Shakya et al. (2026) A generalized three-dimensional manifold for the Budyko hypothesis: analytical derivation and structural stability in open hydrological systems

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-09-11
• Authors: Chandra Mohan Shakya, Rajib Kumar Bhattacharjya
• DOI: 10.1016/j.jhydrol.2026.136406

Research Groups

• Subsurface Hydrology Laboratory, Department of Civil Engineering, Indian Institute of Technology Guwahati

Short Summary

This study presents a three-dimensional extension of the Budyko framework, known as the ShakyaQX (SQX) manifold, which represents hydro-climatic partitioning in open hydrological systems. The SQX formulation shows improved performance over the classical closed-system approach for monthly-scale predictions in the Brahmaputra Basin.

Objective

• To develop a generalized three-dimensional manifold for the Budyko hypothesis that can represent hydro-climatic partitioning in open hydrological systems.

Study Configuration

• Spatial Scale: Basin scale, with application to the Brahmaputra Basin and seven GRDC-gauged basins in the monsoon-dominated Irrawaddy-Chindwin system.
• Temporal Scale: Annual and monthly scales, with a focus on predicting evapotranspiration and runoff.

Methodology and Data

• Models used: ShakyaQX (SQX) manifold, a three-dimensional extension of the Budyko framework.
• Data sources: Satellite data, observation data, and reanalysis data from the GRACE mission.

Main Results

• The SQX formulation shows improved performance over the classical closed-system approach for monthly-scale predictions in the Brahmaputra Basin (NSE = 0.650 versus − 0.005).
• The SQX manifold outperforms the classical baseline under leave-one-out cross-validation and GRACE Monte Carlo uncertainty propagation.
• Diagnostic analyses attribute the limited performance of SQX to numerical conditioning of φ under low dry-season precipitation.

Contributions

• This study presents a novel three-dimensional extension of the Budyko framework that can represent hydro-climatic partitioning in open hydrological systems.
• The SQX formulation provides a single continuous formulation across storage-gain and storage-loss states, relocating the associated input-rescaling singularity to the boundary of the admissible domain.

Funding

• This research was funded by [project/program name and reference code]

Citation

@article{Shakya2026generalized,
  author = {Shakya, Chandra Mohan and Bhattacharjya, Rajib Kumar},
  title = {A generalized three-dimensional manifold for the Budyko hypothesis: analytical derivation and structural stability in open hydrological systems},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.136406},
  url = {https://doi.org/10.1016/j.jhydrol.2026.136406}
}