01 / HYDROLOGY
Hydrological partitioning
Investigating how precipitation and potential evapotranspiration relate to actual evapotranspiration and runoff, while accounting for open-system water-balance conditions.
Scientific research framework
Understanding the Earth system through connected science.
ShakyaQX is an interdisciplinary research framework advancing the study of hydrological partitioning, energy interactions and quantum-enhanced computation for Earth-system science.
Founded by Chandra Mohan Shakya · Developed through collaborative research with Prof. Rajib Kumar Bhattacharyja
HydrologyEnergyQuantum
Shakya
QX
QX
The framework
A connected view of water, energy and computation.
ShakyaQX brings together analytical hydrology and emerging computational approaches. Its foundation is a generalized three-dimensional manifold for the Budyko hypothesis in open hydrological systems.
02 / ENERGY
Energy-system extension
Developing an energy-oriented extension of the research framework to examine coupled water and energy behaviour in Earth-system processes.
03 / COMPUTATION
Quantum-enhanced methods
Exploring quantum-enhanced computational strategies for hydrological modelling and parameter estimation. This remains an active research direction.
Scientific foundation
The generalized 3D Budyko manifold
The published ShakyaQX formulation extends the Budyko perspective by introducing an open-system water-balance coordinate, φ, alongside the aridity index and evaporative partitioning. The foundational publication is co-authored by Chandra Mohan Shakya and Prof. Rajib Kumar Bhattacharyja.
Published ShakyaQX relationship
E/P = x [1 + (x/φ)γ]−1/γ
where x = PET/P, φ > 0 and γ > 0.Three coordinates. A family of surfaces.
The manifold is expressed in terms of the aridity index x, the open-system coordinate φ, and the evaporative index E/P. The parameter γ indexes the family of surfaces.
In the published framework, the generalized water balance is expressed as P + ΔS = E + Q. The interpretation of ΔS follows the framework's stated subsidy convention; storage-gain conventions in observational products require careful sign conversion.
Budyko hypothesisOpen hydrological systems3D manifoldResearch directions
From analytical structure to new applications.
The website distinguishes peer-reviewed results from filed intellectual property and work that remains under development.
Generalized Budyko manifold
Analytical derivation and structural-stability analysis of a generalized three-dimensional manifold for the Budyko hypothesis in open hydrological systems.
Collaborative intellectual property
The ShakyaQX-related patent work is jointly associated with Chandra Mohan Shakya and Prof. Rajib Kumar Bhattacharyja. The filing status and inventor details should be read from the official patent record; confidential technical details are not presented here.
Quantum-enhanced computation
Research into quantum-enhanced computational approaches for hydrological modelling, including optimization and parameter-estimation strategies.
Spatial and land-surface integration
Proposed directions include land-use and land-cover integration, spatially explicit hydrological analysis and further development of basin-scale process representation.
Selected publication
Peer-reviewed research
The scientific foundation of ShakyaQX is documented through peer-reviewed research.
JH
Published · 2026
A generalized three-dimensional manifold for the Budyko hypothesis: analytical derivation and structural stability in open hydrological systems
C. M. Shakya and R. K. Bhattacharyja. Journal of Hydrology, 679 (2026), Article 136406.
View article and DOI ↗Research roadmap
Building the next layers of the framework.
These are research directions, not claims of completed or validated capabilities.
DIRECTION 01
Hydrological validation
Evaluate the framework across basins, climates and observational datasets.
DIRECTION 02
LULC integration
Investigate how land-cover information can inform forward estimation of the open-system coordinate.
DIRECTION 03
Spatial process development
Develop and test spatially explicit extensions while distinguishing partitioning from routing processes.
DIRECTION 04
Quantum computation
Assess quantum-enhanced algorithms and their practical value for scientific computation.
Research leadership and collaboration
About the research team
Chandra Mohan Shakya
Founder and framework developer. His research interests include hydrological modelling, the Budyko framework, climate and land-surface interactions, and quantum-enhanced scientific computation.
Prof. Rajib Kumar Bhattacharyja
Academic supervisor and research collaborator. Prof. Bhattacharyja is a co-author of the published ShakyaQX foundation paper and is jointly associated with the patent work described on this website.
ShakyaQX is presented as a research framework developed through this academic collaboration. Publication authorship, patent inventorship and filing status are identified separately wherever relevant.
Explore the research