicit” are used interchangeably below, unless otherwise noted.

Experiment 1. The added value of spatially explicit parameterization.

This experiment compares the calibration process and simulations between the fully spatially explicit (distributed) and spatial uniform parameter configurations to identify the effects of spatially explicit parameterization on model behaviour. Here, the calibration objective was treated as the controlled condition. Cases 7 and 8 were compared under the single-gauge calibration, while Cases 1 and 5 were compared under the multi-gauge calibration.

Different algorithms were employed for single-objective and multi-objective calibration. For the former, we used the Covariance Matrix Adaptation Evolution Strategy (CMA-ES; Hansen and Ostermeier, 2001), a global, single-objective optimizer based on a generate-and-update paradigm that has demonstrated robust performance in hydrological model calibration (Knoben et al., 2020; Aerts et al., 2024). For multi-objective calibration, we likewise adopted an evolution strategy, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), to ensure a fair comparison by minimizing algorithmic bias. We implemented all optimization algorithms with the DEAP Python package (De Rainville et al., 2012; Fortin et al., 2012). In addition, both optimizers were configured with an identical population size of 20 and shared the same objective function: the modified Kling-Gupta efficiency (KGE) of the streamflow, with the only difference being the number of gauges considered in each case, as given below (Aerts et al., 2022): 10KGE=1-(r-1)2+μsimμobs-12+σsim/μsimσobs/μobs-12 where r is the linear correlation coefficient between observed (obs) and simulated flow (sim), while σand μ denote their respective stand deviations and means. The three terms in Eq. (10) represent, respectively, the correlation between observations and simulations (r), the bias in the mean (β), and the bias in the variability (γ). For both the KGE and its individual components, a value closer to 1 denotes better model performance, with 1 representing perfect agreement. Under the two optimization algorithms, CMA-ES optimizes the KGE at the basin outlet (Shiquan) as the single-objective function (KGE_Q5), whereas NSGA-II performs multi-objective optimization in the multi-dimensional Pareto space, considering the KGE of streamflow at the five subbasin gauges as separate objectives (KGE_Q1, KGE_Q2, KGE_Q3, KGE_Q4, KGE_Q5).

To further support a comprehensive evaluation, we additionally considered several signature metrics, as highlighted in the diagnostic evaluation framework (Gupta et al., 2008). Unlike aggregated performance metrics, hydrologic signatures offer a quantitative measure of specific hydrograph properties or behavior (e.g., total volume, flow peaks, and recession limbs). This allows for a more refined characterization of the temporal dynamics inherent in hydrography and helps pinpoint specific discrepancies in simulated flow patterns. Following Yilmaz et al. (2008) and Casper et al. (2012), a suite of flow duration curve (FDC)-based bias metrics was adopted. Specifically, %PBias was used to characterize overall water volume differences; %BiasFHV quantifies discrepancies in the high-flow segment; %BiasFLV represents differences in the low-flow segment; %BiasFMS describes deviations in the slope of the middle segment; and %BiasFMM measures the percentage differences in mid-range flow levels. The corresponding formulations are given below: 11%PBias=∑i=1N(Qsimi-Qobsi)∑i=1nQobsi×100%12%BiasFHV=∑h=1H(Qsimh-Qobsh)∑h=1HQobsh×100%13%BiasFLV=∑l=1Llog⁡Qsiml-log⁡Qsimmin-∑l=1Llog⁡Qobsl-log⁡Qobsmin∑l=1Llog⁡Qobsl-log⁡Qobsmin×100%14%BiasFMS=log⁡Qsimm1-log⁡Qsimm2-log⁡Qobsm1-log⁡Qobsm2log⁡Qobsm1-log⁡Qobsm2×100%15%BiasFMM=MedianQsim-Median(Qobs)Median(Qobs)×100% where Q denotes the streamflow; i=1, 2, … , N, h=1, 2, … , H, and l=1, 2, … , L are the indices of flow value in the full record, the high-flow segment (exceedance probabilities of 0–0.02 for %BiasFHV₂ and 0–0.01 for %BiasFHV₁), and low-flow segment (defined as 0.7–1.0) of the flow duration curve, respectively. The middle-flow segment is bounded by two thresholds, m1 and m2, corresponding to exceedance probabilities of 0.2 and 0.7, respectively. Note that the original definitions were slightly modified here to ensure consistent sign conventions across all metrics, where negative values indicate an underestimation by the simulations.

The full period from 2003 to 2018 was allocated for warm-up (2003–2004), calibration (2005–2014), and validation (2015–2018) in a 1:5:2 ratio. To ensure computational efficiency while maintaining calibration performance, we conducted 40 calibration trials for each case (amounting to 40 trials × 20 individuals = 800 model runs in total), a number we found sufficient to ensure convergence based on our preliminary tests. All cases implemented in this study were deployed using the Easy VIC Build (EVB) open-source Python framework developed by our team (https://github.com/XudongZhengSteven/easy_vic_build, last access: 25 April 2026), which was designed to streamline the deployment process of the VIC model.

In this section, we first present an overview of the KGE-based streamflow simulation performance across all cases within the EF-SPM. To mitigate calibration uncertainty, the ensemble-mean KGE derived from the five optimal solution sets is reported, synthesizing results from multiple calibration trials (Table 7). As shown, Case 5 and 4 account for the first- and second-best performances in nearly all cases, for both calibration and validation. This behavior is in line with expectations, given that these cases involve a more explicit representation of spatial parameters and tighter calibration constraints. A comparable pattern of enhancement emerges when transitioning from simpler to more complex configurations (e.g., Case 6 to Case 8, and Cases 1–3 to Cases 4–5). Notably, the most substantial performance gain was observed when moving from the simplest (Case 6) to the most complex configuration (Case 5), as anticipated in Exp. 4 (Baseline-Complex). In addition, a spatial dimension to performance differences was also observed, where upstream headwater sub-basins (e.g., Hanzhong and Youshui) consistently underperformed relative to downstream locations.

To further examine the statistical significance of performance differences across various cases, we conducted pairwise t-tests on the KGE at the Shiquan station (basin outlet), as shown in Table S1. It is evident that, at a significance level of 0.05, Case 4 performs significantly better than all other cases, while Case 8 performs significantly worse than all other cases. Moreover, the patterns identified in the previous analysis are further confirmed by this significance test, with the more complex configurations generally outperforming the simpler ones. It is worth noting that this comparison is conducted under a single-objective context, as Cases 6–8 only consider streamflow at the basin outlet as objective functions.

The initial analyses are encouraging, demonstrating that improvements in spatial parameter explicitness and multi-gauge calibration consistently lead to better streamflow reproduction. In particular, the overall simulation performance is satisfactory at the basin outlet (Shiquan station), with calibration KGE exceeding 0.76 across all cases and validation KGE values remaining above 0.67. The results presented here establish the context for analyzing the specific effects of these configuration.

The refinement of spatial representation involves three parameter groups: VIC parameters, soil layer depths, and RVIC parameters. To maintain analytical clarity, this section focuses solely on evaluating their combined effect on simulation in Exp. 1 (Case 1 vs. Case 5 [UD-MG] and Case 7 vs. Case 8 [UD-SG]), leaving the analysis of their individual effects from Exp. 3 to a subsequent section. Note that, for robustness, all results herein represent the ensemble values of the top five optimal solutions, consistent with the previous section.

This section delves into the parameter identifiability and calibration process to determine, via a comparative analysis (Exp. 2-1 [MS-DP]: Case 5 vs. Case 8, Exp. 2-2 [MS-UP]: Case 1 vs. Case 7), whether multi-gauge calibration confers a distinct advantage over its single-site counterpart and to investigate any cross-effect with the spatially explicit parameterization.

For completeness, this section investigates the individual effects of additional MPR refinements (the focus of Exp. 3) on hydrological simulations through specific case comparisons, considering two aspects respectively: soil layer depths (Exp. 3-1 [UD-MG: Depth]: Case 4 vs. Case 5) and the RVIC parameter (Exp. 3-2 [FUD-MG: RVIC]: Case 2 vs. Case 3 vs. Case 4). To ensure consistency between parameters and simulations, the top-ranked solution is adopted for analysis here rather than the ensemble values.