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.).



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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).