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Faculty of Graduate Studies

Matt Bonnyman

Notice of the Final Oral Examination for the Degree of Master of Science

Topic

MODELLING CONTINENTAL CANADA’S HISTORICAL AND FUTURE WATER BALANCE: A PARSIMONIOUS BUDYKO-TYPE MACHINE-LEARNING MODEL DESIGN

Department of Geography

Date & location

  • Friday, April 17, 2026

  • 9:00 A.M.

  • Virtual Defence

Reviewers

Supervisory Committee

  • Dr. David Atkinson, Department of Geography, University of Victoria (Supervisor)

  • Dr. Rajesh Shrestha, Department of Geography, UVic (Co-Supervisor) 

External Examiner

  • Dr. Amanda Szabo, School of Environmental Studies, University of Victoria 

Chair of Oral Examination

  • Dr. Daniel German, Department of Computer Science, UVic

     

Abstract

The Budyko framework provides a widely used approach for describing long-term basin water balance through the relationship between precipitation (P), potential evapotranspiration (PET), and runoff (R). In single-parameter formulations of the original Budyko relationship, such as Fu’s equation, deviations from the non-parametric Budyko curve due to the influence of additional climate and landscape variables are incorporated using the dimensionless parameter ω. Although previous studies have explored controls on ω and applied Budyko-type models to estimate runoff and evapotranspiration (ET), few have applied the framework to Canadian hydrological systems or utilized machine-learning approaches to model ω.  

In this thesis, a data-driven machine-learning model design for modelling ω is designed and applied across continental Canadian hydrological systems. Random forest (RF) machine-learning approaches were used to identify the dominant climate and landscape controls on ω and to model ω across the study region. The model incorporated key predictors representing vegetation, continentality, topography, and seasonal climate conditions, explaining 68% of the spatial variability in ω during training and 62% during cross-validation. Runoff estimates derived from the model achieved a mean absolute error (MAE) of 13%, substantially improving estimates compared to the non-parametric Budyko equation (MAE = 29%).  

The framework was further applied to investigate future hydrological changes using downscaled projections from 13 CMIP6 global climate models for 2071–2100 under SSP2-4.5 and SSP5-8.5 scenarios. A RF model calibrated for the 1961–1990 baseline period explained 72% of spatial variability in ω and estimated historical runoff with an MAE of 12% (compared with MAE of 29% when using the non-parametric equation). Model projections indicate increases in basin aridity (ET/P) by the end of the 21st century - particularly in central and southern regions and under higher emissions scenarios. 

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