A Synthetical Water Dispatching Model Give it or Give up

Wed, 26 Jan 2022 00:00:00 +0000

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:

Service Area Coordination:
- Maps are rasterized, and service areas for two dams are classified using a Comparative Optimization Algorithm.
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.
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:

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