ShakyaQX is a research theme for Earth-system science. Its foundation is the SQX manifold, a peer-reviewed, three-dimensional generalisation of the Budyko hypothesis for open hydrological systems. The theme builds from there towards coupled water–energy behaviour, land-surface information and quantum-enhanced computation.
The published SQX manifold is the first layer. ShakyaQX is meant to grow from it into a connected framework for water, energy and computation in open Earth systems. Each layer below is labelled honestly by its current status.
The SQX manifold makes basin openness an explicit coordinate of the Budyko framework. This covers glacier melt, groundwater depletion, reservoir regulation and inter-basin transfers, which classical theory assumes away.
A dual Budyko view that links how water is partitioned with how surface energy is partitioned, so a basin's hydrological state and thermal state can be read together.
Quantum–classical hybrid methods for calibrating and estimating parameters in Budyko-based models, developed under the filed patent application.
Forward estimation of openness from land-use and land-cover information, together with spatial (GIS) tools that make the framework usable for water planning.
Classical Budyko-type equations describe how precipitation splits into evaporation and runoff in a closed catchment at steady state. Real basins are often open: groundwater is pumped or recharged, storage drains after the monsoon, and water moves across boundaries. SQX makes that openness an explicit state variable instead of treating it as error.
At φ = 1 the surface becomes the Mezentsev–Choudhury–Yang (MCY) Budyko curve, so all classical results are kept as a special case.
Evaporation is limited by energy (E/P → x) in humid climates and by available water, now including storage supply (E/P → φ), in arid ones.
Strictly monotonic and globally concave in x. The input-rescaling singularity is moved to the boundary of the admissible domain (φ → 0) rather than appearing inside it. One continuous equation covers storage-subsidized and storage-depleted states, with no piecewise forms.
Openness enters as a separate axis, so the aridity index keeps its climatic meaning instead of being rescaled by storage terms.
Sign convention. SQX treats ΔS as a net subsidy to the active water balance. ΔS > 0 is a net water gain (for example glacier melt or groundwater inflow), so φ > 1 is storage-subsidized. ΔS < 0 is depletion (for example groundwater extraction or drought), so φ < 1 is storage-depleted. This differs from the usual storage-anomaly convention, so φ should not be read as a direct restatement of GRACE storage change.
Each curve is a slice of the manifold at fixed openness φ, all with γ = 1.454. Storage-depleted states (φ < 1) sit below the classical Budyko curve, and storage-subsidized states (φ > 1) sit above it. The classical curve is the dashed line at φ = 1.
Move the sliders to change the openness coordinate φ and the landscape parameter γ. The curve, the water limit and the readouts update live from the published SQX equation.
Here E/P is drawn over the aridity index x and the openness φ, using the γ value set above. The highlighted line is the curve for your current φ. The classical Budyko curve is the slice at φ = 1.
Drag to rotate. The surface turns slowly until you touch it.
The framework was checked against observed discharge at the Goalpara gauging station, on the Brahmaputra for 2002–2021, using GRACE/GRACE-FO storage and TerraClimate climate data. It was then tested independently on seven basins in Myanmar. The results show both where SQX adds value and where it does not.
Each piece of work is labelled by its status, so peer-reviewed results stay separate from filed intellectual property and from work still in progress.
Analytical derivation, structural-stability proofs and Brahmaputra validation of the SQX surface.
A dual Budyko view that links the hydrological partition to surface energy partitioning in open systems. It is being developed further.
Systems and methods that build on the SQX framework. Applicant: IIT Guwahati.
Climate and human drivers of hydrological change in the Brahmaputra basin, with SQX as the central methodological contribution.
An independent test on seven Irrawaddy–Chindwin basins in Myanmar defines an explicit boundary condition: the present φ = 1 + ΔS/P form is poorly conditioned when dry-season precipitation is low.
Estimating openness as φ = 1 + ω − θ from independent land-surface information, so that it does not inherit the 1/P sensitivity. The plan also includes dynamic γ, routing-corrected φ and tests on more glacier-fed basins.
Shakya, C. M., & Bhattacharjya, R. K.
Journal of Hydrology, 679, 136406. Elsevier.
Shakya, C. M., & Bhattacharjya, R. K.
ESS Open Archive (ESSOAr) preprint. Free to read.
Shakya, C. M., & Bhattacharjya, R. K.
SSRN preprint.
The application covers systems and methods that build on the SQX open-system partition framework. Only the published equation and results are described on this website. The claimed technical details are in the official patent record.
Ph.D. in Civil Engineering at IIT Guwahati, studying hydrological change in the Brahmaputra basin.
Budyko–Fu and machine-learning diagnostics across the basin show where classical assumptions break down.
The priority date is established for the ShakyaQX systems and methods.
Journal of Hydrology 679, 136406: derivation, stability and validation.
Indian patent application by IIT Guwahati, with both researchers as inventors.
Coupled water–energy theory, forward-computed openness and quantum-enhanced calibration.
Subsurface Hydrology Laboratory, Department of Civil Engineering, Indian Institute of Technology Guwahati, Assam 781039, India.
Ph.D. Scholar, Department of Civil Engineering
Indian Institute of Technology Guwahati
Developer of ShakyaQXFirst author · InventorWorks on hydrological modelling and water resources engineering, combining theoretical hydrology with machine-learning analysis across the Brahmaputra and central Indian basins. He has about 3.5 years of teaching experience, including at NIT Raipur and NIT Hamirpur, and was previously a Project Associate/JRF at IIT Mandi on a SERB-funded project.
Interests: Budyko-type frameworks · open-system water balance · ML in hydrology · optimisation of water resources systems
chandra.mohan@iitg.ac.inLinkedIn ↗Professor, Department of Civil Engineering
Indian Institute of Technology Guwahati
Ph.D. SupervisorCo-author · Co-inventorProf. Bhattacharjya has been a Professor at IIT Guwahati since 2015 and received his Ph.D. in Civil Engineering from IIT Kanpur. He has been a visiting faculty member at Dalhousie University, Canada. His research covers optimisation methods, computational hydraulics, the impact of climate change, and surface water–groundwater interaction.
Faculty profile, IIT Guwahati ↗If you use the SQX framework or equation, please cite the original publication:
@article{Shakya2026SQX,
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},
volume = {679},
pages = {136406},
year = {2026},
doi = {10.1016/j.jhydrol.2026.136406}
}