Fractional operator-based mathematical model for hydrological cycle analysis with machine learning integration

Title

Fractional operator-based mathematical model for hydrological cycle analysis with machine learning integration

Creator

Sherly, K.; Veeresha, Pundikala

Description

The most important natural resource for maintaining ecosystems, life, and human civilization is water. Climate patterns, hydrological processes, and energy balance are all impacted by the constant movement of water across different parts of the Earths climate system. A new mathematical model is proposed using a fractional order, and this study investigates the four main elements of the hydrological cycle: atmospheric water, rainfall, surface water, and groundwater. The model uses the Caputo fractional operator to account for memory effects and long-term dependencies in water dynamics. A thorough qualitative and quantitative study examines the systems boundedness, stability, existence, and uniqueness. The AdamsBashforthMoulton (ABM) approach is used for numerical simulations, and it shows improved accuracy, stability, and reduced error metrics compared to traditional methods. Furthermore, bifurcation analysis reveals the systems possible behavior. Data-driven parameter estimation and trend forecasting are achieved by integrating Machine Learning (ML) techniques like the random forest regressor to improve predictive capabilities. Visualization tools such as pair plots, box plots, bar plots, and correlation matrix examines the associations between variables. The suggested method provides a strong framework for hydrological cycle modeling, increasing forecasting accuracy for water resource dynamics and climate-driven hydrological changes. The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

Source

Modeling Earth Systems and Environment;Volume;11;Issue;3;Article No.;168;

Date

01-01-2025

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

AdamsBashforthMoulton method; Bifurcation analysis; Caputo fractional operator; Hydrological cycle model; Machine learning; Stability

Coverage

Sherly K., CHRIST University, Bengaluru, India; Veeresha P., CHRIST University, Bengaluru, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 23636203;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s40808-025-02335-w

https://www.scopus.com/pages/publications/105000032377?origin=resultslist