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Reaching agreements over water management on transboundary rivers is a complex yet necessary endeavour to assure that humans can live within the limits of available resources. The myriad of challenges is both physical and social in nature; the uncertainty of water availability due to natural hydrologic variability is often increased by the involvement of multiple management institutions. Jurisdictions of control are typically defined by political borders, and thus they represent distinct geographic domains and interests. Increasing scarcity, driven by rapidly expanding populations and our growing awareness of climatic non-stationary, increases the urgency to find agreements among these institutions. Although the need is significant and growing, a lack of available approaches exist that considers the physical, technical and political dynamics to address these complex challenges. This thesis describes novel analytical methods to engage in the complex political realm of transboundary river management. Building from an engineering systems analysis approach to engage this topic, the main hypotheses of this thesis are: (1) Existing analytical approaches for water resource development are useful but often constrained in a transboundary negotiation context, and (2) cooperation among co-riparian water management institutions can be significantly increased with strategic implementation of analytical tools to jointly manage current and future risks. To test this hypothesis, this thesis presents an analytical approach that (1) examines previous applications of water resource models to identify their perceived contribution to managing transboundary rivers, (2) develops a new modelling framework that engages with transboundary negotiations, and (3) incorporates methods for risk-based decision making to evaluate the benefits, opportunities and trade-offs of cooperation among co-riparian states. A retrospective analysis is conducted on the Colorado and Murray-Darling River Basins to understand lessons learned from recent applications of analytical modelling tools. New methods are then developed and applied to the rapidly changing Eastern Nile River Basin. The ongoing construction of the Grand Ethiopian Renaissance Dam (GERD) and the implications on downstream countries of Sudan and Egypt provides the context and a relevant case for testing the methods and evaluating the hypotheses. Results from this thesis demonstrate the distinct advantages of an early development of system-wide analytical tools within a transboundary context, which is made available to all parties. Conversely, the challenges of reconciling multiple models used by different institutions after full allocation is reached in a basin is a significant barrier to cooperative management. Results also demonstrate the advantages of developing an analytical tool that is sufficiently accurate, transparent and flexible to seek creative solutions, and the need to select an appropriate breadth and depth of model design that conveys its credibility, saliency and legitimacy to support a decision-making process. The appropriate design of tools to consider multiple future hydrologic scenarios can shift a discourse from rigid water allocations to considering the effects of new developments in terms of changes to risks, and to allow stakeholders to decide whether these changes are tolerable when juxtaposed with the benefits that new infrastructure provides. Finally, the results show how risks among multiple stakeholders can be evaluated under expanding uncertainties, and cooperative solutions can be sought to minimise or balance these risks. The application of the proposed methods to the Eastern Nile Basin indicates that solutions are indeed possible that benefit all three countries. A number of cooperative solutions are identified that suggest operational rules for the new and existing infrastructure. These operations can be responsive to variable climatic conditions and thus encourage dynamic cooperation. In this light, the developments in Ethiopia need not be a risk, but can result in substantial benefits to the downstream countries if agreements can be reached. Embedding highly adaptable analytical tools within a negotiation process can help to overcome the challenges faced at this historic point on the Nile River.