Projecting demand extremes under climate change using extreme ...

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Haagenson et al | http://dx.doi.org/10.5942/jawwa.2013.105.0013 Journal - American Water Works Association Peer-Reviewed

Projecting demand extremes under climate change using extreme value analysis E r i k Ha a g e nso n, 1 Ba l a ji Ra ja g opalan , 2 R. Scott Summers, 2 and J . A l a n R o berso n 3 1Riverside

Technology, Fort Collins, Colo. of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, Colo. 3AWWA Government Affairs Office, Washington, D.C. 2Department

Accurate projections of water demand extremes are essential to all aspects of the planning process (e.g., defining target growth and securing financing). The role of climate on water demand variability is pronounced and will likely increase in the future as a result of climate change. Therefore, a flexible approach that can incorporate climate change scenarios is needed to project water demand extremes. In this research, an integrated approach with two components was developed. First, extreme value models based on climate attributes

were created for both water demand maximums and water demand over a specified threshold; these models were then fitted to the historic water demand and climate data. Second, ensembles of future weather sequences conditioned on climate change projections were generated using a stochastic weather generator. Together these two components provided scenarios of water demand extremes under various climate projections. The city of Aurora, Colo., was used as a case study to demonstrate the utility of this approach.

Keywords: climate change, extreme value analysis, projections, utility planning and management, water demand

Water demand projections help utility managers make shortterm operational decisions about treatment plant production, balancing of supply and demand, and potential water use restrictions during a drought. Every year water utility managers and financial staff develop a projection of the amount of water to sell (water sales) and subsequently project the resultant revenues as part of their annual budgeting process. These demand projections also help managers make long-term decisions about additional supply acquisition, additional treatment capacity, transmission mains, storage tanks, water conservation effects, price elasticity, and demand management (Billings & Jones, 2008). For both short- and long-term financial sustainability, the water system is anchored by accurate long-term demand forecasts. Accurate water demand forecasts are needed for both the short term (operational and financial) and long term (planning and financial). The costs of being wrong can be grave. Inaccuracies in longer-term forecasts may result in significant costs to utilities and their customers. For example, costs can manifest in the form of stranded capital assets, insufficient supply reliability, or a reduced level of service because of treatment plant capacity limitations. All utilities use water demand projections, but many of these are created from simplified models and fail to incorporate nonstationarity and variability from climate change and other uncertainties. Numerous factors are known to affect water demand, including population, employment, technology, weather, climate, price, infrastructure efficiency, conservation programs, socioeco-

nomics, and water awareness (Billings & Jones, 2008). Models have focused mainly on the social and economic variables—which are often difficult to project—resulting in complex, highly uncertain models, many of which are outside the reach of utilities that are small in size or have limited fiscal resources. Both climate and weather play a fairly significant role in modulating water demand, and some research initiatives have used precipitation and temperatures to help model water demand (Billings & Jones, 2008; Nieswiadomy, 1992; Foster & Beattie, 1981). Climatic variables typically are represented as temporal (e.g., seasonal, monthly, annual) averages, but this approach may be limiting in that the effect of precipitation and temperatures may be more pronounced at first and then decrease with time (Maidment & Miaou, 1986). To address this and other issues, spell statistics (i.e., droughts, heat waves) have been considered by various researchers (Billings & Jones, 2008; Smoyer-Tomic, 2003; Foster & Beattie, 1981) and more recently by Haagenson (2012) for use in statistical demand models. Utilities are specifically interested in the high-impact, low-probability water demand situations that drive infrastructure planning decisions and the need for capital to fund such improvements. Accurate projections of peak-hour demand and peak-day demand are necessary for planning capital improvements such as an alternate supply of source water, treatment plant capacity, transmission line upgrades, storage tanks, and booster pumping stations.

2013 © American Water Works Association

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These high-impact, low-probability water demand situations are by definition “extreme events.” One approach that this research found to better model extreme events was the use of extreme value analysis (EVA). Climate change and more extreme weather conditions likely will change peak demands and will need to be considered by water utilities in their future planning, design, and operations. EVA has been used in a variety of fields, including the financial industry (Embrechts et al, 1999), civil engineering (Holmes & Moriarty, 1999), ecology (Eaton et al, 1995), water quality (Towler et al, 2010), and especially climatology (Furrer et al, 2010; Beguería & Vincente-Serrano, 2006; Coles & Simiu, 2003; Katz & Brown, 1995). EVA has been used in hydrology to estimate and forecast flood frequency, model financial loss related to flooding, and model extreme hydrological conditions in watersheds of various sizes (Beguería & Vincente-Serrano, 2006; Coles & Simiu, 2003; Coles, 2001; McNeil, 1997; Eaton et al, 1995; Katz & Brown, 1995; Smith, 1989; Swift & Waide, 1989; Fiorentino & Versace, 1984). A full discussion on EVA and hydrology is available elsewhere (Katz & Naveau, 2002). To date, however, EVA has not been used in the water demand sector. Extreme events exhibit significant variability over time driven by climate fluctuations. For example, an increasing trend in the frequency and intensity of precipitation in the United States has been recognized for more than 15 years (Trenberth, 1999, 1998). The International Panel on Climate Change projects the same trend for much of the world in the coming decades as a result of climate change. Researchers in water resources and hydrology have been working on translating climate change projections from the global climate models to effects on hydrology and water resources. This requires downscaling climate data that are often at coarse spatial and temporal scales to the scales of interest and then driving them through hydrologic models to generate ensembles of stream flows and their consequent effects on water resources. A body of literature exists on understanding water resources variability under climate change in the western United States (Rajagopalan et al, 2009; Christensen et al, 2004). Recently water utilities have undertaken joint efforts to develop tools for water supply and demand with a focus on utility planning decisions (WaterRF, 2012; Ray et al, 2008). The traditional approach of downscaling climate information to process models can be computationally intensive and deter a majority of water utilities from accessing them. Simple, effective, and flexible tools are needed that can translate coarse climate information to specific attributes of decision variables without having to go through computationally intensive process models. Towler and colleagues (2010) developed EVA models to translate monthly precipitation and temperature projections under climate change to projections of stream flow extremes and, consequently, water quality extremes in the northwest United States and also for Aurora, Colo. Such models are effective in providing the projections of extreme events that are essential to water utility managers for planning purposes. Modeling the effects of water demand under climate change is different from modeling the effects of climate change on water supply because of the inherent human response to water demand

changes, which makes the system more complex. Nonetheless the same weather factors (e.g., temperature and precipitation) used in projections for water supply and resources play a significant role in projecting water demand. The current research expanded the EVA approach to apply to projecting water demand extremes and the potential effect of climate change on those extremes. In this article, the authors first present a brief description of the study application, data, and climate change projections and effects. Subsequent sections provide an approach to generating ensembles of water demand extremes under climate change projections, followed by study results and a summary.

Study Area—Data and Climate Change EFFECTS The study location chosen for this research was the water utility of Aurora, Colo., a rapidly growing suburb of Denver with limited water supply in a semiarid region. Recent dry spells (Pielke et al, 2005) have exacerbated the situation, and climate projections portend further stress on the system’s water resources. The utility has instituted short- and long-term demand management (Kenney et al, 2008) and has embarked on the development of a wastewater reuse facility to augment its limited mountain water supply (Binney, 2006). Climate change projections from multimodel global circulation models in conjunction with hydrologic models (Yates et al, 2005) show 10–25% reduction in the runoff in the Colorado Basin and 5–10% reduction in the Arkansas Basin over a 50-year period; both of these sources provide water to Aurora (Ray et al, 2008). Clearly, Aurora—and potentially many other utilities—need to minimize errors in future water demand projections and also understand the potential effects of climate change on these projections. Realistic projections of water demand extremes should be of immense use to all water managers, given that costly infrastructure decisions must be made and the cost of being wrong could have grave implications. Aurora’s daily water production data in million gallons per day were available for the period 1990–2010. In general, water is produced to meet the respective demand, and therefore the production data can be considered water demand. The critical season of high demand for the city is summer, specifically the three-month period of June through August. Monthly maximum demand was computed from the daily data for use in projections. Daily weather data consisting of precipitation and maximum and minimum temperature were obtained from the National Climatic Data Center (NCDC, 2012). A suite of weather attributes (hot/dry and wet/cold spells as well as average weather variables) identified as being related to average water demand and water demand extremes (Haagenson, 2012) were computed from the daily weather data for the summer months in the data period. Table 1 shows the weather statistic thresholds and precipitation used for computation. Table 2 lists the weather attributes and their correlation with monthly maximum water demand. Water demand variability is often more dependent on weather phenomena such as droughts and extreme temperatures or weather spells than on the traditionally used socioeconomic variables (e.g., population, income, and per capita consumption) (Arbués et al, 2003). For the current study, weather spell statistics


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TABLE 1

Thresholds to compute weather attributes for use as covariates in EVA models Weather Statistic Thresholds Minimum Temperature— oF

Maximum Temperature— oF

Precipitation in.

June

57

89

0

July

62

94

0

August

60

89

0

Month

EVA—extreme value analysis

(Table 2) were used as covariates in this analysis, in addition to the daily weather information ascertained from the National Climatic Data Center. The authors computed hot/cold and dry/ wet spells with the thresholds shown in Table 1. The use of weather spells has been recommended for modeling demand attributes (Haagenson, 2012). In the current research, a suite of weather attributes was developed; their correlations with monthly maximum water demand are shown in Table 2. For computational ease, variables with significant correlations were selected for use in modeling water demand extremes with nonstationarity. Because of the complex nature of describing water demand and because the scope of this research focuses exclusively on physical,

TABLE 2

rather than socioeconomic variables, the correlations appear to be low; however, describing a majority of the variability using only weather variables is a marked improvement over current practices. Haagenson (2012) provides additional background on creating weather spell statistics. Projections of precipitation and temperature for the region under different climate change scenarios were solicited from the Joint Front Range Climate Change Vulnerability Study completed in 2012 (Water Research Foundation, 2012). The authors used two projections from an International Panel on Climate Change middle emissions path: increasing temperatures and decreasing precipitation (warm/dry scenario) and increasing temperatures and increasing precipitation (warm/wet scenario). Details of these scenarios are shown in Table 3. Change in annual average temperature over the 30-year planning horizon (2010–40) was used along with two different forecasted precipitation scenarios, i.e., wet and dry. The temperature/precipitation scenarios are referred to here as warm/dry and warm/wet. These projected changes were used in a stochastic weather generator (described subsequently) to generate ensembles of daily weather sequences.

Approach for Projecting Water Demand Extremes As noted previously, two attributes of water demand extremes were of interest in this research: monthly maximum and the number of days that water demand exceeds a certain threshold. The authors propose an approach to projecting these extremes attributes based on future climate projections. The proposed

Weather attributes and their correlation with monthly maximum water demand Covariate

Average monthly maximum temperature

Definition

Correlation*

Daily maximum temperature values averaged over one month

0.35

Average seasonal minimum temperature

Daily minimum temperature values averaged over one month

0.34

Average seasonal precipitation

Daily precipitation values averaged over one month

0.04

Time

A vector of values progressing chronologically

0.05

Preceding month average water demand

Average water demand from preceding month (lag 1)

0.55

Average monthly daily high hot spell in days

Average length in days of a spell with daily high temperatures over a given threshold for each month

0.25

Total monthly days with high temperature above threshold

Total days the maximum daily temperature exceeds a given threshold in a month

0.26

Maximum monthly daily high hot spell

Longest spell with daily high temperatures above a given threshold in a given month

0.25

Average monthly nightly low hot spell in day

Average length in days of a spell with nightly low temperatures above a threshold for each month

0.39

Total monthly nights with low temperature above threshold

Total days with the nightly low temperature above a given threshold for each month

0.48

Maximum monthly nightly low hot spell

Longest spell in days with nightly low temperatures above a given threshold for each month

0.50

Average monthly precipitation spell in days

Average length in days of a spell with precipitation above a given threshold for each month

0.06

Total monthly days with precipitation below threshold

Total days with precipitation above a given threshold each month

0.22

Maximum monthly precipitation spell

Longest spell in days with precipitation above a given threshold each month

0.05

*With monthly maximum demand Bolded values are statistically significant at the 95% confidence level; bolded rows are variables used in the nonstationary generalized extreme value distribution as covariates.


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approach has two main components. First, EVA models based on weather attributes are created for the two variables related to water demand extremes. The second component is a model for generating daily weather sequences and, consequently, the weather attributes, which are then combined with the EVA models to generate projections of water demand extremes. EVA models for water demand extremes. Haagenson (2012) described in detail the motivation for EVA models along with their development for water demand extremes data for the same study location chosen for the current research. The two models are described briefly in the following sections. Modeling monthly maximum water demand. Monthly maximum demand, which is the maximum of a block of a seasonal (June–August) month, is modeled using generalized extreme value (GEV) distribution. This distribution results from statistical theory as the limiting distribution of the maximum of a series of independent and identically distributed observations (Katz & Naveau, 2002; Coles, 2001; Leadbetter et al, 1983). The cumulative distribution function of the GEV is

 –  1+  G (z; ) = e

z–µ 



–1

 – 

(1)

in which  = [µ, s, j] are the location, scale, and shape parameters, respectively, and z is the dependent variable (in this case, monthly maximum demand). The location parameter, µ, indicates the center of the distribution or the mean; the scale parameter, s, represents the spread of the distribution or the variance; and the shape parameter, j, represents the behavior of the distribution in the tail. The GEV is a better modeler of heavy-tailed distributions than traditional probability distributions and therefore is preferable for modeling extremes (Katz & Naveau, 2002). Extremes vary with time and are also modulated by external variables (i.e., nonstationarity). For example, water demand extremes have been shown to be related to weather attributes (Haagenson, 2012), and stream flow extremes have been shown to be modulated by large-scale climate and meteorological variables (Towler et al, 2010; Sankarasubramanian & Lall, 2003). Therefore, to model the nonstationarity, the parameters of the GEV have to be related to the external variables or covariates (Table 2). To this end, the GEV distribution parameters can be modeled as a function of covariates as shown in Eqs 2–4 (Katz & Naveau, 2002): µ(x) = 0,µ + 1,µx1 + … + n,µxn

used in a generalized linear model (Katz & Naveau, 2002). If there are several covariates, the best combination of covariates is selected using a likelihood ratio test. In the likelihood ratio test, models are fit with various combinations of the covariates and then are compared in pairs based on their values of the likelihood function (Katz & Naveau, 2002; Coles, 2001), which selects a skillful yet parsimonious model. Variations of the nonstationary GEV idea have been developed for flood frequency modeling (Rajagopalan, 2010; Sankarasubramanian & Lall, 2003). Towler and colleagues (2010) recently applied the nonstationary GEV approach for modeling maximum stream flow and, consequently, water quality extremes for both seasonal timescale and multiple-decade timescales under climate change. The two forms of extreme value modeling—the block maximums and points-over-a-threshold approach—provide a strong capability to characterize extremes at a variety of time scales that are of use in water supply planning. Modeling water demand exceeding a specified threshold. Block extremes (as described in the previous section) are based on selection of a single value within a block; as a result, significant quantities of data are discarded, which can be undesirable, especially when the dataset is limited. A complimentary approach is to use the points-over-a-threshold method to model the extent to which a threshold is exceeded. In this method, a threshold is selected (often based on the system application), and the probability of exceeding that threshold is modeled as a Poisson process with parameter l, whereas the magnitude by which the threshold is exceeded is modeled using a generalized Pareto distribution (GPD) as in Katz and Naveau (2002) and Coles (2001). The GPD is x F (x; ; ) = 1 – 1 +   



 

– 1–

(5)



in which x is the water demand, s is the scale parameter, and j is the shape parameter. Similar to the GEV described previously, to model nonstationarity, the dependence of the parameters to covariates is introduced as shown in Eqs 6–8: log [(x)] = 0, + 1,x1 + … + n,xn(6)  (tx) = (7)

(2)

log () = 0, + 1,x1 + … + n,(8)

log [(x)] = 0, + 1,x1 + … + n,xn(3)

in which the variables x1, x2, …, xn are the covariates (which can include time as a covariate to consider a temporal trend) and betas are the coefficients. Again, the shape parameter is generally not varied because it tends to be noisy, but like location and scale, it can be varied if desired. As in the case of the GEV, the parameters are estimated via maximum likelihood estimation, and the best combination of covariates is selected using the likelihood ratio test (Katz & Naveau, 2002; Coles, 2001). The point process approach has also been suggested as a way to model—in a single model—water demand exceeding the specified threshold (Furrer et al, 2010; Smith, 1989).

 (t) = (4)

in which the variables x1, x2, …, xn are the covariates that can include “time” to consider a temporal trend and the betas are the coefficients of the regression. The shape parameter, like location and scale, can be varied but generally is not because it tends to be noisy. The form provided here is reminiscent of a generalized linear model (McCullagh & Nelder, 1989). The coefficients are estimated using the maximum likelihood approach commonly


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Generating daily weather sequences under climate change. The covariates in the extreme value models are weather attributes that are based on daily weather information, as mentioned previously (Tables 1 and 2); therefore, daily weather sequences are necessary. A rich literature is available on stochastic weather generation— both traditional parametric techniques (Furrer et al, 2010; Parlange & Katz, 2000; Richardson & Wright, 1984) and recent nonparametric techniques (Apipattanavis et al, 2007; Yates et al, 2003; Rajagopalan & Lall, 1996). Nonparametric weather generators based on time series bootstrapping (Yates et al, 2003; Rajagopalan & Lall, 1996) are simple and robust to implement. Furthermore, they can easily be modified to generate weather sequences conditioned on climate forecasts or projections (Apipattanavis et al, 2007). In the current research, the authors proposed the use of a block bootstrapping approach (Efron & Tibshirani, 1993) in which blocks of historical years—and the entire daily weather sequences associated with them—are selected at random. Sampling blocks of historical data and combining them to generate a rich variety of weather sequences are similar to generation from the multivariate probability density function (Efron & Tibshirani, 1993). In addition to being easy to implement, this approach captures the variability at low frequency. In the current application, the

TABLE 3

Two climate change scenarios used in stochastic weather generation

Scenario

GCM/Ensemble*

30-Year Precipitation Change—%

30-Year Average Temperature Change—°F

Warm/wet

NCAR_CCM3-0.2

3.77

3.40

Warm/dry

Micro3_2_medres1

–8.51

3.40

*GCM ensembles are from leading climate models. CCM3—community climate change model 3, GCM—global climate model, NCAR—National Center for Atmospheric Research

TABLE 4

GEV distribution model

Variable

Nonstationary Model µ = β 0 + β 1(a) + β 2 (b) + β 3 (c) + β 4(d)*

β0

91.08

β1

0.60

β2

–0.97

β3

–0.29

β4

0.33

Location parameter µ

(nonstationary)

Scale parameter σ

9.98

Shape parameter ξ

–0.15

Negative log likelihood

238.82

* In which (a) is the longest monthly spell with minimum temperatures above a threshold, (b) is the longest monthly spell with precipitation above the threshold, (c) is the monthly average maximum temperature, and (d) is time GEV—generalized extreme value

authors chose 30-year blocks. Other sampling approaches based on k-nearest neighbor bootstrap on a daily timescale can be used (Apipattanavis et al, 2007); however, the authors selected the block bootstrap for the sake of parsimony. Precipitation and temperature trends for the simulation horizon were obtained from climate change projections (Table 3). These trends were imposed onto the daily weather sequences from the block bootstrap to obtain sequences conditioned on climate change projections. This approach is widely used in hydrologic applications, and Rajagopalan and co-workers (2009) used this to simulate stream flow in the Colorado River Basin to investigate water supply risk under climate change. Executing bootstrap resampling with an imposed trend enables water demand projections to be used to inform decisions related to water resource needs.

Results A planning horizon of a 30-year period was selected, and the two plausible scenarios—warm/wet and warm/dry—were chosen on the basis of the climate change report for the study region (Ray et al, 2008). Table 3 shows the associated precipitation and temperature trends. Daily weather sequences were generated based on the methods described in the previous section, and the weather attributes were developed from these sequences. Nonstationary models for maximum monthly demand and demand above a threshold were fitted to the historical data; the models are the same as those developed in Haagenson (2012) and are shown in Tables 4 and 5. For each of the EVA models, the fit diagnostics provided confidence that the models were performing well; the figures were not included here in order to focus on the projections. Additional information on the extreme value models used for the current analysis is available elsewhere (Haagenson, 2012). Monthly maximum water demand projections. The authors generated 100 weather ensembles (each 30 years long) for the two climate change projection scenarios and also without the climate change trends to approximate natural variability. Table 2 shows the weather attributes from these ensembles, which were used in the stationary GEV model to generate projections of monthly maximum water demand. Figure 1 shows the water demand projections for the natural variability (part A of the figure), warm/wet (part B), and warm/dry (part C) scenarios. Clearly, water demand trends upward for the city of Aurora under climate change projections. Even under a warm/wet projection in which rainfall is projected to increase, the increasing trend in temperature appears to negate the precipitation effect and increase the water demand. This is likely because increasing temperatures lead to increased evaporative losses and thus create more demand for water (Arbués et al, 2003). The probability density function (PDF) of the monthly maximum demand from the warm/dry scenario is shifted to the right, relative to the PDF from natural variability (Figure 1, part D). This shift translates into increased risk of higher demands, which tend to stress the system and also affect infrastructure planning decisions. Figure 1, part F, shows the number of water demands exceeding 90 mgd for the three climate projections; here, too, the number of water demands over the 90-mgd threshold increases substantially under climate change, relative to natural variability.


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FIGURE 1 Projections of monthly maximum water demand

140

A

140 120 Projected Maximum Monthly Water Demand—mgd

Projected Maximum Monthly Water Demand—mgd

120 100 80 60 40 20 2010

2015

2020

2025

2035

2030

Year

C

100 80 60 40 20 2010

2040

0.07

80 60

2035

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D

0.04 0.03

0.01

20 2010

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100


Year

E

F 60 Monthly Demands Above 90 mgd

0.06 0.05

PDF

2025

0.02

40

0.04 0.03 0.02 0.01 0.00

2020

0.05

100

0.07

2015

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120

PDF


140

B

50

40

30

20 40

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90

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Historical


Warm/Wet

Warm/Dry

Climate Scenario

GEV—generalized extreme value, PDF—probability density function Projections of monthly maximum water demand from the nonstationary GEV model are shown for natural climate variability (part A), warm/wet future climate (part B), and warm/dry future climate (part C). Part D shows the PDFs of monthly maximum water demand projections for a warm/wet future climate (gray lines are from the individual simulations; blue line shows the average) and natural climate variability (red line). Part E shows the PDFs of monthly maximum water demand projections for a warm/dry future climate (gray lines are from the individual simulations; blue line shows the average) and natural climate variability (red line). Part F shows the box plots of the number of monthly maximum demands over the 90-mgd threshold for the three scenarios, i.e., natural variability (historical), warm/wet, and warm/dry.


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TABLE 5

Generalized Pareto distribution and Poisson models used for projections

Variable

Nonstationary GPD Model* σ = β 0 + β 1 (a) + β 2 (b) + β 3 (c) + β 4 (d)

Nonstationary Poisson Model† λ = β 0 + β 1(a 2) + β 2(b 2) + β 3(c2) + β 4(d2)

β0

7.43

–13.119

β1

–0.28

0.111

β2

0.59

0.071

β3

–1.24

3.899

β4

–0.01

0.005

Scale parameter σ

(nonstationary)

Shape parameter ξ

–0.34

Negative log likelihood

623.45

GPD—generalized Pareto distribution Blank cells indicate the parameter does not exist for those models because they are stationary. *In which (a) = daily maximum temperature, (b) = daily minimum temperature, (c) = daily precipitation, and (d) = time †In which (a ) is the longest monthly spell with minimum temperatures above a threshold, 2 (b2) is the longest monthly spell with precipitation above the threshold, (c2) is the monthly average maximum temperature, and (d2) is the preceding month average water demand

Projections for water demand exceeding the threshold. For these projections, the parameter of the Poisson process was estimated based on the covariates and, consequently, the number generated for the times the threshold was exceeded. The threshold selected was 90 mgd, and then the magnitude (i.e., the extent to which the threshold was exceeded) was generated from the GPD model. Figure 2 shows the generated number of times the threshold was exceeded for the three projection scenarios: natural variability (part A of the figure), warm/wet (part B), and warm/dry (part C). As expected, the number increased over time for the warm/wet and warm/dry cases, relative to natural variability. The PDF of these water demands above the threshold from the warm/wet and warm/dry scenarios (Figure 2, parts D and E, respectively) shifted to the right, relative to that from natural variability, indicating higher probability of increased demand above the 90-mgd threshold. The realized differences between Figure 2, parts D and E, are relatively small, however. The GPD model, when coupled with the Poisson model (Table 5), provides the whole picture for water demand, and it will be shown subsequently that the frequency of demand exceeding the threshold (Poisson model) affects water demand to a far greater extent than does the magnitude of the demand (GPD). Figure 3 shows the implications of a varying Poisson model. Part A of the figure shows the PDF of generated magnitude for the warm/wet climate projections, and part B shows the same for the warm/dry scenario. In both cases, it can be seen that the PDFs from climate change projections have shifted to the right (relative to natural variability), indicating higher magnitude of exceeding the threshold. The effect of climate change is more clearly experienced in the frequency rather than in the magnitude of exceeding the threshold. This can be seen in Figure 3,

part C, which shows the box plots of the average magnitude (the extent to which the threshold was exceeded) for the three climate scenarios. For the warm/wet and warm/dry cases, the average magnitude and variability are approximately 1 mgd higher than for natural variability. Moreover, it is clear that temperature was driving the water demand projections because the warm/dry and warm/wet projections were similar. These results were consistent with results from the GEV model and suggest that precipitation has a smaller role than temperature in modulating water demand.

Summary and Discussion The authors proposed an integrated approach to projection of water demand extremes under climate change scenarios. The approach features two main components. First, extreme value models based on climate attributes are created for water demand maximums and water demand exceeding a specified threshold, and these models are fitted to historic water demand data and weather attributes. Second, ensembles of future weather sequences and, consequently, weather attributes are generated, conditioned on climate change projections using a bootstrapping technique that is combined with the extreme value models to generate ensembles of water demand extremes. This approach was demonstrated using water demand extremes data from the Aurora water utility. Two climate change scenarios—warm/wet and warm/dry—were determined for this region (Ray et al, 2008) and were used to conditionally generate daily weather sequences. Monthly maximum water demand and water demand over a 90-mgd threshold were modeled using EVA. The Aurora results suggested that under climate change, both the frequency and intensity of extreme water demand periods were likely to rise and the probability of the city experiencing extreme water demand situations at a frequency and magnitude greater than previously experienced would also increase. The methodology described here for projecting water demand extremes under climate change should be of great use to water utility planners and water managers. The proposed approach provides a framework to translate uncertainties in climate projections to uncertainties in water demand extremes. Such a robust quantification enables more-informed, risk-based decision-making for operational and infrastructure planning. Results suggested that the risk of extreme water demand situations would increase for Aurora. The analysis performed for the city can be applied to other utilities, which could incorporate even more information (based on nuanced knowledge of their individual systems) to provide robust projections of water demand under climate change. Furthermore, additional social and economic variables and their projections could be incorporated into the modeling framework, thus providing flexibility to integrate other knowledge of a system. Sophisticated methods for stochastic weather generation (Apipattanavis et al, 2007; Yates et al, 2003) can be used to generate a rich variety of daily sequences and add further nuance to the approach presented here. Other simulation techniques for demand exceeding a certain threshold, such as those developed by Furrer and colleagues (2010) for heat wave spells, could also be used to enhance these modeling techniques.


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A

15

10

5

0 2010

2015

2020

2025

2030

2035

2040

Monthly Water Demand Above 90 mgd—days


FIGURE 2 Generated number of demands exceeding the 90-mgd threshold for the three projection scenarios B

15

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5

0 2010

2015

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D

0.30

2040

Projections with natural variability Projections with imposed warm/wet trend

0.25 10

0.20 PDF


2035

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5

0.15 0.10 0.05

0 2010

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0.30

0.00

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0.25

PDF

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0

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Projected Monthly Demand Above 90 mgd—days GEV—generalized extreme value, PDF—probability density function Projections of monthly maximum water demand from the nonstationary GEV model are shown for natural climate variability (part A), warm/wet future climate (part B), and warm/dry future climate (part C). Part D shows the PDFs of monthly maximum water demand projections for a warm/wet future climate (gray lines are from the individual simulations; blue line shows the average) and natural climate variability (red line). Part E shows the PDFs of monthly maximum water demand projections for a warm/dry future climate (gray lines are from the individual simulations; blue line shows the average) and natural climate variability (red line).


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FIGURE 3 Implications of a varying Poisson model B

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Projected Magnitude of Water Demand Above 90 mgd—mgd

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Projected Magnitude of Water Demand Above 90 mgd—mgd

Average Magnitude of Water Demand Above 90 mgd—mgd

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Climate Scenario PDF—probability density function Part A shows PDFs of projected magnitude of demand above 90 mgd for a warm/wet climate projection (gray lines), warm/wet average (blue line), and natural variability average (red line). Part B shows PDFs of the magnitude of monthly demand above 90 mgd for a warm/dry climate projection (gray lines), warm/dry average (blue line), and natural variability average (red line). Part C shows box plots of average magnitude of demand above 90 mgd for natural variability (historical) and warm/wet and warm/dry climate projections.

Acknowledgment The authors gratefully acknowledge funding for this research provided by a grant from the National Oceanic and Atmospheric Administration Sector Applications Research Program through AWWA. They also thank Alfredo Rodriguez of Aurora Water in Aurora, Colo., for providing water demand data and the National Center for Atmospheric Research Advanced Study Program 2011, which provided the solid extreme value analysis that served as a foundation for this research.

About the authors Erik Haagenson (to whom correspondence should be addressed) is a water resources engineer with Riverside Technology, 2950 E. Harmony Rd., Ste. 390, Fort Collins, CO 80528; [email protected]. He holds a BS degree in

applied mathematics from Montana State University in Bozeman and an MS degree in civil engineering from the University of Colorado in Boulder. He has worked on the issue of climate change and water demand for three years, focusing on the statistical modeling of water demand and creating enhanced weather attributes to use in water demand modeling. His current work focuses on international water resources management and water resources management under climate change. Balaji Rajagopalan and R. Scott Summers are professors in the Department of Civil, Environmental, and Architectural Engineering at the University of Colorado in Boulder. J. Alan Roberson is director of federal relations at the AWWA Government Affairs Office in Washington, D.C.


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Peer review

Kenney, D.; Goemans, C.; Klein, R.; Lowrey, J.; & Reidy, K., 2008. Residential Water Demand Management: Lessons From Aurora, Colorado. Journal of the American Water Resources Association, 44:1:192.

Date of submission: 08/21/2012 Date of acceptance: 10/29/2012

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