Marinao et al. (2026) hydroMOPSO: A flexible and model-independent multi-objective optimisation R package for environmental and hydrological models

Identification

• Journal: Environmental Modelling & Software
• Year: 2026
• Date: 2026-01-02
• Authors: Rodrigo Marinao, Mauricio Zambrano-Bigiarini, Oscar M. Baez‐Villanueva
• DOI: 10.1016/j.envsoft.2025.106851

Research Groups

• Master of Engineering Science, Universidad de La Frontera, Temuco, Chile
• Department of Civil Engineering, Universidad de La Frontera, Temuco, Chile
• Center for Climate and Resilience Research (CR2), Universidad de Chile, Santiago, Chile
• Hydro-Climate Extremes Lab, Ghent University, Ghent, Belgium

Short Summary

This paper introduces hydroMOPSO, a novel multi-objective, model-independent R package for calibrating hydrological and environmental models. It demonstrates hydroMOPSO's superior performance over the caRamel R package in benchmark problems and its flexibility in calibrating both R-based and R-external hydrological models.

Objective

• To introduce and evaluate hydroMOPSO, a novel model-independent and multi-platform R package designed for the multi-objective optimization of R-based and R-external environmental and hydrological models, comparing its performance against the caRamel R package.

Study Configuration

• Spatial Scale: The Río Trancura antes de Llafenco (RTL) sub-basin in the Andean region of southern Chile, with an area of 1380 km² and elevations ranging from 353 to 3740 m above sea level. Input data resolutions included 12.5 m (DEM), 30 m (land use), 100 m (soil maps), and 0.1° (potential evaporation).
• Temporal Scale: The study period for hydrological data was 1980–2020. Daily precipitation, maximum/minimum air temperature, potential evaporation, and streamflow data were used. Optimization algorithms were run for up to 100,000 model evaluations with 200 random initializations.

Methodology and Data

• Models used:
  • Optimization: hydroMOPSO R package (implements the Novel Multi-objective Particle Swarm Optimizer, NMPSO algorithm).
  • Comparison: caRamel R package (hybrid MEAS and NSGA-II algorithms).
  • Benchmark Functions: DTLZ1, DTLZ2, DTLZ3, and Kursawe (from smoof R package).
  • R-based Hydrological Models: TUWmodel (HBV-based) and GR4J (from airGR package).
  • R-external Hydrological Model: SWAT+ (Soil and Water Assessment Tool Plus).
  • Sensitivity Analysis: Variance-based Global Sensitivity Analysis (GSA) using Sobol’ sequences.
  • Performance Metrics: Hypervolume (HV) and Generational Distance (GD).
  • Objective Functions: Kling–Gupta efficiency (KGE) and the average of KGE and KGE applied to inverse flows (KGElf).
• Data sources:
  • Digital Elevation Model (DEM): Combined TanDEM-X DLR 2017 and ALOS PALSAR (12.5 m resolution).
  • Land Use: CLDynamicLandCover product (30 m resolution, 2018).
  • Soil Type: CLSoilMaps (100 m gridded dataset of physical and hydraulic soil properties).
  • Meteorological Data: CR2MET v2.5 gridded product (daily precipitation, maximum/minimum air temperature).
  • Potential Evaporation: Hourly global hPET gridded product (derived from ERA5-Land).
  • Streamflow Data: Chilean General Water Directorate (DGA).

Main Results

• Benchmark Problems: hydroMOPSO consistently achieved higher Hypervolume (HV) values and lower Generational Distance (GD) values, indicating better accuracy and diversity of the Pareto front, with faster convergence compared to caRamel for DTLZ1, DTLZ2, and DTLZ3. Performance for the Kursawe function was similar between the two algorithms.
• R-based Hydrological Models:
  • For the GR4J model, hydroMOPSO showed a slight advantage in convergence to a higher median HV with less dispersion, suggesting it more consistently avoided sub-optimal solutions. It also surpassed caRamel in accuracy (GD) after 15,000 model runs.
  • For the TUWmodel, both methods exhibited similar median HV evolution, though caRamel showed a small advantage and produced more consistent solutions (narrower envelope). hydroMOPSO required more evaluations to stabilize but maintained stable accuracy, while caRamel's accuracy degraded after 13,000 runs.
• R-external SWAT+ Model:
  • The multi-objective calibration generated a concave Pareto front, highlighting a trade-off between KGE(Q) (range 0.60 to 0.77) and KGElf(Q) (range -4.80 to 0.75). The best compromise solution (BCS) was identified as KGE(Q) = 0.62 and KGElf(Q) = 0.71 after normalization.
  • The envelope of simulated hydrographs achieved a p-factor of 0.71 and an r-factor of 0.6.
  • Flow duration curves revealed that the KGE(Q)-maximizing solution underestimated low flows, while the KGElf(Q)-maximizing solution accurately represented low flows but poorly represented high flows. The BCS performed well across low flows.
  • Parameter analysis showed that alpha_bf was optimal at its maximum value (1), perco influenced performance across its range (KGE(Q) optimal near 1, KGElf(Q) optimal around 0.75), and latq_co and rchg_dp were optimal at 0. soil_awc significantly influenced both objectives, with higher values favoring medium-high flows and lower values favoring low flows. Other parameters (CN, soil_k, flo_min, revap_min, revap) showed dispersion within narrower optimal ranges, suggesting their influence was modulated by other key parameters.

Contributions

• Introduces hydroMOPSO, the first R package specifically designed for multi-objective optimization of both R-based and R-external hydrological and environmental models.
• Provides a flexible, model-independent, and multi-platform tool that implements the robust NMPSO algorithm.
• Offers fine-tuning options and an optimized default configuration for efficient generation of Pareto-optimal fronts with reduced evaluations.
• Demonstrates superior performance over the caRamel R package in benchmark problems and competitive or superior performance in real-world R-based hydrological model calibrations.
• Showcases the package's versatility and ease of use through a complex R-external SWAT+ model case study.
• Facilitates transparent decision-making by automatically generating high-quality, informative outputs such as hydrographs, flow duration curves, and dotty plots of parameter values.
• Supports parallel processing to significantly reduce computational calibration times.
• Adheres to the FAIR guiding principles for scientific data management and stewardship.

Funding

• ANID, Chile PCI-NSFC 190018 (Management of global change impacts on hydrological extremes by coupling remote sensing data and an interdisciplinary modelling approach)
• ANID, Chile Fondecyt 1212071 (The catchment’s memory: understanding how hydrological extremes are modulated by antecedent soil moisture conditions in a warmer climate)
• NLHPC, Chile (CCSS210001)
• TanDEM-X, Europe DEMGEOL0845 and DEMGEOL0707 projects
• European Space Agency project CCI Land Evaporation, Europe (contract no. 4000147355/25/I-LR)

Citation

@article{Marinao2026hydroMOPSO,
  author = {Marinao, Rodrigo and Zambrano-Bigiarini, Mauricio and Baez‐Villanueva, Oscar M.},
  title = {hydroMOPSO: A flexible and model-independent multi-objective optimisation R package for environmental and hydrological models},
  journal = {Environmental Modelling & Software},
  year = {2026},
  doi = {10.1016/j.envsoft.2025.106851},
  url = {https://doi.org/10.1016/j.envsoft.2025.106851}
}