Competition: Mathematical Contest in Modelling Award: Finalist (Top: 2% among 27,205 Teams) Awarded by: the Consortium for Mathematics and Its Applications

Water Loss in Dams Due to Climate Change: A Mathematical Approach

Water loss in dams resulting from climate change has become a prominent problem in recent years, thus influencing humans’ life and production. To help address this issue, mathematical models are required to be established.

Problem 1

Problem 1 can be divided into three parts:

1. Service Area Coordination:

   • Maps are rasterized, and service areas for two dams are classified using a Comparative Optimization Algorithm.

2. Comprehensive Dispatching Model for Water:

   • Demand Side: An AIR Model is established to capture water demands, resulting in:
     • 11858569 m³ to be drawn from the Glen Canyon Dam.
     • 40978282 m³ to be drawn from the Hoover Dam.
   • Supply Side: Analysis of water levels and water volumes is conducted, with water-electricity generation fitted through Polynomial Interpolation, laying the foundation for subsequent analysis.

3. Dynamic Programming Model:

   • Calculates the time until demands are unmet at fixed water levels:
     • For the highest water level, the time is 495 days.
   • Additional water as a function of time is derived (see Section 4.6).
   • To consider Mexico’s residual claims, a Water-Supply Corridor Model is proposed, balancing respect for rights and interests (see Section 4.7).

Problem 2

A Multi-Interest Tradeoff Model is developed using Goal Programming and Input-Output Theory:

1. Economic Benefits as Criteria:
   • Four “players” of competing interests are identified.
   • Results include:
     • 11848077 m³ drawn from the Glen Canyon Dam.
     • 39125274 m³ drawn from the Hoover Dam.
   • Reallocation results in increased water for industry and decreased water for agriculture (see Section 5.2, Table 5).

Problem 3

When supply cannot meet all water demand:

• Inspired by the NSGA-II Algorithm (a type of Genetic Algorithm), specific approaches are recommended:
  1. Reducing the scale of industries with low water-use efficiency and allocating more water to efficient industries.
  2. Promoting technological innovation in industries with low water-use efficiency to improve resource utilization.

Conclusion

To ensure robustness, sensitivity analysis is conducted, and a summary article containing findings and suggestions has been written for the Drought and Thirst Magazine.