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For ofﬁce use only Team Control Number For ofﬁce use only

T1 ________________ 43443 F1 ________________

T2 ________________ Problem Chosen F2 ________________

T3 ________________ E F3 ________________

T4 ________________ F4 ________________

2016!

MCM/ICM!

Summary Sheet!

(Your team's summary should be included as the first page of your electronic submission.)

Type a summary of your results on this page. Do not include the name of your school, advisor, or

team members on this page.

In this paper, we formulate an “excess water ratio” (EWR) metric for water

scarcity that improves upon currently used metrics such as the Water Stress Index

(WSI) by computing the per capita excess water available in a region. This provides a

more illuminating description of the impact of water shortages on individuals. To

determine the amount of excess water in a region, we start with the amount of

naturally available water, then subtract out water usage from each primary category:

personal use, industrial use, and agricultural use. Dividing this by the total

population of a region allows us to determine the annual amount of water that is

available but unused for every individual, a goal which is unique to our model. We

note as well that depriving an ecosystem of all available water carries serious

environmental consequences. In our case study, we apply our model to India, which

in addition to having the second largest population in the world, also suffers from a

large scale lack of safe drinking water and a high rate of waterborne diseases. In

applying our model to predictions of India's water scarcity in 2031, we ﬁrst model

growth rates for the environmental and social factors that inﬂuence water use to

determine the growth of water needs over the next ﬁfteen years. We develop a

secondary model on MATLAB that utilizes local predictions of water use and

population growth from the Indian government to extrapolate our EWR measure.

Taking these two models together, we conclude that the excess water per capita in

India will be around half of its current level by 2031. We proceed to explore several

intervention measures for India's water crisis that emphasize the need to address the

supply and demand sides of the water equation, including watershed development,

waste treatment, and broader cultural changes in food production. We ﬁnd the

cumulative impact of the proposed infrastructure improvements to be minimal.

Implementing both these changes would delay the point at which India's EWR

diminishes to zero by just one year (from 2083 to 2084). When we assume changes in

agriculture we begin to see more impact. Speciﬁcally, switching all rice and wheat

production in the country to millet over a thirty year period pushes the year India

hits zero EWR back to 2097. All of this means that large cultural shifts in demand for

water will ultimately be necessary for India to achieve long-term water

sustainability.

Page 2 Control # 43443

1 Introduction

Water has been absolutely critical for all humans, everywhere, since the be-

ginning of time. Every human needs at a bare minimum 20 liters of water to

survive. [1] The need for that water is rooted deeply in our biology: at 1% water

deﬁciency humans get thirsty, a 5% shortfall causes fever, at 10% short we are

rendered immobile, and death strikes after just a week of 12-15% water loss. [2]

Given these biological realities, it is not a surprise that the ﬁrst and most basic

category of water use in human society is personal consumption.

However, it is not enough to simply have suﬃcient water to drink. In terms

of total water consumption, personal use is actually a fairly small – if absolutely

essential – piece of the pie, just 5% on average of a given country’s consumption.

[3] By far the majority of water that all societies consume, 75% on average, is

used not to keep from dying of thirst but rather to keep from dying of hunger;

on agriculture. And in the middle, at 20% of water consumption, is industry.

On the face of it, it is hard to imagine why water scarcity could ever be an

issue on a planet that is 70% covered with water [4]. The problem arises when

we consider the conditions that make water usable: it must be fresh (not too

salty), liquid, and physically accessible. The ﬁrst condition eliminates all but

2.5% of all water from consideration, the second eliminates two thirds of that

which remains, and the ﬁnal condition brings the total fresh, liquid water near

or at the surface (ie usable water) down to just 0.003% of earth’s fresh water.

[3]

All that said, due to natural replenishment through the water cycle, even

that tiny fraction of available water has managed to sustain all human life that

has existed since antiquity. The main reason to expect that condition to be dif-

ferent going forward is that the exponential nature of human population growth

that has been occurring since roughly the Industrial Revolution is completely

unprecedented historically. To contextualize the current situation, realize that

it took almost 12,000 years for the human population to go from zero (circa

10,000 BCE) to one billion (circa 1800 CE). It took 125 years to go from one

billion to two circa 1930, 30 years to get from two to three billion in 1959, and

15 years or less to acquire each remaining billion, all the way up to today’s

current global population: about 7.3 billion people. [5] [6] And globally we are

continuing to grow; the UN projects that there will be over 11 billion people by

the year 2100. [7]

This ongoing massive increase in the number of people around the world

drives up water usage in all three categories. More people means more direct

individual consumers of their 20 daily liters, it means that more societies will

develop water intensive industry, and most importantly it means that everyone

must grow more crops. Incidentally the latter two have also historically and

currently contributed to increasing pollution, thereby even further decreasing

the total amount of usable water available. [8]

In short, humanity currently faces conditions of water scarcity that are com-

pletely unprecedented in human history. As a global community accurately

modeling future water needs and developing strategies we are all able and will-

Page 3 Control # 43443

ing to implement to bring necessary water consumption down to (or preferably

somewhere far below) the upper limit of physical water availability will be one

of the deﬁning challenges of our time. But we must ﬁnd a way; the survival of

the human race hangs precariously in the balance.

2 Model for Water Needs

2.1 Outline of Our Approach

In formulating a quantitative measure of water scarcity, we start with a reﬂection

of the Water Stress Indicator (WSI) which was created in 2005 by Smakhthin,

et al. [9] This model has credibility due to its precedent of use in informing

international policy making, as the UN Environmental Programme uses the

W SI as its measure of water scarcity on public maps.[10] The WSI is calculated

using the following formula:

Water Stress Indicator(W SI) =

Water Withdrawals

Mean Annual Runoﬀ(M AR)

Water withdrawals are thus interpreted as a reﬂection of water use and the

MAR is interpreted as a reﬂection of water availability. According to the U.S.

Geological Survey, mean annual runoﬀ is equivalent to the diﬀerence between

water available from precipitation and water lost due to evaporation.[11] Water

withdrawals are taken as a sum of water withdrawals for the primary uses of

water within a region: industrial, agricultural, and personal. Beyond its use in

the WSI, this summation has precedent in Vorosmarty’s index of local relative

water use and reuse (2005) and Shiklomanov and Markova’s water resources

vulnerability index (1993). [10]

A signiﬁcant weakness with the use of the WSI is that it does not allow

for any conclusions to be drawn about the average impact of water scarcity on

an individual level. Two regions with the same levels of water availability and

water use will have diﬀerent strains on the daily living of individuals within the

regions depending on their populations. Thus a more thorough reﬂection of a

region’s water scarcity should be dependent on the population of the region.

Our approach in developing our model is thus to use data that is representative

of water use and availability and formulating a ratio that determines how much

water this leaves per capita for recreational, commercial, or hygienic uses.

2.2 Assumptions

There are a myriad of cultural and environmental factors that impact the avail-

ability of water and how much water is needed to sustain the standards of living

of the region. Because it is impossible to account for the impact of each of these

factors on the overall water demands and availability, we adopt a number of

simplifying assumptions for our model:

Page 4 Control # 43443

• The only source of water for a region is its MAR. There is precedent for

this assumption in the prevailing models of the Water Stress Indicator

(WSI) and the USGS. The assumption is reasonable because while other

technologies exist to acquire water, these are not yet widespread enough

to present long term solutions to water shortages.

• Utility from water use for individuals is a strictly increasing monotonic

function. This assumption allows us to conclude that individuals, regard-

less of current water levels, would enjoy having more water available to

them. Therefore, although cultural practices in various regions create a

perceived need of diﬀerent water levels, we assume that an increase in

water availability would be appreciated by any individual.

• The current aggregate level of water use is in a temporary equilibrium, as

the region seeks to eﬃciently use all of the water that it has available based

on existing demands and technologies. This assumption is reasonable be-

cause to assume the opposite would imply that the region is currently

using more water than is physically present.

• Government policy and individuals are informed about the safety of the

water available to them and accordingly use the available water for appro-

priate purposes. Historically, this assumption has not always held because

the assumption of unclean water has led to diseases. A more complex

model would take into account the ubiquity of this knowledge throughout

the population.

• Geographic distribution of water sources and consumption is not a factor

in a country’s water scarcity. In reality, available water in one region

does not necessarily provide adequate water to another region due to the

economic and logistical challenges of transporting large quantities of water.

However, because people commonly settle and farm in land with abundant

water, we do not consider the eﬀects of transportation of water in our

model.

2.3 An Approach to Projecting Water Availability

In the ﬁrst formulation of the model, we use the process outlined above to come

up with a general formula for water use and water availability, and then create

an Excess Water Ratio (EWR). The excess water ratio represents the amount

of unused water in a region that is available per person. A higher ratio implies

that more water is available per person, and thus a higher EWR for a region

suggests that water scarcity is less of a concern for the region:

Water Use = Water Use from Industry + Water Use for Agriculture

+ Water Use for Personal Use

Water Availability = Mean Annual Runoﬀ

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