Sensitivity Analysis of Soil Hydraulic Parameters for Improved Flow Predictions in an Atlantic Forest Watershed Using the MOHID-Land Platform

Abstract

Soil controls water distribution, which is crucial for accurate hydrological modeling. MOHID-Land is a physically based, spatially distributed model that uses van Genuchten–Mualem (VGM) functions to calculate water content in porous media. The hydraulic soil parameters of VGM are dependent on soil type and are typically estimated from experimental data; however, they are often obtained using pedotransfer functions, which carry significant uncertainty. As a result, calibration is frequently required to account for both the natural spatial variability of soil and uncertainties estimation. This study focuses on a representative Atlantic Forest watershed. It assesses the sensitivity of channel flow to VGM parameters using a mathematical approach based on residuals derivative, aimed at enhancing soil calibration efficiency for MOHID-Land. The model’s performance significantly improved following calibration, considering only five parameters. The NSE improved from 0.16 on the base simulation to 0.53 after calibration. A sensitivity analysis indicated the curve adjustment parameter ($n$) as the most sensitive parameter, followed by saturated water content (${\theta }_s$) considering the 10% variation. Additionally, a combined change in ${\theta }_s$, $n$, residual water content (${\theta }_r$), curve adjustment parameter ($\alpha$), and saturated conductivity ($K_{sat}$) values by 10% significantly improves the model’s performance, by reducing channel flow peaks and increasing baseflow.

1. Introduction

Soil hydraulic properties play a crucial role in hydrological soil modeling, as they dictate the distribution of water content and fluxes within the soil profile, directly influencing key land surface processes, such as infiltration, surface energy balance, lateral flow, and runoff [1,2,3]. The accurate representation of hydrological processes relies on the soil water characteristic curve (SWCC), which delineates the relationship between soil water content and matric potential. Matric potential serves as a dual indicator, reflecting both the energy required for water extraction and the soil’s moisture retention capacity during drying. The shape of this curve is influenced by a combination of intrinsic and extrinsic factors. Intrinsic factors include soil physical properties such as texture (particle-size distribution), bulk density (which affects soil compaction and pore space), organic matter content, and structure (which generally has a lesser influence compared to the other factors). Furthermore, extrinsic factors exert considerable influence, including biological activity (such as root dynamics, microbial processes, and soil fauna), antecedent moisture conditions, land use patterns, and topographic attributes, all of which indirectly modulate soil water behavior and, consequently, the SWCC [4,5].

Given their broad impact, understanding and precisely estimating soil hydraulic properties is essential not only for reliable soil hydrological modelling but also for improving the accuracy of water flux simulations within the soil profile [6,7]. These properties are particularly relevant in environmental studies, water resource management, and flood prediction, where precise parameterization enhances decision-making processes and strengthens the predictive capability of hydrological models.

Multiple empirical models have been developed to describe the SWCC and hydraulic conductivity, each defined by specific adjustment parameters and equations. Among the most recognized formulations are those proposed by Gardiner [8], Brooks and Corey [9], van Genuchten [10], and Fredlund and Xing [11]. Among these, the van Genuchten (VG) model, when combined with the Mualem hydraulic conductivity model, is widely applied due to its ability to express unsaturated hydraulic conductivity as a function of both water content and soil pressure head [12,13]. This combined van Genuchten–Mualem (VGM) model provides a comprehensive framework for describing both water retention and hydraulic conductivity in soil profiles, making it a fundamental tool in hydrological modelling.

Water movement within the soil, particularly under non-steady conditions, is governed by the Richards Equation, a nonlinear parabolic partial differential equation that accounts for pressure gradients and hydraulic conductivity [14]. Due to the strong non-linearity of hydraulic parameters, accurately simulating these fluxes requires numerical methods capable of resolving complex interactions within the soil matrix.

In this study, the MOHID-Land model was selected as the modelling framework due to its finite volume approach, which effectively integrates VGM theory to compute water fluxes in porous media. This integration allows for a more detailed representation of soil–water interactions, thereby improving the accuracy of hydrological predictions under a variety of environmental conditions.

As a spatially distributed and physically based hydrological model, MOHID-Land is designed to simulate the various phases of the water cycle within a catchment. Its versatility has been demonstrated in numerous studies worldwide, including crop transpiration fluxes for soil water balance [15], streamflow modelling [16], urban flood simulations [17], rainfall–runoff modelling [18,19], and sediment transport analysis [20].

Despite its broad application, existing MOHID-Land studies lack explicit documentation on the parameter selection process and calibration criteria for porous media. This gap presents a significant challenge, as proper calibration is critical for ensuring model accuracy and reliability. In hydrological modelling, sophisticated calibration methods often rely on optimization algorithms and exhaustive approaches that involve multiple simulations [21]. These strategies can significantly enhance parameter estimation, reducing uncertainty and improving predictive performance. However, their application is highly dependent on the computational efficiency of the model being used.

For MOHID-Land, the calibration process typically follows a trial-and-error approach [22] due to the model’s high computational cost. While optimization-based methods have been successfully applied in other hydrological models, their feasibility in MOHID-Land remains limited. Running multiple simulations to explore parameter spaces requires substantial computational resources, making it challenging to apply more systematic, automated approaches. As a result, users often resort to manual adjustments based on expert judgment.

Efforts to automate the calibration process in MOHID-Land have been explored in specific contexts. For instance, Telles et al. [23,24] demonstrated the feasibility of automated calibration for flood prediction in a small urban watershed, obtaining promising results within short simulation periods using a carefully selected set of parameters. However, extending this methodology to long-term simulations in larger watersheds presents additional challenges. The computational demand of exhaustive calibration methods makes them impractical, reinforcing the need for adaptable strategies that balance model accuracy with computational feasibility.

Given these constraints, improving MOHID-Land calibration requires a deeper understanding of the physical processes underlying parameter behavior, enabling more insightful adjustments that optimize both model performance and efficiency.

The study by Oliveira et al. [22] marked a significant step forward as the first structured sensitivity analysis for MOHID-Land, aiming to assess the influence of specific parameters on model behavior. By examining key variables such as hydraulic conductivity, anisotropy ratio, number of layers, and soil thickness, the study provided valuable insights into how porous media parameters affect hydrological processes [22]. However, some critical processes remained unexplored, highlighting the need for additional sensitivity analyses and calibration efforts to achieve a more comprehensive understanding of soil–water interactions within MOHID-Land.

Although progress has been made, no standardized methodology for calibrating soil parameters in MOHID-Land has been established, and the influence of parameter variations on river flow remains poorly understood. This study addresses this gap by conducting a structured sensitivity analysis using residual derivatives to evaluate the impacts of the VGM parameters: the saturated soil water content (${\theta }_s$), the residual soil water content (${\theta }_r$), the fitting parameter ($n$), the fitting parameter ($\alpha$), and the saturated hydraulic conductivity ($K_{sat}$), on river discharge. By reducing uncertainties in flux simulations, the research enhances the calibration process and provides a more robust framework for parameter optimization in MOHID-Land.

Our findings demonstrate that calibrating MOHID-Land based on the sensitivity of VGM parameters significantly enhances the prediction of baseflows and peak discharges, leading to more reliable hydrological modelling. To facilitate this process, we developed a computational tool, the MOHID SOIL TOOL (MST), designed to expedite soil data processing and assist in parameter calibration [25].

This study was conducted in a representative watershed within Brazil’s Atlantic Forest, a region where previous research [26,27] identified porous media flux prediction as a key limitation in hydrological modelling. A novel aspect of this study is the incorporation of high-resolution soil texture data from the Brazilian Agricultural Research Corporation (EMBRAPA, Brasília, Brazil), headquartered in Brasília, Brazil, which had not been previously used as input in MOHID-Land watershed models. By integrating this detailed dataset, this study enhances the accuracy of soil parameter estimations, potentially benefiting a wide range of hydrological and environmental applications.

2. Materials and Methods

2.1. Study Area

The Pedro do Rio watershed covers an area of approximately 420 km², covering about 55% of the city of Petrópolis. It is located at the mountainous region of Rio de Janeiro, within the Serra do Mar range, an internationally recognized biodiversity hotspot that harbors diverse ecosystems and a high concentration of endemic species. The watershed is an integral component of the Piabanha/RJ watershed, which, in turn, is part of the larger Paraíba do Sul watershed. The Paraíba do Sul watershed, extending across São Paulo, Minas Gerais, and Rio de Janeiro, plays a critical role in supplying water for domestic consumption, industrial activities, and irrigation, as shown in Figure 1.

Due to its relevance, the Pedro do Rio watershed is one of three sites selected within the framework of the Integrated Studies in Experimental and Representative Basins (EIBEX) Project, an ongoing national initiative led by the Brazilian Geological Service (EIBEX-CPRM). This project aims to conduct long-term hydrological and environmental monitoring in key representative watersheds across Brazil, with a focus on areas that share critical physical, environmental, economic, and social characteristics with the larger river basins they are part of [28]. Additionally, the watershed plays a crucial role in supporting hydrological model calibration, water resource management, and public policy formulation, given the presence of an official monitoring station (refer to Figure 1).

According to the most recent census data (2022), the population of Petrópolis is 278,881 inhabitants, with a population density of 352.50 inhabitants per square kilometer [29]. This relatively high population density translates into an increased demand for natural resources, particularly water, and places heightened pressure on the local ecosystem. The region’s economy is significantly driven by agriculture, particularly the cultivation of cereals, legumes, and oilseeds [29]. However, while these activities are crucial for local development, they also contribute to water resource depletion, soil degradation, and river sedimentation due to agrochemical runoff [30].

The elevation of the representative watershed ranges from 645 m at the outlet to 2200 m, with an altitudinal difference of approximately 1450 m. Terrain features include strongly wavy slopes (20–35%), which cover 44.6% of the watershed area, and mountainous slopes (45–75%), comprising 36.4% of the area. Climate patterns vary with altitude: higher regions experience a humid tropical climate with annual rainfall exceeding 2000 mm, while lower areas have a subhumid climate, with average rainfall around 1300 mm. The seasons are well defined, and rainfall distribution remains consistent throughout the year [31].

The watershed is a unique mix of urban and rural features, interspersed with preserved fragments of the Atlantic Forest. Most of the watershed, about 62%, is covered by dense forest, including a significant portion of the Serra dos Órgãos National Park. Agriculture and livestock farming, primarily along riverbanks and slopes, occupies approximately 26% of the watershed area [28]. Urban development, which accounts for roughly 7% of the area, has seen a marked increase due to the watershed’s proximity to the city of Rio de Janeiro. This urban growth has contributed to an increase in landslides and floods. The remaining area is characterized by rocky outcrops on the mountain’s slopes.

2.2. MOHID-Land Model

MOHID-Land is a hydrological model developed to simulate hydrological processes at the watershed scale. This approach enables the model to capture spatial heterogeneities in land cover, soil types, and subsurface hydrodynamics with high resolution, making it highly versatile and suitable for a wide range of hydrological studies, from small catchments to large river basins.

The model uses the Finite Volume Method (FVM) to solve mass and momentum conservation equations. It operates through both horizontal and vertical discretization: the horizontal discretization employs a regular grid with a user-defined spatial resolution, while the vertical discretization specifies soil horizon thicknesses, extending to a user-defined maximum depth beyond which no flow occurs. The drainage network is derived from elevation data, with channels formed by linking surface cell centers down the slope, creating nodes where calculations are performed.

The model calculates the exchanges between the river, ground surface, and soil media based on the pressure gradient. The Saint-Venant equation is used to solve the flow in the drainage network (1D domain) and runoff (2D domain) [19,22].

Plant growth is simulated using a modified version of the Environmental Policy Integrated Climate (EPIC) model [32], which incorporates the total temperature accumulated until the plant reaches maturity, based on the heat unit theory. Additionally, it simulates root growth, leaf area index, canopy height, and total biomass, enabling the removal of water from the soil through evapotranspiration or rain interception by the canopy.

MOHID-Land also enables the assignment of a crop coefficient for each stage of plant development, which is crucial for the simulation of evapotranspiration. The water stress is calculated according to Feddes et al. [33] model, which predicts four critical points of suction pressure for the plants water stress. In the condition where $h_2$ < $h$ < $h_3$, the stress value is minimal, and thus, absorption is maximal. Conversely, there is a linear increase in stress when $h$ > $h_2$ or $h$ < $h_3$, becoming maximum when $h$ < $h_4$ and $h$ > $h_1$. Finally, the model does not directly simulate the atmosphere, instead, meteorological data are imposed as boundary conditions.

2.2.1. Porous Media Fluxes and VGM Parameters

In contrast to SWAT, a widely utilized hydrological model where soil water flow is predicated on the saturated capacity of individual layers—with excess water from saturated layers becoming input for subsequent layers and lateral flow occurring when underlying layers are also saturated [34]—MOHID-Land employs a more complex approach, simulating soil profile flows within a three-dimensional grid.

In the MOHID-Land model, the boundaries of the porous media are represented by two main interfaces. The first is the interface with the bottom, where it is assumed that the soil reaches an impermeable bedrock layer. When water reaches the bottom of the soil, it follows the slope of the digital terrain model, allowing subsurface flow. The second boundary is the interface with the air, where atmospheric conditions are imposed, with precipitation being the primary water input into the system. Additionally, variables such as temperature, solar radiation, cloud cover, wind speed, and relative humidity are used to calculate evapotranspiration, which represents the primary water output from the system.

The water movement through the soil is driven by the pressure gradient. This is mathematically represented by the Buckingham–Darcy equation (Equation (1)), used to calculate infiltration. Upon soil saturation, hydraulic conductivity reaches its maximum, termed saturated conductivity. As the soil desaturates, unsaturated conductivity becomes a function of soil water content. The rate of water accumulation within the three-dimensional domain is then determined by the integration of the Buckingham–Darcy equation with the continuity equation, resulting in the Richards Equation (Equation (2)). To further refine the determination of water content, MOHID-Land incorporates van Genuchten–Mualem functional relationships [10,12], according to Equations (3)–(5):

$$Q_i=-K\left(\theta \right){\displaystyle \frac{\partial H}{\partial x_d}}A$$

(1)

$${\displaystyle \frac{\partial \theta }{\partial t}}=-{\displaystyle \frac{\partial Q_i}{x_d}}-S\left(h\right)={\displaystyle \frac{\partial }{x_d}}\left(K\left(\theta \right){\displaystyle \frac{\partial H}{\partial x_d}}\right)A-S\left(h\right)$$

(2)

$$K\left(\theta \right)=K_{sat}{S}_e^L{(1-{(1-S_e^{1/m})}^m)}^2$$

(3)

$$S_e={\displaystyle \frac{{\theta \left(h\right)-\theta }_r}{{{\theta }_s-\theta }_r}}={\left[{\displaystyle \frac{1}{1+{\left(\alpha h\right)}^n}}\right]}^m$$

(4)

$$\theta \left(h\right)={\theta }_r+{\displaystyle \frac{{\theta }_s-{\theta }_r}{{\left[{1+\left(\alpha \left|h\right|\right)}^n\right]}^m}}$$

(5)

where $K\left(\theta \right)$ is the unsaturated hydraulic conductivity [m/s], $Q$ is the fluxes [m³/s], $A$ is the area [m²], $\theta$ is the water content [m³/m³], $H$ is the hydraulic gradient (topography + hydrostatic pressure + suction pressure) [m], $x_d$ is the direction, $S\left(h\right)$ is the term for water uptake from the soil by plant roots [m³/s], $\theta \left(h\right)$ is the water retention curve [m³/m³], ${\theta }_s$ is the saturated water content [m³/m³], ${\theta }_r$ is the residual water content [m³/m³], $h$ is the suction pressure [m], $K_{sat}$ is the saturated hydraulic conductivity [m/s], $S_e$ is the effective saturation [dimensionless], $\alpha$ is the curve adjustment parameter, related to the inverse of the air entry [m⁻¹], $n$ is the curve adjustment parameter, related to the pore size distribution [dimensionless], $m$ is obtained from relation $1-1/n$, and L is the empirical pore connectivity [m], equal to 0.5 [12].

The parameter ${\theta }_s$ is a key variable in soil science, representing the maximum volumetric water-holding capacity of soil. It is defined as the fraction of the total soil volume that is occupied by water when the soil is fully saturated.

The parameter ${\theta }_r$ represents the lower limit of available water in the soil, specifically indicating the moisture content which can no longer be extracted due to the strong adhesion of water molecules to the soil matrix. Mathematically, within the framework of the VG model, ${\theta }_r$ signifies the point on the SWCC where the slope ($d\theta /dh$) approaches zero under high suction pressures. This indicates that while water is still present in the soil, it is bound too tightly for plant uptake, resulting in minimal or negligible flow of water. Luckner et al. [35] define ${\theta }_r$ as the water content at a specific suction pressure where fluid flow ceases, primarily due to the strong retention of moisture films by the solid phase of the soil.

The parameter $n$ is closely associated with grain size distribution and plays a significant role in determining the slope of the SWCC in the VG equation. According to Gonçalves [36], when soil particles are more uniform in size, as seen in sandy soils, the retention curve tends to be steeper, which corresponds to higher values of $n$. This steeper slope enhances the characteristic “S” shape of the retention curve, resulting in reduced water-holding capacity within the capillary region and rapid drainage after the air entry point.

In contrast, soils with a more varied particle size distribution, such as clay-rich soils, exhibit a more gradual slope in the capillary region of the SWCC. This gradual slope, associated with lower values of $n$, allows for a more extended capillary region, effectively increasing water retention capacity. This effect is due to the smaller particles, which create stronger adhesive forces, slowing down drainage and enhancing the soil’s ability to retain moisture under increasing suction pressure.

The parameter $\alpha$ lacks a direct physical meaning; however, it is associated with the inverse of air entry. This parameter shifts the curve towards regions of higher and lower suction pressures. The incorporation of air into the water retention curve is tied to the initial suction phase, which corresponds to the area of maximum porosity (where saturation is at its peak). The air entry can be defined as the pressure difference between water and air required to induce drainage in the macropores [37]. This is contingent on the soil texture, such that in conditions with a higher clay presence, water entry occurs in areas of higher suction pressure, implying a higher water retention capacity [11]. Conversely, in sandy soils, air entry takes place in the region of lower suction values (smaller saturated region), leading to a reduced retention capacity.

Hydraulic conductivity, denoted as $K$, is a fundamental physical property that defines a soil’s capacity to transmit water, playing a crucial role in understanding the hydrological processes occurring within terrestrial environments. This parameter quantifies the ease with which water moves through the soil’s porous spaces, reflecting the intricate interplay between the material’s physical and chemical properties [38]. Soil texture is a significant factor influencing hydraulic conductivity; sandy soils, with larger and interconnected pores, generally have higher conductivity than clay soils, which have finer, more restricted pores that limit water flow. Additionally, soil structure—the arrangement of soil particles—affects water movement; well-structured soils with stable aggregates facilitate flow by allowing a mix of pore sizes. The presence of organic matter can also improve soil structure and increase hydraulic conductivity, while soil compaction reduces pore size and diminishes water transmission capacity [39].

2.2.2. Model Set-Up (Reference Simulation—S0)

A regular grid of 0.002° (approximately 200 m resolution) was used to cover the entire modeled domain, consisting of 160 rows and 200 columns. The grid’s origin is defined by the coordinates 43.36133° W and 22.58743° S. Computational operations are limited to the cells within the watershed delineation, excluding the rest of the grid. The Digital Elevation Model (DEM), sourced from the Topodata Project [40], has a spatial resolution of 30 m and was interpolated to match the project’s grid resolution.

The river cross-sections were obtained from field measurements conducted between 2019 and 2021 by the Piabanha Watershed Committee. The cross-sections were modeled as trapezoidal shapes to represent the natural geometry, with dimensions determined based on the drainage area (

Table 1. Cross-sections dimensions based on measurements.

Heights (m)	Top Width (m)	Bottom Width (m)	Drainage Area (km2)
1.50	3.00	1.00	2.00
2.00	4.60	1.00	6.32
2.00	5.10	2.00	12.60
2.00	8.70	2.00	34.40
5.00	11.20	6.00	49.18
5.00	14.00	6.00	103.45
5.00	19.00	6.00	419.33

). The model then linearly interpolated values for the nodes between the measured points.

The river cross-sections were obtained from field measurements conducted between 2019 and 2021 by the Piabanha Watershed Committee. The cross-sections were modeled as trapezoidal shapes to represent the natural geometry, with dimensions determined based on the drainage area (Table 1). Each node in the drainage network is associated with a specific drainage area. For nodes where data were available, the cross-sections described in the table were assigned. For intermediate nodes without data, a linear interpolation was applied to estimate the values between the measured points

The MapBiomas project provided a land use map with a 30 m spatial resolution, which was instrumental in identifying vegetation types and calculating the Manning coefficient. Three primary classes of vegetation were defined: forest, pasture, and agriculture (tomato). Based on these classes, the crop coefficient ($K_c$) values were determined for all growth stages. The Manning coefficient, the $K_c$, and the Feddes values used are outlined in

Table 2. Surface and vegetation coefficients.

Land Use Classes	Manning Coefficient	${\mathit{K}}_{\mathit{c}}$			Feddes
		Initial	Mid-Season	End Season	${\mathit{h}}_1$	${\mathit{h}}_2$	${\mathit{h}}_3$	${\mathit{h}}_4$
Dense Forest	0.160	0.95	1.00	1.00	0	−1	−3.3	−150
Pasture	0.038	0.40	1.05	0.85	−0.1	−0.25	−8	−80
Agriculture	0.045	0.60	1.15	0.90	−0.1	−0.25	−15	−80
Urban	0.040	-	-	-	-	-	-	-
Rocky Outcrop	0.030	-	-	-	-	-	-	-

Note: Manning estimate according to Chow [41]; $K_c$ defined according to Allen et al. [42]; pasture and agriculture Feddes obtained from HYDRUS 1D model [43]; and forest Feddes defined according to Grinevskii [44].

. The other culture growth parameters used in the EPIC model were defined according to the MOHID-Land database.

In MOHID-Land, the soil domain has been discretized to a maximum depth of 7 m and divided into 7 layers utilizing all 6 EMBRAPA layers, as shown in

Table 3. Vertical discretization of the 3D domain.

Model Layers		EMBRAPA Layers
ID	Thickness
1	5 cm	0–5 cm
2	10 cm	5–15 cm
3	15 cm	15–30 cm
4	30 cm	30–60 cm
5	40 cm	60–100 cm
6	300 cm	100–200 cm
7	300 cm

. For the two deepest layers (6 and 7), the hydraulic parameters from the 100–200 cm EMBRAPA horizon have been considered.

Soil properties were obtained from EMBRAPA, including sand, clay, and silt fractions, and bulk density derived from a nationwide sampling. These properties were interpolated and spatialized into 90 m pixels across various depths (0–5, 5–15, 15–30, 30–60, 60–100, and 100–200 cm), making them versatile for various applications. The dataset generated is from 2021, although the specific dates of the samples are not mentioned. The interpolation method is based on using seventeen geospatial covariates (eight from climate and nine from relief) and an ensemble of seven predictive models. These models, optimized by ten-fold cross-validation, included methods like random forest and extreme gradient boosting. Hence, the combined predictions, processed with caret and caret Ensemble in R, produced high-resolution (90-m pixel) maps [45,46].

Meteorological data required for calculating reference evapotranspiration using the FAO Penman–Monteith method [34]—including air temperature, wind speed, relative humidity, solar radiation, and cloud cover—were obtained from the global ERA5 model. The model provides wind speed data at 10 m, which is subsequently adjusted to 2 m following the methodology outlined by Allen et al. [47]. The ERA5 model offers hourly atmospheric data on a 0.25° × 0.25° grid and includes a long-term series that extends back to 1950 [39]. Since its introduction, the reliability of ERA5-Land indicators has been examined in several studies, including evaluations of their performance in Brazil and other regions. Research by Liu et al. [48], Braga et al. [49], de Araújo et al. [50], and Matsunaga et al. [51] has confirmed that the ERA5-Land data are accurate and suitable for their intended applications. Based on these conclusions, we have considered the ERA5 dataset to be appropriate for the variables listed above.

Daily precipitation data were gathered from thirty-nine stations across the watershed, sourced from four institutions: ANA, CPRM, Rio de Janeiro State Environmental Institute (INEA), and the National Center for Natural Disaster Monitoring and Alerts (CEMADEN). Subsequently, the station timeseries were grouped into fifteen synthetic stations using a clustering method based on the median of neighboring stations.

To address any missing values in the time series, the HyKit tool, developed at UNESCO-IHE [52], was employed. This tool fills the data gaps by weighing the values of synthetic stations according to their distance and elevation. To ensure uniformity across all timeseries, the double mass method [53] was utilized. This method involves cumulating precipitation values from each station and comparing them with the cumulated data from a reference station to assess linearity between the series. The complete methodology and dispersion of the stations can be accessed in Costa et al. [54].

2.3. Sensitivity Analysis Framework

Given that MOHID-Land is a physically based, spatially distributed hydrological model, implementing a global sensitivity analysis, like the approach of Ghasemizade et al. [55], would be impractical due to the extensive computational cost required for each simulation. As a result, we opted for a local sensitivity analysis approach, wherein we systematically altered one parameter at a time—referred to as perturbation—and assessed its impact on model outputs. This analysis was conducted with a sensitivity analysis based on the derivative of residuals—a Differential Sensitivity Approach (DSA)—with respect to model parameters. The MST software, version 4.0.3, was used to assist with hydraulic parameters perturbation. The flowchart of the sensitivity analysis can be seen in Figure 2.

2.3.1. MOHID Soil Tool

VGM parameters were initially computed using MST software, version 4.0.3, executable available at the GitHub (https://github.com/dhiegosales/MOHID-SOIL-TOOL, accessed on 12 December 2024), a tool developed for this study to process soil texture data. This software, is compatible with Windows 10/11 × 64 operating systems. The MST features an intuitive graphical user interface and is implemented using Python 3. The software encompasses six principal steps: (i) data importation, (ii) data processing, (iii) soil compaction assessment, (iv) calculation of hydraulic properties, (v) adjustment of VGM parameters, and (vi) data export. A comprehensive overview of the MST is available in Sales et al. [25].

In this study, soil texture maps were classified based on the average characteristics of each soil type polygon. The MST was provided with (i) raster data representing the fractions of sand, silt, and clay, as well as bulk density for all available soil layers, and (ii) a high-resolution shapefile of the state of Rio de Janeiro. To enhance the transparency and reproducibility of this research, a dataset was created and made available in the Zenodo repository [56].

The MST estimates soil hydraulic properties using the Rosetta model (version 3), a widely used pedotransfer function that employs Artificial Neural Networks to derive hydraulic parameters from readily available soil properties such as sand, silt, and clay percentages, along with bulk density [57]. Leveraging EMBRAPA’s soil texture database, the MST utilizes the Rosetta API (compatible with versions 1, 2, and 3) to estimate all VGM parameters: ${\theta }_s$, ${\theta }_r$, $n$, $\alpha$, and $K_{sat}$. These parameters are then adjusted by multiplying each value by a user-defined factor, where 1 represents the default Rosetta estimate, 1.1 increases the value by 10%, and 0.9 decreases it by 10%. This approach reduces the need for extensive direct measurements while enabling seamless integration with hydrological models.

2.3.2. Differential Sensitivity Approach (DSA)

The DSA was performed using the centered finite difference method, as described by [58,59,60] and adapted in this study. This method provides a comprehensive sensitivity analysis of model parameters, enabling researchers to identify which variables have the greatest impact on hydrological model performance. By applying this sensitivity assessment on a daily basis, it is possible to evaluate how parameter variations influence simulated flows under different climatic conditions, particularly during extreme events, such as intense rainfall or prolonged droughts.

Furthermore, by correlating the sensitivity results with cumulative precipitation, we gain deeper insights into how precipitation magnitude influences the model’s daily parameter responses. This analysis not only offers valuable insights into model behavior during heavy rainfall periods but also enhances our understanding of parameter dynamics under drought conditions. Consequently, combining DSA sensitivity analysis with precipitation variability improves model sensitivity analysis, thus enhancing the representation of hydrological processes in response to diverse hydrologic regimes.

This approach is suitable for numerically estimating the sensitivity of a model output—in this case, simulated flow—to small perturbations in model parameters. For each parameter $P_j$ of the VGM model, where $j=\in \{{\theta }_s,{\theta }_r,n,\alpha ,\mathrm{a}\mathrm{n}\mathrm{d} K_{sat}\}$, we individually perturb the parameter to evaluate its influence on flow output.

To apply this method, for each parameter $P_j$, an increment $\Delta P_j$ is selected, and the parameter value is perturbed both positively and negatively to generate two modified model simulations: one where $P_j$ is incremented by $\Delta P_j$, resulting in, $P_j+\Delta P_j$, and another where $P_j$ is subtracted by $\Delta P_j$, resulting in ${,P}_j-\Delta P_j$. These perturbations yield two distinct simulations from which forward and backward flow residuals, denoted as $R_i^{+}$ and $R_i^{-}$, are computed for each day $i$, where $i=1,2,\dots ,N$. The $R_i^{+}$ and $R_i^{-}$, are calculated as follows:

$$R_i^{+}={\left(Q_{i{,P}_j+\Delta P_j}-Q_i^{obs}\right)}^2$$

(6)

$$R_i^{-}={\left(Q_{i{,P}_j-\Delta P_j}-Q_i^{obs}\right)}^2$$

(7)

where $Q_{i{,P}_j+\Delta P_j}$ and $Q_{i{,P}_j-\Delta P_j}$ are the flows simulated on day $i$ using the perturbed parameters forward and backward, respectively [m³/s], and $Q_i^{obs}$ is the observed flow on day $i$ [m³/s].

The sensitivity of the residual flow to changes in $P_j$ is quantified through the centered numerical derivative, which approximates the rate of change in residuals:

$${\displaystyle \frac{\partial R_i}{\partial P_j}}\approx {\displaystyle \frac{R_i^{+}-R_i^{-}}{2\Delta P_j}}$$

(8)

The centered finite difference method provides a robust approximation of the derivative by considering perturbations in both directions, thereby minimizing numerical truncation errors. To compare sensitivity values for parameters with different units and magnitudes and to determine whether a coefficient is sufficiently large or too small, we employed the approach of scaled sensitivity coefficients, adapting the methodology described by Lugon Junior and Silva Neto [45]. Sensitivity is then calculated by multiplying the numerical derivative (Equation (8)) by the parameter value from the reference simulation for the current parameter ($P_j^{ref}$):

$${\displaystyle \frac{\partial R_i}{\partial P_j}}\approx {\displaystyle \frac{R_i^{+}-R_i^{-}}{2\Delta P_j}}\ast P_j^{ref}$$

(9)

Hence, the magnitude and sign of $\partial R_i/\partial P_j$ reveal the effect of $P_j$ on the residuals. A positive derivative indicates that an increase in the parameter leads to an increase in the residual, suggesting a larger discrepancy between the model prediction and observed data. Conversely, a negative derivative indicates that an increase in the parameter leads to a decrease in the residual, suggesting improved model alignment with observed data. Derivatives near zero imply low sensitivity, meaning variations in the parameter have minimal impact on the residuals, while larger derivatives (positive or negative) indicate a higher sensitivity to the parameter. By applying this method daily, we can capture the temporal variability in parameter sensitivity, particularly during extreme events like heavy rainfall or prolonged droughts. This allows us to identify periods when the model is sensitive to specific parameters, and to adjust the calibration strategy accordingly.

By associating the interpretation of the derivative of residuals with the bias (Equation (10)) in the discharge series arising from positive and negative perturbations of a given parameter, we can capture not only the model’s sensitivity but also the expected response of discharge to parameter variations.

$$BIAS={\displaystyle \frac{{\sum }_{i=1}^N(Q_i^{sim}-Q_i^{ref})}{N}}$$

(10)

This analysis provides a detailed understanding of the model’s sensitivity to each parameter and the anticipated direction of discharge response to these changes, ultimately contributing to more precise calibration.

2.3.3. Scenario Developed for Parameter Perturbation

To evaluate the perturbation effect, we selected a 10% deviation as an attempt to introduce a small yet meaningful adjustment to the VGM parameters based on baseline data from EMBRAPA, headquartered in Brasília, Brazil. This threshold was selected to provoke minimal parameter variation while maintaining consistency across all parameters. Larger variations could result in disproportionately large jumps for sensitive parameters or overemphasize effects on less sensitive ones, given the inherent nonlinearity of parameter behavior. Consequently, we designed a set of 10 scenarios where each parameter was varied by ±10% relative to the reference simulation, as detailed in

Table 4. Description of simulation scenarios.

Simulation	Parameter		MST Multiplying Factor
S1	${\theta }_s$		0.9
S2			1.1
S3	${\theta }_r$		0.9
S4			1.1
S5	$n$		0.9
S6			1.1
S7	$\alpha$	0.9
S8		1.1
S9	$K_{sat}$	0.9
S10		1.1

.

The sensitivity analysis simulations were conducted over the period from 2006 to 2008, with 2006 designated as a warm-up period and therefore excluded from the analysis. The following two years were considered suitable for assessing the impact of parameter variations while optimizing computational cost. This period was divided into a wet season (October to March) and a dry season (April to September), reflecting a typical tropical rainfall distribution—a division similarly adopted by Costa et al. [31].

2.4. Influence of Combined VGM Parameters

After individually analyzing the parameters, a combination of optimal conditions for each was proposed. A long-term simulation was then conducted to evaluate the combined calibration performance. This simulation covered the period from 2007 to 2016, spanning a full decade. The calibration range was carefully selected due to data gaps in the time series for 2017 and 2018. Consequently, the focus was placed on the longest continuous period without interruptions, ensuring the reliability and robustness of the calibration assessment.

Different metrics were used to quantify the fit of the simulation, including the Nash–Sutcliffe efficiency (NSE) coefficient, the percentage bias (PBIAS), and the coefficient of determination (R²), respectively, as given in Equations (11)–(13):

$$NSE=1-\left[{\displaystyle \frac{\sum _{i=1}^p{(Q_i^{obs}-Q_i^{sim})}^2}{\sum _{i=1}^p{(Q_i^{obs}-Q_{mean}^{obs})}^2}}\right]$$

(11)

$$PBIAS={\displaystyle \frac{\sum _{i=1}^p(Q_i^{sim}-Q_i^{obs})}{\sum _{i=1}^p{Q}_i^{obs}}}\times 100$$

(12)

$$R^2={\left({\displaystyle \frac{\sum _{i=1}^p(Q_i^{obs}-Q_{mean}^{obs})(Q_i^{sim}-Q_{mean}^{sim})}{\sqrt{\sum _{i=1}^p{(Q_i^{obs}-Q_{mean}^{obs})}^2}\sqrt{\sum _{i=1}^p{(Q_i^{sim}-Q_{mean}^{sim})}^2}}}\right)}^2$$

(13)

where $Q_i^{sim}$ is the simulated flow for day i [m³/s]; $Q_i^{obs}$ is the observed flow on day i [m³/s]; $Q_{mean}^{obs}$ is the observed mean flow for the period under consideration [m³/s]; $Q_{mean}^{sim}$ is the simulated mean flow for the period under consideration [m³/s]; and $p$ is the total number of days in that same period.

The NSE is a metric that assesses the accuracy of a model by comparing the residual variance to the variance of the observed data. The NSE value ranges from negative infinity to 1. An NSE value less than 0 indicates that the mean observed value is a more accurate predictor than the simulated value. The range of 0.0 to 1.0 for NSE values is divided into specific performance categories, each indicating a different level of model fit. Specifically, for flow, an NSE greater than 0.80 is considered “Very Good”, 0.70 to 0.80 is “Good”, 0.50 to 0.70 is “Satisfactory”, and below 0.50 is “Not Satisfactory” [61]. The PBIAS is another commonly used metric, with an ideal value of 0. Positive PBIAS values indicate model overestimation, while negative values indicate underestimation. For flow, a PBIAS within ±5 is “Very Good”, ±5 to ±10 is “Good”, ±10 to ±15 is “Satisfactory”, and greater than ±15 is “Not Satisfactory” [61]. The R² measures the proportion of variance in the observed data explained by the model, ranging from 0 to 1, where higher values indicate a better fit. For flow, an R² greater than 0.85 is “Very Good”, 0.75 to 0.85 is “Good”, 0.60 to 0.75 is “Satisfactory”, and below 0.60 is “Not Satisfactory” [61].

3. Results

3.1. Daily Sensitivity Analysis of VGM Parameters

In the wet season (Figure 3a), the derivative with respect to the parameter $n$ exhibits a strong negative trend during days of intense precipitation, indicating high sensitivity to this parameter. This suggests that increasing $n$, which controls soil pore size distribution, would significantly reduce flow residuals by enhancing infiltration. In turn, this would decrease surface runoff, improving the alignment between simulated and observed flows. Similarly, the derivative with respect to ${\theta }_s$ shows negative values during heavy precipitation, implying that increasing ${\theta }_s$ would also help reduce flow residuals by increasing the soil’s capacity to retain water and promoting greater infiltration.

The analysis of flow residual derivatives with respect to model parameters offered important insights for optimizing each variable to minimize discrepancies between simulated and observed flows. By monitoring the behavior of these derivatives over time, it was possible to identify whether adjusting a specific parameter upwards or downwards could help reduce residuals.

The derivative of $K_{sat}$ exhibits a slightly negative trend during precipitation peaks, suggesting that increasing $K_{sat}$ would promote greater infiltration, reduce surface runoff, and bring simulated flows closer to observed values. However, $K_{sat}$ demonstrates relatively low sensitivity, implying that more substantial adjustments are needed to induce a significant effect on streamflow.

In contrast, the derivative of parameter $\alpha$ remains near zero throughout the wet season, signifying minimal influence on flow residuals. Nonetheless, slight negative adjustments could still be explored if needed. Finally, the derivative of ${\theta }_r$ shows a stable but slightly positive trend, indicating that a slight reduction in ${\theta }_r$ could be beneficial, though its impact is minor compared to $n$ and ${\theta }_s$.

In summary, despite differing magnitudes and signs, all the parameters exhibit sensitivity to intense precipitation. Following significant rainfall events, the sensitivity profile remains intact, albeit at varying intensities. Once precipitation ceases, the residual derivatives approach zero, indicating reduced sensitivity under dry conditions.

In the dry season (Figure 3b), when there is no precipitation, the river’s baseflow relies solely on the soil’s ability to release stored water. Under these conditions, derivatives for $K_{sat}$, $\alpha$, and ${\theta }_r$ approach zero, indicating low sensitivity to changes in these parameters. However, parameter $n$ retains a slightly negative derivative, suggesting that a modest increase in $n$ could help align baseflow more accurately. Similarly, ${\theta }_s$ shows a minor negative trend, indicating that a small increase may further refine the baseflow alignment under dry conditions.

Regarding baseflow, this assessment is based on the fact that during the winter period—characteristic of tropical regions—precipitation tends to decrease, as shown in Figure 4. Considering that the watershed is relatively small (420 km², as described in Section 2.1), local knowledge confirms that, in the absence of precipitation, river discharge is primarily sustained by baseflow. Therefore, during the winter period, when no new precipitation input is observed, river flow predominantly reflects the contribution of baseflow from the soil. Consequently, any increase in river discharge resulting from changes in VGM parameters can only be attributed to an enhancement in baseflow dynamics.

When an intense precipitation event occurs over dry soil, a pronounced increase in parameter sensitivity becomes evident, as illustrated in Figure 3b (e.g., 29 July 2007). Unlike the relatively stable sensitivity patterns observed for ${\theta }_r$, ${\theta }_s$, and $n$, a notable reversal in the derivative signs of both $K_{sat}$ and $\alpha$ emerges during the dry-to-wet transition. This initial wetting phase is characterized by resistance to water infiltration, primarily driven by air entrapment in soil pores, a phenomenon consistent with the “ink-bottle” and “rain-drop” effects described by Li et al. [38].

The “rain-drop” effect relates to how raindrops impact the soil surface. When raindrops strike dry soil, they can compact and seal the surface, forming a crust that initially hinders water infiltration. This surface sealing effect amplifies the resistance to water entry, particularly at the onset of precipitation. Simultaneously, the “ink-bottle” effect pertains to the geometry of soil pores, which often feature narrow necks connected to larger voids. Similar to the structure of a bottle, the narrow necks act as barriers to water movement. During the early infiltration phase, water preferentially fills the larger pores. However, progression into the smaller pores requires overcoming capillary tension at these narrow necks, a process made more difficult when air becomes trapped within them [62].

This interplay of air displacement and the progressive filling of larger soil pores underscores the complexity of early infiltration processes. The combined effects of surface sealing by raindrops and pore geometry constraints not only govern the initial resistance to infiltration but also illustrate how dynamic soil–atmosphere interactions shape hydrological responses during the transition from dry to wet conditions [63].

Hence, since both $K_{sat}$ and $\alpha$ undergo this sensitivity inversion at the same time, it reinforces the hypothesis that this transient behavior is associated with the air presence within the system. Interestingly, this observation becomes evident on a daily scale but is imperceptible when analyzed over longer periods, where habitual patterns dominate. Another noteworthy point is that being a physically based model, MOHID-Land effectively captured this interaction, which is well documented in the literature. This capability highlights the robustness of the model in simulating complex hydrological processes, even those influenced by transient soil conditions.

3.2. Sensitivity Analysis of VGM Parameters by Season

To optimize simulation accuracy and reduce flow residuals, it is recommended to increase the values of $n$, ${\theta }_s$, and $K_{sat}$ during the rainy season, as the negative derivatives of these parameters indicate that residuals decrease with their increase. Conversely, a slight reduction in the values of $\alpha$ and ${\theta }_r$ may also favor residual reduction. During the dry season, a slight increase in $n$ and ${\theta }_s$ is advisable, while adjustments to other parameters should be considered to have a limited impact.

To guide parameter adjustments across seasons,

Table 5. Mean of residual derivatives for each parameter in both wet and dry season.

Parameter	$\mathit{d}\mathit{R}/\mathit{d}\mathit{P}$ (Mean—Wet)	$\mathit{d}\mathit{R}/\mathit{d}\mathit{P}$ (Mean—Dry)
$n$	−1912.01	−40.81
${\theta }_s$	−425.25	−6.62
$K_{sat}$	−188.85	−3.70
${\theta }_r$	101.20	1.78
$\alpha$	74.72	0.36

presents the mean derivatives of each parameter. The strongly negative mean derivative for $n$ (−1912.01) during the wet season suggests that an increase in $n$ significantly reduces flow residuals, as it enhances infiltration and reduces surface runoff. Similarly, ${\theta }_s$ shows a moderately negative mean derivative (−425.25), indicating that an increase would allow the soil to hold more moisture and reduce peak flows. $K_{sat}$ shows a moderate negative sensitivity (−188.85), supporting infiltration adjustments, though less influential than $n$ and ${\theta }_s$. In contrast, ${\theta }_r$ and α have positive mean derivatives, suggesting that slight reductions may reduce residuals by slightly impacting runoff generation.

In the dry season, while flow magnitudes are lower than in the wet season, the overall pattern remains proportionally consistent. This suggests that, despite reduced flows, the flow dynamics in the dry season exhibit a proportional trend similar to that observed during the wet season. With smaller deviations between observed and simulated flows in the dry period, the squared residuals contribute less to the model’s total error, making this period less influential in terms of error magnitude. This outcome indicates that the significant deviations observed during intense rainfall events in dry soil, as well as the temporary reversal of $\alpha$ and $K_{sat}$ derivative signs on a daily scale, do not alter the average parameter behavior across the entire dry season, which remains consistent with the wet season in terms of overall trends.

The mean derivative for $n$ is −40.81, indicating a moderate but consistent negative sensitivity, where a slight increase in $n$ would bring the baseflow closer to observed values. Similarly, ${\theta }_s$ exhibits a low negative sensitivity (−6.62), suggesting that a small positive adjustment could enhance the fit to the observed baseflow in dry conditions. Conversely, the mean derivatives for $K_{sat}$ and ${\theta }_r$ near zero (−3.70 and 1.78, respectively), indicating minimal influence on flow residuals; hence, these parameters are lower priorities for adjustment during the dry season. However, a positive adjustment for $K_{sat}$ and a negative adjustment for ${\theta }_r$ may still be considered. Likewise, $\alpha$ shows a near-zero mean derivative (0.36), indicating that modifications to $\alpha$ are unlikely to significantly influence model performance in low-flow conditions, although a negative adjustment could be evaluated.

Once the adjustment direction for each parameter has been determined, a bias analysis of the simulated flows can be employed to assess the response of flow rates to each increment or decrement in the parameter values.

Table 6. Streamflow BIAS for wet and dry season.

Wet Season		Dry Season
Simulation	BIAS	Simulation	BIAS
S1	10.88	S1	−1.10
S2	9.57	S2	−0.38
S3	10.07	S3	−0.66
S4	10.38	S4	−0.82
S5	9.93	S5	−0.85
S6	10.50	S6	−0.63
S7	13.22	S7	−1.76
S8	8.27	S8	−0.20
S9	10.51	S9	−0.72
S10	9.97	S10	−0.75

represents bias during the wet and dry seasons.

During the wet period, the BIAS of all simulations is positive, indicating that in all cases, the model overestimates the observed flow. This implies that promoting adjustments to the parameters and consequently reducing the residuals would result in a decrease in flow. In contrast, during the dry period, all bias values are negative, suggesting that the model tends to underestimate the observed flow during low-flow conditions. Thus, all efforts aimed at reducing the residuals are directed toward increasing baseflow.

The combination of interpreting the sign of the derivative associated with the bias allows for a generalization that facilitates understanding the effects of the parameters, thereby aiding in the manual adjustment of the model, as illustrated in

Table 7. General interpretation of VGM parameters perturbation.

Parameter	Sensitivity	Parameter Perturbation	Streamflow Effect (Wet)	Streamflow Effect (Dry)
$n$	High	Increase	Decrease	Increase
${\theta }_s$	Middle–high	Increase	Decrease	Increase
$K_{sat}$	Middle	Increase	Decrease	Increase
${\theta }_r$	Middle–low	Decrease	Increase	Decrease
$\alpha$	Low	Decrease	Increase	Decrease

. Notably, an inverse perturbation—applying the opposite direction of the adjustment—will lead to a corresponding inversion in the effects on flow outcomes. This understanding enhances the predictability of model adjustments, enabling a more refined calibration approach.

3.3. Impact of Combined VGM Parameters on Streamflow

Guided by the findings of the sensitivity analysis, calibration values were carefully selected to enhance baseflow and attenuate flow peaks. Each parameter underwent rigorous assessment of its impact, culminating in the formulation of the following percentage calibration combination: (i) ${\theta }_s$: +10%; (ii) ${\theta }_r$: −10%; (iii) $n$: +10%; (iv) $\alpha$: −10%; and (v) $K_{sat}$: +10%.

NSE values (

Table 8. Error metrics for assessing the combined impact of VGM parameters.

	Reference			Combined Parameters Effects
	Full Period	Wet Season	Dry Season	Full Period	Wet Season	Dry Season
PBIAS	27.48	43.19	−3.56	21.89	28.11	9.60
R2	0.70	0.66	0.71	0.69	0.64	0.72
NSE	0.16	−0.03	0.57	0.53	0.44	0.66

) demonstrate the greatest impact of calibration. In the reference simulation, NSE values are unsatisfactory in both the full period (0.16) and wet season (−0.03), where negative NSE suggests poor predictive performance. The dry season NSE of 0.57, however, meets the satisfactory threshold, suggesting the model performs acceptably under low-flow conditions. In contrast, the calibrated model yields substantially improved NSE values across all periods. With a full period NSE of 0.53 and wet season NSE of 0.45, the calibration brings these values closer to the satisfactory range, demonstrating enhanced model responsiveness to observed variations. Notably, the dry season NSE increases to 0.64, further reinforcing the model’s robustness in low-flow conditions post-calibration.

A visual inspection of Figure 4 reveals that the calibrated model significantly improves the simulation of both low- and high-flow events. The reference simulation tends to overestimate peak flows and underestimate low flows, leading to a poor representation of the overall flow regime. In contrast, the calibrated model captures the timing and magnitude of peak flow more accurately, while also providing a better representation of low-flow conditions. This improvement in model performance is attributed to the calibration process, which adjusted the parameters to better match the observed data.

In the reference simulation, PBIAS values (refer to Table 8) reveal a tendency toward overestimation across the full period (27.48%) and wet season (43.19%), as evidenced by positive values that exceed the satisfactory range of ±15%. This overestimation is most pronounced during the wet season, suggesting the reference model struggles to capture peak flow events accurately. Conversely, the dry season PBIAS of −3.56 indicates a slight underestimation, aligning more closely with observed values and providing a balanced representation of lower flow conditions.

The calibrated simulation with VGM parameter adjustments shows an improvement in PBIAS across all periods, reducing overestimation to 21.89 for the full period, 28.11 for the wet season, and achieving a positive bias of 9.60 during the dry season. This suggests that parameter calibration effectively moderates the model’s bias, particularly under high-flow conditions in the wet season. However, although reduced, the PBIAS values for the full period and wet season remain outside the ideal range, indicating potential areas for further refinement.

R² values remain largely consistent between the reference and calibrated simulations, with minimal differences across the periods. For both simulations, R² values during the full period (0.70 vs. 0.69) and dry season (both at 0.71 vs. 0.72) meet Moriasi et al.’s [61] criteria for satisfactory model performance. The wet season R², at 0.66 for the reference and 0.64 for the calibrated simulation, also indicates a reasonable fit, though it slightly underperforms relative to the full and dry periods. These values suggest that the calibration adjustments did not markedly affect the model’s capacity to explain the variance in observed data.

Building on the global analysis conducted between 2007 and 2016, the selection of the hydrological year from September 2015 to August 2016 is particularly relevant. This period encompasses the severe water crisis experienced by the basin in 2014 and 2015, as depicted in Figure 4, followed by the highest flow recorded in the historical series. By capturing both the extreme drought conditions and the peak flow event, this hydrological year serves as a critical reference for assessing model performance. The model’s effectiveness for this specific period was evaluated through the NSE, which improved significantly from 0.16 for the reference simulation to 0.62 after calibration. This enhancement underscores the model’s capacity to simulate both dry periods and peak flow events with high accuracy, as shown in Figure 5. Such results demonstrate the model’s robustness in replicating diverse hydrological conditions, highlighting its reliability for scenarios with sharp contrasts in water availability.

Figure 6 and

Table 9. Numerical summary of water balance components for the 2015/2016 hydrological year: reference vs. calibrated simulations.

Month	Reference				Calibration
	Precipitation (mm)	Soil Contribution (mm)	EvapoT (mm)	Outlet Flow (mm)	Soil Contribution (mm)	EvapoT (mm)	Outlet Flow (mm)
September-15	110.99	29.95	55.39	25.56	27.86	58.08	24.98
October-15	39.02	−45.90	71.56	13.34	−50.68	73.43	16.27
November-15	209.58	117.63	51.47	38.50	118.81	56.86	32.47
December-15	192.92	57.59	50.57	85.08	69.78	56.22	67.03
January-16	500.03	132.57	36.95	329.89	201.67	43.00	254.49
February-16	230.76	4.20	70.29	152.77	3.75	77.10	147.65
March-16	140.08	−51.81	64.03	131.44	−56.74	69.15	130.06
April-16	37.97	−89.00	72.13	56.06	−101.97	75.32	65.67
May-16	46.41	−38.14	51.69	33.01	−49.14	52.76	42.95
June-16	101.29	20.83	34.88	45.81	14.68	36.28	50.56
July-16	7.79	−51.33	36.52	22.79	−59.96	37.69	30.25
August-16	60.48	−15.04	52.97	22.35	−21.34	53.52	28.13

present a comparative analysis of the reference and calibrated simulations of the water balance, focusing on the temporal dynamics of soil water storage, evapotranspiration, outlet flow, and precipitation. For each month, the first column represents the reference simulation, while the second corresponds to the calibrated simulation.

A key observation from Figure 6 is the improvement in soil water storage capacity in the calibrated simulation, especially during high-precipitation events. This is particularly evident in January 2016, when a significant precipitation event led to greater infiltration into the soil in the calibrated scenario. Consequently, the increased soil water storage resulted in a reduction in the basin outlet flow, as excess precipitation was predominantly retained within the soil profile (positive soil water storage values indicating water entering the soil). Conversely, during dry periods, when precipitation is limited or absent, the soil becomes the primary source for channel flow. As shown in Figure 6, between March and May 2016, the calibrated simulation exhibited a significantly higher release of stored soil water compared to the reference simulation (negative soil water storage values indicating water leaving the soil), leading to an increase in basin outlet flow.

It is important to note that the “Outlet Flow (mm)” presented in Table 9 refers to the total flow leaving the basin, which includes contributions from surface runoff, base flow, and water already present in the river system. Although the MOHID-Land model does not explicitly separate base flow from surface runoff in its output files, the model dynamics observed in Figure 6 suggest that during dry periods, the soil acts as the primary contributor to the outlet flow. This indicates a predominance of base flow during these months, as the soil releases stored water into the river system when precipitation is low or absent.

3.4. Computational Cost

For the sensitivity analysis, four dedicated computing units—two desktops and two notebooks, all with SSD storage—were employed to execute the simulations (

Table 10. Computation times for each simulation during sensitivity analysis.

Computer	Core	RAM	Simulation	Total Time (h:min:s)	Days
Desktop 1	i7 2.10 GHz/20 threads	32 GB	S0, S1, S9	419:31:04	17.48
Desktop 2	i5 3.00 GHz/4 threads	16 GB	S2, S7, S8	414:10:04	17.25
Notebook 1	i7 2.6 GHz/8 threads	16 GB	S4, S5, S6	650:06:48	27.09
Notebook 2	i5 1.8 GHz/8 threads	8 GB	S3, S10	515:52:20	21.50

). Over the span of 82 cumulative days, 11 simulations covering three-year periods were completed, with processing time distributed among the four devices (approximately 20 days per computer). Despite the intensive computational workload, RAM usage consistently remained below 50%, highlighting that memory was not a limiting factor for simulation speed. Among the devices, Desktop 2 proved to be the most efficient, followed closely by Desktop 1. Among the notebooks, Notebook 1 achieved faster processing times compared to the Notebook 2, underscoring a notable variation in performance across different hardware setups.

The two desktop computers were used to execute the calibration phase. Desktop 1 undertook the reference simulation, while Desktop 2 handled the calibration simulation, both spanning the period from 2006 to 2016. The reference simulation consumed a total of 559 h, equivalent to approximately 23.29 days. In contrast, the calibration simulation required a total of 676 h, corresponding to around 28.16 days.

These results highlight the substantial computational cost involved in running the simulations, which are inherently time-consuming due to the complexity and scale of the physically based, 3D-distributed model employed. The extended duration of the calibration process underscores the significant challenge of model calibration, which requires multiple iterations to fine-tune model parameters and achieve an acceptable level of performance.

4. Discussion

4.1. Role of Individual VGM Parameters in Streamflow Variability

Our analysis highlights the critical role of ${\theta }_s$ in regulating soil water retention and release, influencing hydrological responses during both high-flow and low-flow periods. ${\theta }_s$ defines the soil’s maximum capacity to store gravitational water, directly affecting baseflow and peak flow dynamics. A decrease in ${\theta }_s$ reduces the soil’s retention capacity, leading to lower baseflow during dry periods and greater sensitivity to peak flows during wet events. This effect is intensified by limited groundwater buffering, with excess water redirected to surface runoff during high-flow periods [64]. Conversely, higher ${\theta }_s$ values enhance water storage and facilitate groundwater recharge, reducing surface runoff, particularly in areas with steep topography [65,66].

The parameter ${\theta }_r$, which complements to ${\theta }_s$, governs moisture retention beyond the capillary limit, influencing baseflow availability. A reduction in ${\theta }_r$, along with an increase in ${\theta }_s$, promotes gravitational discharge and enhances water storage. However, elevated ${\theta }_r$ values restrict groundwater recharge by retaining more water in the soil matrix, limiting baseflow contributions. This interplay highlights the contrasting effects of ${\theta }_s$ and ${\theta }_r$ on specific yield and flow variability [67,68].

The parameter $n$ plays a crucial role in influencing both peak flow and baseflow dynamics by controlling runoff during wet periods and water retention during dry periods. Lower $n$ values lead to rapid runoff, while higher $n$ values help moderate peak flows and improve soil moisture retention, thus enhancing drought resilience. These findings align with Rattan et al. [69], who demonstrated that a steeper soil water characteristic curve (SWCC) enhances drainage and reduces capillary retention, particularly in soils with uniform pore size distributions, such as sands. In contrast, finer soils, like clays, with lower $n$ values, retain more water, supporting baseflow during dry spells [70,71].

Moreover, the relationship between $n$ and $K_{sat}$, as described by Mualem’s model, underscores how higher n values increase conductivity, accelerating water movement through the soil profile and influencing drainage rates. Finally, the α parameter, which influences air entry pressures and soil moisture retention, exhibited minimal impact at average scales, but its sensitivity was more pronounced during intense rainfall events following dry periods. This dynamic, observed in this study’s data, confirms the significant role of α in moderating flow under specific hydrological conditions.

The resistance to water infiltration in dry soil, particularly through the Dry Soil Layer (DSL), further complicates water dynamics, as the DSL creates resistive forces that oppose water entry. Hysteresis in soil water retention also contributes to this complexity, with soils retaining water differently based on their prior saturation state, particularly in smaller pores [72,73].

Hysteresis in soil water retention adds another layer of complexity to infiltration dynamics. Higo and Kido [74] showed that water retention states differ between wetting and drying cycles, meaning soils retain water differently depending on their prior saturation state. This can slow the wetting front in previously dry soils, particularly in smaller pores, where water movement is sensitive to pore structure and trapped air.

Moreover, wetting-drying cycles alter soil structure and pore size distribution, which in turn affects water retention and infiltration capacity. Pires [75] highlighted how these cycles increase suction resistance and modify pore dynamics, complicating water movement, especially during the initial wetting phase.

This behavior underscores an important point: while $\alpha$ remains relatively stable on average, isolated high-rainfall events in dry conditions can drastically amplify its effect. Such anomalies introduce significant deviations in daily NSE values, potentially impacting overall model evaluation due to squared residuals. It is worth noting that precipitation data in this study were carefully validated, with extreme events cross-checked across multiple stations to ensure consistency in recorded rainfall magnitudes, as described in Costa et al. [54].

According to Equation (3), conductivity is dependent on soil water content. At maximum saturation, conductivity peaks, and $K\left(\theta \right)$ equals $K_{sat}$, derived from the Rosetta model and calculated by MST. As soil moisture decreases, conductivity declines non-linearly. The conductivity curve remains steady under saturated conditions until reaching the air entry point, influenced by $\alpha$. Beyond this threshold, conductivity drops sharply [36]. It is essential to note that $K\left(\theta \right)$ depends on $S_e$, which in turn is influenced by $\alpha$ and n (Equation (4)). Therefore, changes in these parameters will affect conductivity, with a 10% variation in $K_{sat}$ reflecting a change in maximum conductivity under saturation.

Despite its low sensitivity, $K_{sat}$ is critical for soil profile analysis. Hydraulic conductivity plays a vital role in calculating fluxes, as it governs the partitioning of precipitation and irrigation water into surface runoff and soil water, as well as regulating water movement in the vadose zone [76]. As the maximum rate of water transmission through soil, $K_{sat}$ is indispensable for groundwater modeling [77]. At a daily scale, $K_{sat}$’s sensitivity increases after prolonged dry periods followed by heavy rainfall events, displaying similar behavior to $\alpha$. This sensitivity shift is linked to air entry and hysteresis effects, as previously described for $\alpha$.

It is also important to note that, although Rosetta can estimate the VGM parameters using only sand, silt, and clay fractions, this study incorporates local bulk density data, provided by EMBRAPA. This inclusion is particularly relevant given the strong dependence of bulk density on $K_{sat}$, as observed by Tian et al. [78]. Moreover, explicitly considering bulk density reinforces the methodological rigor of this analysis, providing additional support for the middle sensitivity classification of $K_{sat}$ in our results.

Thus, considering the nature of the parameters and the results obtained, we conclude that a variation of up to 10% for ${\theta }_s$ and $n$ may be appropriate, as these parameters exhibit high sensitivity and significantly influence the SWCC. This is considering the nature of the parameters and the results obtained, provided it is applied cautiously, particularly due to the pronounced nonlinearity associated with the parameter $n$, which can result in significant nonlinear behaviors. In contrast, for ${\theta }_r$, which exhibits lower sensitivity, a variation of 10% may not yield a significant impact, and larger adjustments may be more suitable. However, for $\alpha$ and $K_{sat}$, a variation of 10% has been deemed insufficient, indicating the necessity for further studies to explore a broader range of variations. Should a larger variation be contemplated for these parameters, it is crucial to assess the shape of the SWCC and the local characteristics of soil texture and structure to ensure that any adjustments maintain the physical consistency of the calibration.

4.2. Combined VGM Parameter Insights and Limitations in Streamflow Modelling

The performance metrics in Table 8, alongside the water balance data in Table 9, indicate a notable improvement from the reference simulation to the calibrated model, though the model consistently overestimates streamflow, particularly during peak flow events. At first glance, this overestimation seems to be associated with peak precipitation events, suggesting that precipitation may not be adequately represented. In this regard, Pang et al. [79] and Redding and Devit [80] emphasize the crucial role of precipitation intensity in driving flow towards runoff and infiltration processes, which would help explain the observed overestimation in the model.

However, after thoroughly verifying the precipitation data through cross-referencing with multiple stations, as described by Costa et al. [54], it appears that the discrepancies are more likely due to issues with the flow measurements. Unlike precipitation, which underwent rigorous verification, flow data are subject to uncertainties related to the discharge rating curve, which could be especially problematic under extreme hydrological conditions.

In this context, a plausible concern emerges. It is possible that the monitoring station failed to capture the of streamflow during peak events, resulting in an incomplete representation of actual flow conditions. This may occur due to limitations in equipment sensitivity, recording intervals that miss transient but critical flow surges, or even reading failure [81].

Another point, and perhaps more critically, is the likelihood that the flow measurements approached or even exceeded the extrapolation limits of the rating curve. Rating curves are inherently calibrated for specific flow ranges based on measured data, and their accuracy diminishes significantly when extrapolated beyond these ranges. During extreme events, where discharge surpasses the upper calibration limits, the absence of direct measurements—such as those obtained through advanced tools like flow meters or the Acoustic Doppler Current Profiler (ADCP)—leaves the rating curve as the sole estimation basis. This situation introduces significant uncertainties, as the extrapolated estimates may deviate substantially from actual flow conditions [82].

These potential inaccuracies in flow measurements have significant implications for the model’s performance evaluation. They not only contribute to the observed overestimation of simulated streamflow during peak events but also introduce biases into performance metrics, such as NSE, that penalize large deviation [83]. This may suggest that while the model might be adequately simulating streamflow, the uncertainty in the flow measurements could be negatively influencing the performance metrics, leading to a downward bias in model evaluation.

The issue of accurately calibrating low-flow conditions remains nuanced, as both the overestimation and underestimation of baseflow can yield adverse consequences for water resource management. Initially, our model demonstrated a tendency to underestimate baseflows during the dry season. This underestimation posed challenges like those encountered by Villas Boas [27] in SWAT modelling for the study of watershed, where substantial discrepancies in low-flow predictions hindered effective water quality management and allocation decisions. However, following calibration, the model shifted towards a slight overestimation of baseflows, reflecting a marked improvement but still requiring a delicate balance between accuracy and application specificity.

Underestimating baseflow, particularly in dry periods, can be equally problematic as overestimation. Low-flow underestimation may lead to overly conservative water management strategies, misinforming decisions on water quality, pollutant loads, and allocation. As Hasanyar et al. [84] indicate, reduced flows concentrate pollutants, making accurate flow predictions crucial for managing water quality, especially during seasons when dilution is limited.

Following calibration, the model offered a more reliable baseline for decisions regarding drought interventions, pollutant dilution capacity, and ecological assessments, aligning with the broader findings of Jasechko et al. [85] regarding the risks of misjudging low-flow availability. Additionally, as Zheng et al. [86] argue, accurate baseflow estimation is pivotal for sustainable allocation and avoiding the issuance of unsustainable water extraction permits, which our model’s improved calibration supports.

Ultimately, the calibration choice between minimizing the overestimation or underestimation of baseflows will hinge on the model’s specific purpose—whether for drought management, water quality regulation, or ecological preservation. Nevertheless, this calibrated model represents a significant advancement in addressing baseflow accuracy challenges, as we have now achieved a more balanced representation of baseflow conditions. Despite the challenges overcome by Villas Boas [27], dealing with low-flow underestimation in SWAT, our approach highlights a pathway to more nuanced baseflow modelling, though further refinement is essential for precision. This progress underscores an evolving understanding of low-flow calibration and provides a reliable foundation for complex water resource management decisions.

The calibrated model achieved substantial improvements in simulating both low-flow and high-flow events, advancing model’s previous limitations in overestimating peak flows while underestimating baseflows. This dual enhancement underscores a significant step forward in capturing the hydrological regime’s dynamics, a critical requirement for the Pedro do Rio watershed. The enhancement of the calibration can be attributed to the fine-tuning of the VGM, which is essential for accurately modelling soil water retention and movement.

The combined effects of the calibrated parameters demonstrate a significant improvement in model predictions, emphasizing the synergistic interactions among VGM parameters. This interplay suggests that the model’s overall performance could be further enhanced by exploring various combinations of parameter adjustments. Future studies should investigate a wider range of parameter variations, particularly those that reflect realistic physical processes within the watershed. For example, while our sensitivity analysis highlighted a low sensitivity of parameters like $K_{sat}$ and $\alpha$, this does not diminish their importance; instead, it indicates that their impacts could be amplified through more substantial adjustments. Thus, additional research aimed at exploring a broader spectrum of physically consistent variations in these parameters could be instrumental in optimizing model performance.

The current state of MOHID-Land calibration predominantly relies on manual processes and the trial-and-error method [22], which are time-consuming and inefficient. In this context, the framework presented in this study represents a significant advancement, offering a more systematic approach to calibration. By enhancing the efficiency of the calibration process, it has the potential to markedly reduce the calibration time—an often-substantial burden due to the high computational demands of physically based, 3D-distributed models in porous media. This research, therefore, makes a valuable contribution to improving the overall efficiency of calibration procedures, with significant implications for future modelling efforts in hydrology and related fields.

5. Conclusions

This study underscored the critical role of soil parameters, particularly those from the VGM model, in enhancing the performance of the MOHID-Land model, especially in representing baseflow. Our findings revealed that $n$ and ${\theta }_s$ were the most influential parameters in improving model accuracy, while $K_{sat}$, $\alpha$, and ${\theta }_r$ contributed to overall model stability but exhibited lower sensitivity. Given the high computational cost of MOHID-Land, we concluded that it is crucial to focus calibration efforts on the most impactful parameters. Thus, our work provided valuable insights for researchers and engineers by identifying $n$ and ${\theta }_s$ as key parameters for a more efficient and targeted calibration process.

Although this study focused solely on the VGM parameters that govern the fluxes of porous media, it paves the way for further improvements. The model’s performance has shown notable enhancement, with the NSE improving from 0.16 to 0.53. However, this performance still leaves room for further refinement to reach a more satisfactory level. The watershed under study, which is predominantly forested, suggests that vegetation-related parameters—such as interception and evapotranspiration—are crucial for more accurately representing the hydrological processes. Additionally, optimizing the dimensions of the transfer section could improve the model’s flow representation.

Future research should extend on the sensitivity analysis for $n$ and ${\theta }_s$, exploring broader variations to refine the model’s response to peak flow and overall stability. Moreover, field-based soil sampling and laboratory analyses across different soil types are necessary to ensure the numerical parameterization aligns with real-world conditions, enhancing MOHID-Land’s predictive accuracy in hydrological applications.

6. Patents

This study resulted in the development of a computational tool, the MOHID SOIL TOOL (MST), created to streamline the calibration of soil hydraulic parameters within the MOHID-Land hydrological model. As a result of this innovation, a patent was registered with the National Institute of Industrial Property (INPI) under the certificate BR512024000870-5.