Estimating Unit Costs of Water Supply Options

The method for estimating water reliability benefits involves a two-step process. First, water managers define the level of reliability benefit they want to maintain or achieve. For example, they might want to ensure that enough water is available to meet demand in 39 out of 40 years, on average. Second, they compare options by adjusting average unit costs to get constant-reliability-benefit unit costs. The following example briefly illustrates the method (see Appendix D of Cooley et al. [2006] for the mathematical details).

Suppose a community is served by supply from a local river with a normal distribution of hydrology.^{1} Our example assumes the extractable yield in average years is 10,000 acre-feet (AF) and the standard deviation of annual flow is 1,000 AF. Low and high flows are increasingly rare as they get further from the average. The relative flatness of the bell is described by the standard deviation of the normal distribution. The larger the standard deviation as a percentage of the mean (this ratio is called the coefficient of variance), the flatter the bell, and the more variable is the annual flow available for human extractive purposes.

The average flow and the flow two standard deviations below the average are marked in Figure D-1. A property of the normal distribution is that in 2.5 percent of the years, flow will be less than the lower of these two marks. In our illustration, the flow two standard deviations

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Appendix D
Estimating Unit Costs of Water Supply
Options
The method for estimating water reliability benefits involves a two-
step process. First, water managers define the level of reliability benefit
they want to maintain or achieve. For example, they might want to
ensure that enough water is available to meet demand in 39 out of 40
years, on average. Second, they compare options by adjusting average
unit costs to get constant-reliability-benefit unit costs. The following
example briefly illustrates the method (see Appendix D of Cooley et al.
[2006] for the mathematical details).
Illustration of Constant-Reliability-Benefit Unit Costs
Suppose a community is served by supply from a local river with a
normal distribution of hydrology.1 Our example assumes the extractable
yield in average years is 10,000 acre-feet (AF) and the standard deviation
of annual flow is 1,000 AF. Low and high flows are increasingly rare as
they get further from the average. The relative flatness of the bell is
described by the standard deviation of the normal distribution. The larger
the standard deviation as a percentage of the mean (this ratio is called the
coefficient of variance), the flatter the bell, and the more variable is the
annual flow available for human extractive purposes.
The average flow and the flow two standard deviations below the
average are marked in Figure D-1. A property of the normal distribution
is that in 2.5 percent of the years, flow will be less than the lower of
these two marks. In our illustration, the flow two standard deviations
1
The normal distribution is used for convenience. Hydrologic phenomena are
usually better described by other distributions (e.g., log-normal, Pearson Type
III, etc.).
286

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Appendix D 287
below the mean is 8,000 acre-feet per year (AFY). Flow available for
human use will be lower than the lower mark (8,000 AFY) in only 1 out
of every 40 years over a long period of time.
Now let us consider demand. The demand numbers in our illustration
are conveniently chosen to match some of the numbers in the description
of supply, above. Any other numbers could be assumed, but they would
make the illustration harder to follow. Assume that current drought-year
demand (labeled DE in Figure D-1)2 is at the lower tick mark. Then the
community served by this water system will experience a water shortage
only 1 year out of 40. As defined above, this is a reliability level of 97.5
percent.
Suppose drought-year demand is projected to grow by 2,000 AF over
the next decade.3 As drought-year demand grows, reliability will
decrease in the sense that the likelihood of a water shortage will increase
from 1 in 40 to 1 in 2. That is, the reliability level would fall from
FIGURE D-1. Normal distribution of annual hydrologic flows.
SOURCE: Cooley et al. (2006).
2
We define drought-year demand as the demand that would exist when flow is
at a point chosen by the planner on the horizontal axis of Figure D-1—in this
case, demand when flow is at the lower tick mark. Note that drought-year
demand will often be higher than average-year demand because outdoor water
use will increase when rainfall is below average or temperature is above
average.
3
A water demand projection is based on many factors, such as projected growth
in population and employment in the service area.

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288 Desalination: A National Perspective
97.5 percent to 50 percent, because enough water would be extractable in
only half the years. Water managers may decide this is unacceptable and
choose to maintain the current level of reliability at 97.5 percent. In this
case, the amount of physical water (or water-use efficiency) required to
satisfy growth in drought-year demand is the difference between future
drought-year demand (DF) and existing drought-year demand (DE). This
has been labeled DN in Figure D-1, and in our example is 2,000 AF. If a
supply option were to provide exactly this amount in every year, the
planner should procure DN of new supply. Water from advanced
treatment processes (e.g., desalinated seawater or recycled wastewater)
has this characteristic if treatment facilities are designed with enough
redundancy to prevent downtime other than for regularly scheduled
maintenance.4
But if the water supply option is variable from year to year, the
planner must procure enough of it to have DN available 39 out of 40
years, or reliability will decline. For example, when the chosen option is
a surface water source, the amount available in an average year must be
greater than DN in order to ensure DN is available in a dry year.
The amount of water supply greater than DN that has to be purchased
from the new water source depends on two factors: the new source’s
standard deviation of annual yield and the correlation of annual yield
with the existing supply. The higher the new source’s standard deviation
of annual yield, the more water that needs to be procured from the new
source to ensure adequate water in a low-flow year. The lower the
correlations of annual yield between the new source and the existing
source, the less of the new source will be required, on average, to ensure
DN is available in a dry year.
What this means is that comparing unit costs for options based on the
average amount of water each option will deliver leaves out an important
piece of the economic picture. For illustration purposes suppose that
advanced treatment of impaired water, a new surface water supply, and
outdoor conservation all have an average unit cost of $600/AF. Ignoring
reliability impacts, there is no financial difference between these sources.
But suppose further that the new surface water supply has a similar
pattern of wet and dry years to the old surface water supply but is more
variable. Then ensuring the 2,000 AF of new supply that will be needed
in a drought year requires that the new source be sized to deliver more
than 2,000 AF of water each average year, just as the old source was
4
Some indoor water conservation measures may also have this characteristic of
supplying exactly DN every year if they are designed carefully.

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Appendix D 289
capable of providing 10,000 AF on average but only 8,000 AF with the
desired level of reliability. If the new surface water source has a
coefficient of variance (the standard deviation over the mean) of 20
percent, the water planner will need to procure 3,333 AF in an average
year to ensure 2,000 AF in the constant-reliability-benefit design year
(3,333 – (2 × 0.2 × 3,333) = 2,000). This in turn implies that each unit of
water during drought will cost $1,000/AF on a constant-reliability-
benefit basis ($600/(1 – 2 × 0.2) = $1,000).5 See Figure B-2 for an
illustration of the average and constant-reliability benefit of surface
water in this example.
If an outdoor water-conservation measure were to save more water
during dry weather,6 its constant-reliability-benefit unit cost would be
less than the assumed $600/AF. If it were perfectly countercorrelated
with the current surface water source, and had a coefficient of variation
of 10 percent, its constant-reliability unit cost would be $500/AF =
($600/(1 + 2 × 0.1)). That is, ensuring 2,000 AF of water in a drought
year would require outdoor conservation measures sized to deliver only
1,667 AF in an average year. The countercorrelation implies that, during
a drought where flows in the current supply source are two standard
deviations below its mean, outdoor conservation would save two
standard deviations above its mean, which equals 2.0 when the mean is
1.667 and the standard deviation is 0.1667 (10 percent of the mean).
Figure D-2 summarizes the average unit costs and constant-
reliability-benefit (drought-year) unit costs under these assumptions.
5
Stated differently, the utility could pay 67 percent more per average unit of
water from the advanced treatment facility (1000/600 = 1.67) compared to each
average unit in the new surface water alternative—and provide the same
economic benefit at the same cost to customers. Note that the premium is not in
total, but per unit. The smaller advanced treatment facility is just as good as the
larger surface water facility at reliably providing 2,000 AF, so a per unit
premium is justified.
6
For example, laser leveling, drip or microspray irrigation, scheduling
improvements, ET controllers, and adjustments in sprinkler heads to improve
distribution uniformity reduce the percent of applied water that percolates or
evaporates. Since applied water must go up during drought, these measures will
save more water during drought than during average or wet weather. Auto-rain
shutoff devices, by contrast, save more water when it rains than when it is dry.

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290 Desalination: A National Perspective
1200
Dollars Per Acre-Foot 1000
800
600
400
200
0
New Surface Water Outdoor Advanced
Conservation Treatment
Average Unit Costs
Constant-Reliability Benefit (Drought Year) Unit Costs
FIGURE D-2. Average and constant-reliability benefits of surface water
alternatives, assuming equal average unit costs for each example. SOURCE:
Cooley et al. (2006).
Accounting for variance and correlation between water sources—as is
done for securities when managing a portfolio of financial assets—is
clearly important. Water-supply planners who do not consider these
factors might think options are similar in cost when they are in fact quite
different once reliability benefits of the options are equalized. Worse yet,
an apparently inexpensive source might turn out to be very expensive on
a constant-reliability-benefit basis, or an apparently expensive source
might turn out to have the lowest cost per acre-foot when reliability is
considered.
SOURCE: Cooley et al. (2006).