Comparison of Hydrus-1D and Aquacrop models with differential and reservoir-based approaches in simulating soil water dynamics in an irrigated wheat field

Introduction
Soil moisture in the vadose zone is a fundamental variable controlling key hydrological and agro-environmental processes, including actual evapotranspiration, root water uptake, deep percolation, and crop productivity. In irrigated agriculture, accurate characterization of soil water dynamics is essential for improving water use efficiency and minimizing deep losses. However, continuous field-scale monitoring of soil moisture is often constrained by high costs, spatial heterogeneity, sensor calibration requirements, and limited temporal and depth coverage. As a result, simulation models have become indispensable tools for reconstructing soil water dynamics and evaluating water balance components. Among these models, Hydrus-1D and Aquacrop represent two fundamentally different modeling philosophies. Hydrus-1D is a physically based numerical model that solves the Richards equation to simulate water flow in saturated and unsaturated porous media, explicitly accounting for hydraulic gradients and nonlinear soil hydraulic properties. In contrast, Aquacrop is a lumped root-zone, crop-oriented model that simulates soil water dynamics through a water balance approach linked to crop development and yield response to water. These conceptual differences may lead to significant discrepancies in model outputs, particularly under conditions where nonlinear flow processes and vertical gradients are dominant. Therefore, the objective of this study was to compare the performance of Hydrus-1D and Aquacrop in simulating soil moisture, actual evapotranspiration, and deep percolation in an irrigated wheat field and to identify the structural causes of differences between the two models.
Materials and Methods
The study was conducted in a 20-hectare irrigated wheat field located at the research farm of Ferdowsi University of Mashhad, Iran. Field measurements were collected throughout the growing season and included soil moisture, irrigation amounts, daily meteorological data, and soil physical and hydraulic properties. Volumetric soil water content was measured using a PR2 profile probe at multiple depths and monitoring stations to capture spatial and temporal variability. Meteorological data, including minimum, mean, and maximum air temperature, rainfall, relative humidity, and solar radiation, were obtained from a nearby weather station. Soil properties such as texture, bulk density, saturated hydraulic conductivity, and characteristic water contents (saturation, field capacity, and permanent wilting point) were obtained from a previous study conducted at the same site. In Hydrus-1D, water flow was simulated by numerically solving the Richards equation using the van Genuchten–Mualem hydraulic functions. Soil hydraulic parameters were calibrated using inverse modeling with the Levenberg–Marquardt optimization algorithm, while atmospheric boundary conditions incorporating irrigation, rainfall, and evapotranspiration were applied. In AquaCrop, model inputs included climate data, soil characteristics, irrigation schedules, and crop parameters. Key crop and soil parameters were calibrated using field observations of soil moisture and canopy development. Model performance was evaluated using statistical indicators including root mean square error (RMSE), Pearson correlation coefficient (r), and Nash–Sutcliffe efficiency (NSE). The analysis focused on both statistical agreement and structural interpretation of model behavior.
 
 
Results and Discussion
The results showed that both models were able to reproduce the general temporal pattern of soil moisture with acceptable accuracy. This was evidenced by Pearson correlation coefficients (r) ranging from 0.76 to 0.97 and RMSE values between 0.9% and 4.55%. Specifically, the NSE was 0.56 for Aquacrop, while for Hydrus-1D, it ranged from 0.52 to 0.90 across the four monitored depths, indicating a satisfactory to very good fit for both models. Hydrus-1D demonstrated a higher capability in capturing depth-dependent variations and short-term fluctuations, particularly at the 10 and 40 cm depths where $r$ exceeded 0.95. This superiority is due to its physically based formulation and explicit representation of unsaturated hydraulic conductivity. In contrast, Aquacrop, due to its lumped root-zone structure, represented soil moisture dynamics as an averaged response, resulting in smoother temporal variations and a slightly higher RMSE of 4.55%. Differences were also evident in the simulation of actual evapotranspiration. Aquacrop provided a more management-oriented estimation by incorporating crop coefficients and canopy cover, leading to a more realistic estimation of seasonal water consumption. Hydrus-1D, on the other hand, estimated actual evapotranspiration based on root water uptake and soil hydraulic limitations, making it more sensitive to soil drying. The most significant divergence between the two models was observed in deep percolation. In Aquacrop, deep percolation occurs only when soil water content exceeds field capacity, whereas in Hydrus-1D, it is governed by hydraulic gradients and can occur even under unsaturated conditions. Additionally, the atmospheric boundary conditions in Hydrus-1D impose limitations on infiltration rates, while Aquacrop incorporates irrigation water more directly into the soil water balance. These findings indicate that differences between the models are primarily structural rather than parametric.
Conclusion
The findings of this study indicate that Hydrus-1D is more suitable for process-based analysis of soil water movement, as it provides a physically rigorous representation of water flow in the soil profile based on the Richards equation and nonlinear hydraulic functions. It is particularly effective for analyzing vertical gradients, layered soil behavior, and transient flow processes such as infiltration and redistribution. In contrast, Aquacrop is more appropriate for irrigation management, crop performance assessment, and applications under data-limited conditions, as it provides a simplified yet robust representation of root-zone water balance and crop response to water. However, each model has inherent limitations. Hydrus-1D requires detailed soil hydraulic data, accurate boundary condition definition, and careful calibration, and it may exhibit high sensitivity to parameter uncertainty. Aquacrop, due to its simplified structure, has limited capability in representing vertical flow processes and nonlinear hydraulic behavior. From a theoretical perspective, the study highlights the importance of considering structural differences between differential and reservoir-based models when interpreting simulation results. From a practical standpoint, model selection should be based on study objectives, spatial scale, data availability, and required accuracy. The development of integrated modeling frameworks that combine the physical rigor of Hydrus-1D with the crop growth and management capabilities of Aquacrop could significantly improve the simulation of soil–water–plant systems and enhance decision-making in agricultural water management.