SAFE Water Strategy

My team was designated Meritorious Winner. Out of 5636 international teams, we placed among the top 16%. Less than 1% of the teams that competed placed in a higher tier. This year was my second time competing in COMAP's Mathematical Contest in Modeling (MCM). MCM is a competition that challenges teams of students to clarify, analyze, and propose solutions to open-ended problems. The problems were released on

**January 31, 2013**at 6:00pm. The papers were due on**February 4, 2013**at 6:00pm. My teammates were Claudio Gonzales and Camilla Hutchison.

This year, my team chose Problem B:

Fresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, and cost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outlining your approach, its feasibility and costs, and why it is the 'best water strategy choice.'

Countries: United States, China, Russia, Egypt, or Saudi Arabia

## Executive Summary

**SAFE Water Strategy**

Saudi Arabia Feasible and Eﬃcient Water Strategy

The goal of our model is to create a realistic simulation of the hydrological situation of Saudi Arabia in 2025, from which we can determine the best water strategy. To ensure that our strategy was eﬀective we required that our models provide the entire population with suﬃcient water. We guaranteed our strategy would be feasible by only using current technology and undertaking construction that can be completed within 12 years. We determined whether a strategy was cost-eﬃcient by comparing the yearly cost to Saudi Arabia’s current annual water budget. We considered the best strategy to be one which fully satisﬁes Saudi Arabia’s annual water demands, minimizes cost, and minimizes the environmental impact.

We created two diﬀerent models to examine numerous water strategies. The ﬁrst, the BOD model, estimates the cost of building enough desalinization facilities to fully support projected Saudi Arabian water demand in 2025, given a parameter of future agricultural use. Our SDW model simulates the movement, storage, production, and conservation of water in Saudi Arabia circa 2025.

The SDW model relies on geographic information. Without knowledge of the exact population density mapping of Saudi Arabia in 2025, we instead create a randomly distributed pseudo-nation. The algorithm generates this geographic data using a pairing of partitions and the beta distribution. The resulting map is designed to emulate important geographic features of Saudi Arabia.

Seasonality was an important factor in our model given the extensive timeline of our simulations. We successfully accounted for this using the Riemann approximation of a sinusoidal curve, whose peak reﬂected the particularly high summer water usage. When determining the order in which reservoirs are replenished, desalinization facilities ﬁrst replenish areas who are nearby and have low water reserves. The algorithm then considers further areas with low reserves and nearby regions with lesser demand. Lastly, areas that are far away with low demand are replenished.

The results of the BOD model suggest that it is very unlikely Saudi Arabia can sustain current levels of agricultural water usage. Data from the SDW model support this claim. Surprisingly, when agricultural water usage is decreased to a sustainable level, it is no longer necessary to add desalinization facilities to fulﬁll the water demands of the 2025 population. The results from this model also showed that recycling wastewater is necessary to keeping costs manageable. We discovered that reservoir capacity was a key element, optimized at about 3%.

After analyzing the data from our models, and considering the real-world implications of their values, we have arrived at the following recommendations for the Saudi Arabian government:

• Agricultural water usage should be decreased as much as politicical situation allows.

• Money for infrastructure should go towards increasing waste water recycling and building piping infrastructure as opposed to desalinization facilities.

• Local reservoirs for each area should hold approximately 3% of that area’s annual water demand.

We created two diﬀerent models to examine numerous water strategies. The ﬁrst, the BOD model, estimates the cost of building enough desalinization facilities to fully support projected Saudi Arabian water demand in 2025, given a parameter of future agricultural use. Our SDW model simulates the movement, storage, production, and conservation of water in Saudi Arabia circa 2025.

The SDW model relies on geographic information. Without knowledge of the exact population density mapping of Saudi Arabia in 2025, we instead create a randomly distributed pseudo-nation. The algorithm generates this geographic data using a pairing of partitions and the beta distribution. The resulting map is designed to emulate important geographic features of Saudi Arabia.

Seasonality was an important factor in our model given the extensive timeline of our simulations. We successfully accounted for this using the Riemann approximation of a sinusoidal curve, whose peak reﬂected the particularly high summer water usage. When determining the order in which reservoirs are replenished, desalinization facilities ﬁrst replenish areas who are nearby and have low water reserves. The algorithm then considers further areas with low reserves and nearby regions with lesser demand. Lastly, areas that are far away with low demand are replenished.

The results of the BOD model suggest that it is very unlikely Saudi Arabia can sustain current levels of agricultural water usage. Data from the SDW model support this claim. Surprisingly, when agricultural water usage is decreased to a sustainable level, it is no longer necessary to add desalinization facilities to fulﬁll the water demands of the 2025 population. The results from this model also showed that recycling wastewater is necessary to keeping costs manageable. We discovered that reservoir capacity was a key element, optimized at about 3%.

After analyzing the data from our models, and considering the real-world implications of their values, we have arrived at the following recommendations for the Saudi Arabian government:

• Agricultural water usage should be decreased as much as politicical situation allows.

• Money for infrastructure should go towards increasing waste water recycling and building piping infrastructure as opposed to desalinization facilities.

• Local reservoirs for each area should hold approximately 3% of that area’s annual water demand.