Working Paper 2008-09
Forecasting Single-Family Residential Water Consumption for Phoenix and
Paradise Valley, Arizona
Jamie Patterson and Elizabeth A. Wentz
Forecasting single-family residential water consumption for Phoenix and Paradise
Valley, Arizona
Jamie Patterson a,*
and
Elizabeth A. Wentz a
a
Arizona State University
School of Geographical Sciences
Tempe, AZ 85287-0104
USA
* corresponding author, jpatterson44@gmail.com
wentz@asu.edu
Submitted to Computers, Environment and Urban Systems, July 2008
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Forecasting single-family residential water consumption for Phoenix and Paradise
Valley, Arizona
Abstract. We developed four scenarios to forecast the impacts of policy measures
affecting new housing unit lot sizes on single-family residential water consumption for
the City of Phoenix and Town of Paradise Valley, Arizona. Policies approximated the
statistical distribution of year 2000 lot sizes or produced smaller lot sizes. Policies
mirrored the year 2000 spatial pattern of lot sizes or were distributed with higher
densities (smaller lots) near transportation corridors. Along with lot size, we used census
tract level parameters from year 2000 water estimates for percent homes with pools,
percent homes with mesic landscaping, and mean household size to forecast water
consumption. Each scenario was modeled with a local geographically weighted
regression (GWR) model and a global ordinary least squares regression (OLS) model.
This is the first study to apply GWR to forecasting. A policy mirroring the year 2000
spatial pattern of lot sizes with smaller lots produced the lowest mean annual housing unit
water consumption at 214.77 ccf. Higher density lots along transportation corridors
would have little impact on consumption. GWR forecasted lower per capita water
consumption than the OLS for all scenarios. Our approach should be used in other
forecasts exploring policy implications for natural resource management.
Keywords: spatial forecasting, residential water consumption, geographically weighted
regression
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1. Introduction
Water is essential for human existence requiring extensive management,
particularly in urban areas where supplies and infrastructure must meet the needs of a
heterogeneous and growing population. As population grows in urban areas, ensuring a
long-term, safe and reliable source of potable water becomes essential. Determining the
amount of water needed by residents is an integral component to water management. The
research here focuses on forecasting single-family residential water consumption for the
City of Phoenix and Town of Paradise Valley under different growth and development
plans. Management for water in the City of Phoenix and Town of Paradise Valley is
needed because climatic uncertainty threatens future water supplies in an area where
projections show the Phoenix metropolitan statistical area doubling in population around
the year 2050 (ADES, 2006).
Residential water consumption research has investigated aspects such as the
overall cost of water (Arbues, Barberan, & Villanua, 2004; Kenney, Goemans, Klein,
Lowrey, & Reidy, 2008), the use of different billing practices (Olmstead, Hanemann, &
Stavins, 2007), the impact of policy decisions (Vickers, 1993), and the effectiveness of
water conservation (Michelsen, McGuckin, & Stumpf, 1999). For desert cities, such as
Phoenix, research into water use has evaluated residential water use from several
perspectives, including the impact of the urban heat island, factors that influence
residential water consumption, and the employment of Bayesian Maximum Entropy
(BME) to handle uncertainty associated with modeling (Lee, Balling, & Gober, 2008).
Guhathakurta and Gober (2007) found a temperature rise of 1°F, due to urban heat island
effects, would increase monthly residential housing unit water demand in the City of
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Phoenix by 290 gallons. Wentz and Gober (2007) modeled the effects of indoor and
outdoor residential characteristics single-family residential water consumption rates in
the City of Phoenix, Arizona. They found that household size, the presence of a pool,
irrigated landscaping, and lot size significantly influenced water consumption. Missing
from the above research is an approach to better understand the effects of planning and
policy choices on the spatial distribution of future residential water consumption.
A broad set of literature exists on the theory, techniques, and applications of
forecasting in fields including economics and econometrics, finance, technology,
demographics, energy, climate, crime, implementation research, psychology, uncertainty
in decision making, and evaluation of forecasting methods and approaches (Hyndman,
2007). Scenario generation has been an established tool in land use planning for many
decades (Xiang & Clarke, 2003). Ordinary least square (OLS) regression has been
successfully used for modeling and forecasting dependent variables. Briggs et al (1997)
modeled traffic-related air pollution in Amsterdam, Huddersfield, and Prague with OLS.
Mapped comparisons of modeled versus actual pollution across referenced points
revealed accuracies ranging from 79 to 87 percent. In a geographic context, OLS assumes
coefficients are globally constant, or stationary, over an entire region. Given that many
social processes are not stationary, this assumption is frequently violated. Fotheringham
et al (2002) developed geographically weighted regression (GWR), which assumes some
relationships between variables are non-stationary over geographic space. GWR not only
identifies the degree to which variables influence outcomes, it sheds light on how local
conditions influence variables. Location-specific insights may be used to generate new
hypotheses and build more effective models. To date, GWR has been confined to
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historical or existing environments, largely in social science research. In a recent
example, Yu (2007) modeled owner-occupied single-family house values in the City of
Milwaukee, Wisconsin and determined housing unit characteristics, including floor size,
air conditioners, number of bathrooms, and fireplaces add more value to houses in
wealthier areas than in less affluent areas.
Given the successful application of GWR in historically-based studies, a logical
next step is its inclusion in forecasting to estimate future outcomes. Our research does
this, expanding the approach and dataset of Wentz and Gober (2007) to the realm of
forecasting. The research here is two-fold. The first objective is to forecast water
consumption rates for the City of Phoenix and Town of Paradise Valley, Arizona with
four different arrangements of single-family residential housing (Table 1). Lots for new
housing units either approximate the statistical distribution of year 2000 mean lot sizes or
they have smaller lots sizes than the year 2000 distribution. New lots either mirror the
spatial distribution of year 2000 lot sizes or they are distributed as high (smaller lots),
medium, or low density, based on their distance to transportation corridors. The second
aim is to compare these four scenarios using two different modeling techniques, ordinary
least squares (OLS) and geographically weighted regression (GWR).
The scenarios are compared by assessing which ones identifies a management
plan that reduces mean per capita water consumption and which ones reduces overall
water consumption for the study area. We anticipate that the scenario with smaller lots
and new residential growth occurring along transportation corridors will be the best
performing scenario for goals (a) and (b). We also hypothesize that the use of local
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parameters for GWR models would more accurately estimate water consumption than the
use of global coefficients for OLS models.
[Table 1]
2. Background on urban water consumption
A set of complex issues arising from urban environments make water
management a challenging task. Infrastructure must accommodate high demands for a
diverse set of uses. Consumers exhibit various behaviors that may correlate with
residential characteristics, some difficult to capture in models. Some studies shed light on
urban water use through the assessment of variables with indirect effects. Grove et al
(2006) measured the impacts of population density, lifestyle behavior, and social
stratification on urban vegetation. They determined lifestyle behavior was the best
predictor of vegetation cover on private lands. This type of relationship could be used to
show the indirect effects of behavior on water consumption.
Peculiar climatic conditions arise in cities where pavement and building materials
retain heat for a longer period of the day than objects in the natural environment. The net
result is an “island” of higher urban temperatures. Studies suggest heat island effects
contribute to increased housing unit water consumption rates in Phoenix (Guhathakurta &
Gober, 2007). This is relevant to our study because alternate distributions of residential
density may lead to different heat island patterns that could influence single-family water
consumption rates.
Various resource management studies quantify factors affecting demand. Recent
approaches include econometrics (Babel, Das Gupta, & Pradhan, 2007; Mylopoulos,
Mentes, & Theodossiou, 2004; Reynaud, 2003), agent based modeling (Athanasiadis,
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Mentes, Mitkas, & Mylopoulos, 2005), and fuzzy logic (Altunkaynak, Ozger, &
Cakmakci, 2005).
Residential water demand is often estimated as a function of housing unit
characteristics. Mayer et al. (1999) studied housing unit water consumption in twelve
U.S. cities. They concluded variation in indoor use was affected by household size
(persons) and building square footage. Variation in outdoor consumption was most
strongly affected by the presence of a pool. The addition of a pool would more than
double usage compared to a home without a pool. Jacobs and Haarhoff (2004a; 2004b)
created a model for residential water demand where end-uses, such as bathing, toilet
flushing, gardening, and pool use are represented as parameters that can predict indoor
and outdoor demand.
Newer approaches to addressing water demand include fuzzy logic. This is based
on fuzzy set theory where elements or objects are attributed varying degrees of
membership in the set. This is counter to the traditional notion of a set where an object
must have full membership or none at all. In one example of this, Altunkaynak, Ozger,
and Cakmakci (2005) applied a fuzzy logic to water consumption forecasting in Istanbul,
Turkey. This method predicted future monthly water consumption rates from prior water
consumption amounts, which served as independent variables. Predicted values possessed
an error rate of less than ten percent from actual values.
Williamson, Mitchell, and McDonald (2002) captured changes in water
consumption behavior for the Yorkshire Water region in the United Kingdom by
reweighting spatially detailed synthetic microdata to demographic trends. Results
forecasted overall domestic water increasing by 30 percent from 1991–2025 and ranging
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from 11 percent to 46 percent among electoral districts. Bradley (2004) surveyed multiple
regions for determinants of water consumption including the United Kingdom, Malaysia,
South Korea, and South Africa. He concluded gains in socio-economic status would not
necessarily lead to the same increase in consumption for all study areas. Instead he
advocates a micro-area approach to urban water projections to account for local
conditions.
3 Methods
3.1 Study area
The study area includes the City of Phoenix, the economic, cultural, and political
hub of Arizona and the neighboring upscale Town of Paradise Valley, Arizona. Covering
approximately 500 square miles, Phoenix is the largest city in the southwestern United
States, an area even larger than Los Angeles (City of Phoenix, 2008a). Paradise Valley
covers only 16.5 square miles (MAG, 2008). With just over 1.5 million residents, the
City of Phoenix recently surpassed Philadelphia as the fifth largest city in the nation (US
Census Bureau, 2006). Phoenix averages about 3,000 persons per square mile. In
contrast, Philadelphia averages over 11,000 persons per square mile (US Census Bureau,
2006). This difference has significant implications for the underlying determinants of
housing unit water consumption. The lower mean density suggests that single-family
residential housing units in Phoenix have larger lots than in Philadelphia. This likely
translates into a higher share of outdoor water use per housing unit for Phoenicians,
mostly from pools and landscaping. This is confirmed by a study suggesting 74 percent
of residential water consumption in Phoenix is for outdoor uses (Mayer et al., 1999).
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Recent efforts to revitalize downtown Phoenix and the vicinity with a stronger
sense of social and economic gravity include the development of sporting venues,
restaurants, and high-rise condominiums in and around Copper Square, and the ongoing
construction of a light-rail system that will link downtown with Sky Harbor Airport,
Tempe, and Mesa. Due to limits on developable land, new home construction in these
areas will be sparse, most likely with small lots and modestly sized houses. These factors
would translate into a large share of water consumption coming from indoor, rather than
outdoor sources. Citywide, this area is expected to have little impact on changes in future
water consumption rates.
Despite these initiatives, growth in Phoenix is being propelled outward by the
automobile. Major freeway expansions are underway, ensuring expanded urban footprints
over the coming decades. Most future single-family residential development is expected
to occur north of the Loop 101 freeway and south of downtown in the vicinity of the
South Mountains (Figure 1). Residential construction is expected to continue at a steady
pace, replacing desert habitats and agricultural lands.
[Figure 1]
While the trend in new single-family residential construction for Phoenix is
smaller lots than in previous decades, it is difficult to predict new density patterns. This is
due to the fact that most new growth will predominantly occur in vast stretches of land
where the number of existing housing units is low. In Paradise Valley land use is mostly
residential, zoned for one acre lots with one house per lot (MAG, 2008). Therefore, it is
reasonable to assume the density of new development and the resulting levels of water
consumption will follow historical patterns more closely than in Phoenix.
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The vitality of Phoenix and Paradise Valley depends on the availability and access
to natural resources, especially water for human consumption. The juxtaposition of a
large metropolis with the arid Sonoran desert necessitates a vast system of canals and
reservoirs to supply residents with water from distant sources. The population of the City
of Phoenix is projected to grow to over 2.2 million by 2030, and to exceed six million in
Maricopa County by 2030 (MAG, 2007b). These projections, coupled with the risk of
drought and potentially dwindling water supplies, make forecasting of residential water
consumption a critical need for long-term regional planning.
3.2 Data
The dependent variable in this study is mean water consumption per census tract
(measured in ccf) for single family residential housing for the year 2000. We obtained
these data from the City of Phoenix, Water Services Department. Consumption rates for
Paradise Valley are included in the dataset and accordingly are used for this study.
We used four dependent variables used by Wentz and Gober (2007) to capture
variation in indoor and outdoor water consumption. One dependent variable, singlefamily residential household size per census tract, for the year 2000, which we obtained
from the U.S. Census Bureau, accounts for indoor usage. The intuitive notion that larger
households (more people) in Phoenix typically use more water, mostly through indoor
appliances and plumbing fixtures, has been confirmed by empirical studies (Mayer et al.,
1999).
Other independent variables from Wentz and Gober (2007) are hypothesized to
capture variation in outdoor consumption. Data on lot sizes and the presence of pools
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were acquired from the Maricopa County Assessor’s office. Only houses built through
year 2000 were included in these variables. We hypothesize that lot size is positively
correlated with consumption. More land increases the possibility of larger building
footprints with more plumbing fixtures that might lead to greater water demand. A likely
outcome of larger lots is outdoor areas being used for pools and landscaping, both
requiring significant amounts of water.
A spatial breakdown of mesic versus xeric landscaping practices was quantified
through an expert systems land use classification, based on a 1998 Landsat TM image
(Stefanov, Ramsey, & Christensen, 2001). This system produced an overall accuracy of
85 percent. Most new residential houses in Phoenix have instituted xeriscaping practices,
with native Sonoran Desert vegetation that requires minimal watering. Mesic practices
usually include lawns and leafy plant species not native to arid environments that require
intensive irrigation to thrive in the dry, hot climate of the Valley.
We queried and mapped existing and future single-family residential land uses
(Figure 1) from a spatial database from the Maricopa Association of Governments
(MAG, 2007a). We used a “full-growth” decision rule to account for single-family
residential development for all four scenarios. At “full-growth” all potentially
developable land in the City of Phoenix and Town of Paradise Valley would be converted
to developed land categorized as commercial, industrial, mixed use, office, other
employment, transportation, water, multi-family residential, or single-family residential.
The remaining undeveloped lands, such as mountain preserves, become classified as open
space. MAG classifications are based on a combination of existing land use, active,
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planned and proposed developments, and the general plans of the member communities
of MAG, including Phoenix and Paradise Valley (MAG, 2007a).
3.3 Analytical approach
To reiterate we assumed single-family residential development achieves “full
growth”. The first step in estimating developable land for housing units was to estimate
and remove the area in the land use class ‘residential’ that is not part of the residential
lots, such as roads and sidewalks. To do this we calculated the average ratio (R) of total
housing unit lot area from the Maricopa County Assessor’s Office to the MAG year 2000
total single-family residential area (Equation 1). This R value is 0.67.
R=
AssessorLo tArea
MAG _ SingleFamilyresident ialArea
(Equation 1)
The total area per census tract covered by new lots (A) was calculated by
multiplying (R) by the total single-family residential area from the MAG land use data
(Equation 2).
A = R * MAG Single-family residential area
(Equation 2)
To forecast the number of housing units per A for each census tract, we estimated
the average lot size per census tract. We used a random number generator program to
create a normal (Gaussian) distribution of lot sizes (Equation 3), assigning a unique mean
lot size (G) to each census tract. Randomly generated values were calculated at a 95
percent confidence level. The distribution of mean lot sizes for new housing units for
scenarios 1 and 3 was created with the intent of continuing current single-family
residential density levels for new development by mirroring the spatial pattern of existing
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(year 2000) mean lot size per census tract. That is, the lot sizes were ranked from smallest
to largest so that the census tract with the smallest existing mean lot size would also have
the smallest mean lot size for new housing units, and so on. We calculated the log of
existing mean lot sizes per census tract to overcome the problem of negative outputs in
the random value generator. A short-coming of the log transformations is a smaller
standard deviation (421 square meters) than the existing lot size distribution (580.22
square meters).
(Equation 3)
A similar approach was used to randomly generate a normal (Gaussian)
distribution of lot sizes for scenarios 2 and 4. The purpose of these scenarios is to
demonstrate the effects of smaller lot sizes on water consumption than lot sizes in
scenarios 1 and 3. Scenarios 2 and 4 are characterized by a mean lot size per census tract
of 773.97 square meters (8,330.94 square feet) and minimum lot size per census tract of
320.25 square meters (3,447 square feet). This mean lot size was selected to show a
noticeable difference in lot sizes from scenarios 1 and 3, while maintaining a minimum
lot size to meet local housing market expectations. A housing unit with this minimum lot
size in the City of Phoenix, conforming to city zoning ordinances, could fit a one-story
housing structure with as much as 101 square meters (1,084 square feet) of living space
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or a two-story housing structure with as much as 202 square meters (2,186 square feet) of
living space (City of Phoenix, 2008b).
In scenarios 3 and 4 we assigned the statistical distributions of lot sizes according
to decision rules setting maximum housing unit distances from transportation corridors
(Table 1). High density tracts were assigned to census tracts located within a quarter-mile
of the soon-to-be-completed light rail line. A quarter-mile is often used among urban
planners as a measure of the maximum distance most people are willing to walk from
their house to a public transit station. Medium density tracts are located within a halfmile of the light rail or one mile from any highway. All other census tracts beyond the
required distances from transportation corridors are classified as low density. The
densities were chosen with these decision rules to strike a balance with roughly half the
census tracts located in high or medium density areas and roughly half located in low
density areas. The larger objectives of transportation-oriented development are efficient
use of transportation infrastructure and reducing urban sprawl.
Housing unit counts (C) were forecasted at each census tract by dividing the
estimated lot area (A) by the unique randomly generated lot size (G) for that tract
(Equation 4).
C
A
G
(Equation 4)
Overall housing unit counts at “full growth” were calculated by adding the existing
(through year 2000) counts from the Maricopa County Assessor’s office to the forecasted
counts (C). The overall forecasted mean lot size per census tract (F) was calculated
according to Equation 5:
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F
( ExistingLotsize * ExistingHouseholds )  ( NewLotsize * NewHouseholds )
ExistingHouseholds  NewHouseholds
(Equation 5)
3.31 Forecasting single-family residential water consumption
As was mentioned previously, Wentz and Gober (2007) investigated the
determinants of year 2000 single-family residential water consumption in Phoenix. By
comparing the performances of global (OLS) and local (GWR) models, they were able to
identify and analyze four variables (pool size, lot size, percent mesic landscaping, and
household size) that significantly affect consumption. Our study follows that analytical
approach, comparing OLS and GWR models with the independent variables from Wentz
and Gober (2007). We forecasted mean housing unit consumption rates per census tract
for all (existing and new) single-family residential housing units using parameters from
the year 2000 estimates (Tables 2 and 3). Year 2000 data values for percent pools,
household size, and percent mesic landscaping were applied to new housing units
aggregated by census tract for all scenarios. Lot size is the only independent variable that
we changed depending on scenario rules (Table 1). Scenario performance in this study is
based on two factors (a) reducing mean per capita single-family residential water
consumption and (b) reducing overall consumption for the study area. The performance
of “what if” scenarios is grounded in the reliability of the historical data and models on
which they are based.
[Table 2]
[Table 3]
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4. Results
4.1 New lot distributions
The four scenarios in this study differ according to unique combinations of
statistical and spatial distributions of new lots (Table 1). Table 4 summarizes the
statistical distributions of lot sizes for new single-family residential housing units. The
randomly generated normal (Gaussian) distribution of values for new housing unit lots in
scenarios 1 and 3 consists of a mean of 973.12 square meters, a minimum of 336.36
square meters, a maximum of 3,400.82 square meters, and a standard deviation of 421
square meters. The result is a smoothed curve, compared with the statistical distribution
of existing lots, such that low and high values for new lots are lower than their existing
mirrored counterparts, while middle values are higher than existing counterparts (Figure
2a).
[Table 4]
[Figure 2]
When a different randomly generated normal (Gaussian) distribution was created
for new housing unit lots in scenarios 2 and 4, the result was smaller lot sizes than
scenarios 1 and 3 (Table 4). Scenarios 2 and 4 are characterized by a mean of 773.97
square meters, a minimum of 320.25 square meters, a maximum of 2,202.62 square
meters, and a standard deviation of 284.51 square meters. Results show a smoothed
distribution curve for scenarios 2 and 4, compared with the distribution of existing lot
sizes (Figure 2b). In this case, the new lot sizes are all smaller than their mirrored
counterparts from the existing distribution.
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Mean lot sizes for new housing units mirror the spatial pattern of existing housing
unit mean lot sizes (scenarios 1 and 2) or they mirror the spatial pattern of existing
housing unit lot sizes within high, medium, or low density classifications based on
proximity of census tracts to transportation corridors (scenarios 3 and 4) (Figure 3). This
classification scheme produced six high density census tracts, 152 medium density census
tracts, and 144 low density census tracts.
[Figure 3]
The addition of new lots changed the statistical distribution of mean lot sizes from
existing levels. Scenario 1 consists of a mean of 954.43 square meters, a minimum of
448.16 square meters, a maximum of 4,318.60 square meters, and a standard deviation of
487.82 square meters. Scenario 2 is characterized by a mean of 910.82 square meters, a
minimum of 438.87 square meters, a maximum of 3,932.07 square meters, and a standard
deviation of 428.13 square meters. Scenario 3 produced a mean of 949.60 square meters,
a minimum of 483.40 square meters, a maximum of 4,318.60 square meters, and a
standard deviation of 481.07 square meters. Scenario 4 consists of a mean of 906.58
square meters, a minimum of 464.11 square meters, a maximum of 3,932.07 square
meters, and a standard deviation of 422.53 square meters.
4.2 Single-family residential housing unit distribution
We calculated the distribution of single-family housing units by dividing the total
area of new residential land use allocated for lots by the mean lot size for a given census
tract. New housing unit counts were combined with existing housing unit counts to
produce forecasted total housing unit count per census tract (Table 5). The greatest
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number of total housing units was generated by scenario 2 (538,844), followed by
scenario 4 (535,060), scenario 1 (485,954), and scenario 3 (483,681).
The scenarios show little difference in the spatial distribution of housing units.
This is due to the fact that most new housing units are forecasted in a handful of large
census tracts in the northern and southwestern Phoenix, most notably tract 303.42 in the
far northwest corner of the city (Figure 4). Centrally located tracts would experience only
slight changes in housing unit patterns.
[Table 5]
[Figure 4]
4.3 Water usage
There was distinct spatial variation in year 2000 single-family residential housing
unit water consumption rates for Phoenix and Paradise Valley (Wentz & Gober, 2007).
The highest mean housing unit rates were predominantly located in wealthier areas in
Paradise Valley. GWR estimates by Wentz and Gober (2007) suggest increased lot sizes
for those residents would increase water consumption. The lowest average housing unit
consumption rates were found in southwestern and northern Phoenix. Wentz and Gober
(2007) determined that lot size had a slightly positive, or in some cases negative,
relationship with water consumption in those areas.
The addition of new housing units at “full-growth” would nearly double overall
consumption from year 2000 levels (Table 6). A comparison of estimated water usage
among scenarios reveals differences in the contribution of new housing units to total
consumption (Table 6). The highest total consumption for the study area is Scenario 2
(OLS) at 122,352,001 ccf, while the lowest total consumption is Scenario 3 (GWR) at
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105,525,043 ccf. For all scenarios OLS estimated higher total consumption than GWR.
Differences between OLS and GWR range from 8,934,986 ccf for Scenario 3 to
6,624,213 ccf for Scenario 2.
[Table 6]
At 1,633,921 ccf, residents of census tract 303.42 consumed the most water of
any tract in year 2000 (Table 6). In all forecasts residents of tract 303.42 also generated
the highest overall consumption (Table 6). Forecasted consumption for the tract ranges
from 15,819,660 ccf for scenario 2 OLS (almost a ten-fold increase from year 2000) to
9,939,277 ccf for scenario 3 GWR (about a six-fold increase from year 2000).
Changes in the mean lot sizes and spatial distribution of new housing lots among
the scenarios resulted in departures from the mean household unit consumption for year
2000 of 222.05 ccf. Mean housing unit consumption ranged from 214.77 ccf in Scenario
2 (GWR) to 236.64 ccf in Scenario 3 (OLS).
The spatial distributions of mean housing unit water consumption for GWR and
OLS models are illustrated in Figures 5 and 6. The scenarios generally retained the
spatial pattern of mean year 2000 housing unit consumption, where residents of Paradise
Valley consumed the highest average levels of water and residents in scattered locations
throughout central Phoenix consumed lower amounts of water.
[Figure 5]
[Figure 6]
4.4 Scenario comparisons
Comparisons of scenarios are organized based on shared spatial and statistical
distributions of lot sizes. To account for the effects of transportation corridors on water
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consumption, we subtracted mean housing unit water consumption per census tract for
Scenario 1 (mirrors existing lot sizes and pattern) from Scenario 3 (mirrors existing lot
sizes with transportation corridors) (Figures 7a and 7b). To account for the effects of
smaller lot sizes on water consumption, we subtracted mean housing unit consumption
for scenario 1 (mirrors existing lot sizes and pattern) from Scenario 2 (smaller lot sizes,
mirrors existing lot size pattern) (Figures 7c and 7d).
Mean housing unit water consumption rates are lower along transportation
corridors in central Phoenix for Scenario 3 compared with the mirrored pattern of lot
sizes in Scenario 1. Lower density developments with larger lots are located on the
fringes of Phoenix, such as census tract 303.42. The mixed pattern of consumption
produced little change in overall consumption between Scenarios 1 and 3 (Table 6). This
indicates that transportation corridors would not be an effective tool in reducing water
consumption.
The introduction of smaller lots led to lower mean water consumption for most
census tracts (Figures 7c and 7d). This is most pronounced in Paradise Valley for the
GWR model. In contrast, lot size for the GWR model appears to have a minor or even
negative relationship with mean housing unit consumption in southern Phoenix.
[Figure 7]
5. Discussion
5.1 Patterns of lot distribution
Changing the mean lot size and spatial distribution of lot sizes impacted patterns
of lot distribution. Regardless of the introduction of smaller lots or high density
transportation corridors, only subtle shifts in lot counts appear in central Phoenix where
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there is little room for new single-family residential growth. In north Phoenix and, to a
lesser degree, southwest Phoenix where large areas of land are available for development,
reducing mean lot size (scenarios 2 and 4) had the effect of increasing the overall number
of housing units for the study area, while reducing mean consumption per housing unit.
With smaller lot sizes scenario 2 produced 52,890 more new housing units than scenario
1, an increase of almost 11 percent. Scenario 4 generated 51,379 more new housing units
than scenario 3, an increase of almost 11 percent. In this instance, 37,679 new lots are
from tract 303.42. This lesser role is due to the inclusion of higher densities along
transportation corridors that led to larger lots being assigned to tract 303.42.
With higher density development along corridors, Scenario 3 generated 2,273
fewer housing units than Scenario 1 where lot sizes mirrored the pattern of existing
housing units. Scenario 4 generated 3,784 fewer lots than scenario 2. The slight reduction
is number of households in these cases suggests transportation corridors would only have
a marginal influence on urban growth rates. Given the small amount of land designated
for single-family residential development in the vicinity of the light rail corridor (Figure
1), the area had little effect on lot distributions in any of the scenarios. In addition, there
is limited land for new residential development along the I-17 and SR 51 freeways in
central Phoenix (Figure 1).
5.2 Water consumption patterns
“Smart growth” promotes higher density development in the urban core, along
with transit-oriented development, as part of a larger objective of limiting excessive
urban sprawl. Ideally, this would reduce the impact of development on the natural
21
environment, while reducing the overall demand for single-family residential water use.
In our study higher density development is represented, in part, through smaller lot sizes
(scenarios 2 and 4) and also through higher density development along transportation
corridors (scenarios 3 and 4). Forecasts reveal smaller lots played a significant role in
reducing per capita water consumption by allowing less area for outdoor sources of
consumption, including landscaped vegetation and pools. They also reduce the size of
building footprints, possibly restricting indoor water consumption. Forecasts indicate
higher density development along transportation corridors had a minimal effect on
consumption rates. The existing pattern of lot sizes mirrored for new development in
scenarios 1 and 2 is already more dense in central Phoenix where most transportation
routes are located.
At 214.77 ccf per housing unit scenario 2 (GWR) was the most effective scenario
with respect to goal (a): reducing mean per capita water consumption for the study area.
Mirroring the existing pattern of lot sizes with higher density along transportation
corridors, scenario 3 was the worst performing scenario with a mean housing unit
consumption of 236.64 ccf. With respect to goal (b): reducing total water consumption
for the study area, scenario 3 (GWR) was the best performing scenario with 105,525,043
ccf of consumption. Scenario 2 OLS was the worst performing scenario at 122,352,001
ccf of water consumption.
The main take-home message of this study is that planners and policy-makers
should aim to implement rules that promote small lots for new single-family residential
housing to reduce per capita water consumption. This approach is reflected in scenario 2.
As the population of the Phoenix metropolitan area increases, this plan will accommodate
22
growth, while minimizing water consumption. With large expanses of land available for
development throughout Maricopa County, it would be reasonable to steer more
households on smaller lots to centrally located Phoenix and Paradise Valley, limiting
excessive urban sprawl and reducing per capita water consumption.
5.3 Local versus global model performances
The findings of Wentz and Gober (2007) from modeling OLS and GWR on year
2000 water consumption is a starting point for analysis of water forecasting in this study.
Wentz and Gober determined that GWR generally performed better than OLS with a
mean r2 of .85 versus an r2 of .64 for OLS. In our study GWR estimates for housing unit
water consumption in all four scenarios were lower than OLS estimates. The difference in
r2 from Wentz and Gober (2007) suggests GWR is an improvement over OLS. But
without knowing how the relationships between the variables change, this is not
conclusive.
Any model estimating real world phenomena possesses inherent limitations,
including limited or uncertain data and mathematical constraints. A weakness of GWR is
that as lot parameters change, the local model should also change – assuming stationarity
in the parameters. Unfortunately, there is no known mathematical approach to deal with
this problem.
5.4 Strengths and weaknesses of the modeling approach
The modeling approach was effective in several ways. While OLS performed well
in estimating year 2000 water consumption rates, GWR was a substantial improvement
23
over OLS (Wentz & Gober, 2007). The inclusion of existing housing units in the global
and local forecasts tempers the uncertainty of estimating new housing unit distributions.
Other forms of land use are frequently converted to residential use, but rarely does
residential convert to another use. Exceptions such as eminent domain of houses in new
freeway corridors or redevelopment of older urban neighborhoods should not be
overlooked. Overall, it is safe to assume the general spatial pattern of existing housing
units remain intact in the foreseeable future. What are more likely to change are
residential housing unit characteristics due to demographic, policy, or planning changes.
These unforeseen changes could alter future water consumption rates and patterns.
The scenario rules (Table 1) used statistical and spatial distributions of lots sizes that
translated into different rates and patterns of water consumption. The basic message from
this is that planning or policy alternatives impact residential water consumption. The
scenarios developed in this research could be translated into rudimentary planning
regimes or policy alternatives with long-term planning and policy implications for singlefamily residential water consumption. Lot sizes would, perhaps, be restricted through a
planning measure where zoning ordinances set maximum lot sizes. Not surprisingly,
affluent areas will likely continue to consume water at a higher rate than less affluent
areas. Lessening this disparity might be accomplished through pricing controls, by
changing social attitudes towards owning pools, changing landscaping practices, or
implementing conservation measures. Policies to reduce water consumption should
account for variations in patterns and local relationships between housing units.
Due to the scarcity of available land for new single-family residential
development along the light rail line, policies to encourage such development would have
24
little direct influence on consumption rates. Any future plans to expand the light rail to
the fringes of the urban footprint might have a more direct impact on consumption rates.
Lempert, Popper, & Bankes (2003) offer a critique of forecasting with a small
number of scenarios pointing out that some new modeling and forecasting approaches
generate hundreds or more scenario alternatives or iterations. One approach to forecasting
seeks more effective ways to understand how the future will unfold based on measurable
conditions. Another approach explores and estimates the conditions or factors that would
lead to a particular outcome. We acknowledge our approach explores consumption given
certain policy restraints, showing only a small subset of the potential range of scenarios.
A fuller picture of the range of possible effects of urban growth and housing
characteristics could be achieved through a sensitivity analysis.
Another issue with this study is that year 2000 census tract boundaries stay the
same size as residential growth continues. In fact, large tracks in north and southwest
Phoenix, such as tract 303.42, would be divided as population levels increase. Interstate
17 runs through tract 303.42. With smaller census tracts and some tracts along this
transportation corridor could shift to higher density lots, ultimately increasing
consumption in those areas. These divided tracts would not necessarily grow with the
same density patterns, or take on the same housing unit characteristics, such as
landscaping practices or pools. Some new subdivisions might be more family-oriented
with pools and larger lots; others sold as retirement communities with smaller lots and
small household sizes. Lots sold on an individual basis might be less predictable in their
housing unit characteristics than lots in a subdivision.
25
Growth in Phoenix will include annexations of nearby lands. This will occur
predominantly on the northern edges of the city. Gila River Indian Community lands
restrict southward expansion and other municipalities restrict eastward or westward
expansion. Little change is expected for the boundaries of Paradise Valley. Uncertainty
about future land annexations limits our forecasts. Further research could apply other
local models or simulation approaches to estimate the housing unit characteristics and
water consumption in these areas.
6. Conclusions and future research
Our study has shown that there is the potential for per capita water savings with
smaller lot sizes, which has the effect of reducing outdoor water consumption. The
distribution of these lots, however, does little to influence either overall water
consumption or per capita consumption. We demonstrated that for Phoenix and Paradise
Valley, there is the potential for only a small amount of per capita water consumption
savings due to high density development along transportation corridors. This is mostly
due to the lack of open land for development in these areas.
The use of GWR shows how alternate planning or policy regimes may lead to
spatial variation in the patterns and levels of single-family residential water consumption.
More specifically, it reveals how particular housing unit characteristics translate into
higher or lower consumption rates locally. The hope is that local scale modeling will be
developed and applied in additional water forecasting tools and other social-science and
environmental forecasting studies. Alternate simulation methods, like agent based
modeling, also offer promise in spatial forecasting. Residential data values or coefficients
26
from Wentz and Gober (2007) could be incorporated into a simulation program such as
UrbanSim.
This research evaluates only a small portion of possible “what if” scenarios for
urban water management in Phoenix and Paradise Valley. Questions about the long-term
water supply are equally as important as demand issues. The desert southwest is the
fastest growing part of the United States; it is also the region with the most precarious
balance between human needs and water resources. Phoenix shares upstream Colorado
River water with Las Vegas and southern California. Forecasting the likely range of
future supplies against the backdrop of climatic uncertainty is a vital ingredient for
effective political agreements.
There are several avenues for additional research. One obvious approach would
modify the existing scenarios, perhaps to represent the effects of other planning or policy
measures on water consumption. Another variation would be to generate a non-Gaussian
distribution for the lot sizes. This new distribution might be skewed to more accurately
reflect the distribution of existing lot sizes. Aside from modifications to the existing
scenarios, our research question could be expanded to include more than four scenarios.
An obvious starting point is to model the other parameters used in water estimation from
Wentz and Gober (2007), including percent of homes with a pool, household size
(persons), and percent mesic landscaping. Household size would be a good starting point
as it exhibited spatial non-stationarity according to the results of Wentz and Gober
(2007). Other local characteristics, such as the urban heat island effect, have been
modeled for Phoenix (Guhathakurta & Gober, 2007). The inclusion of this measure
27
would be a good way of factoring in the effects of climatic conditions on water
consumption rates.
Beyond modifying statistical distributions, new research could change the spatial
distribution of new lot sizes. For example, the maximum distance for density
classifications along transportation corridors could be altered. This study applied one
quarter mile buffers for the high density classification along the light rail line, with only
six qualifying census tracts. A larger buffer would lead to a more pronounced high
density core. Likewise, changing the corridor size around highways might have effects on
the spatial patterns of consumption throughout Phoenix. Another useful modification for
this study would make the number of new housing units constant for all scenarios where
population could be tied to some future projection. Multiple categories of residential
development might be included in the forecasts. The inclusion of multifamily housing
units would allow larger lots to remain of the fringes with more housing units in smaller
lots or multistory buildings along transportation corridors.
28
Figure captions
1. Existing and new single-family residential land use at “full-growth” in the City of
Phoenix and the Town of Paradise Valley, Arizona. Data source: MAG 2007b.
2. Forecasted mean lot size per census tract: (a) Scenarios 1 and 3, (b) Scenarios 2
and 4.
3. Single-family residential lot density classifications based on proximity to
highways and the light rail line.
4. Forecasted total (existing and new) single-family residential housing units per
census tract (a) Scenario 1, (b) Scenario 2, (c) Scenario 3, (d) Scenario 4.
5. Mean annual single-family residential housing unit water consumption (ccf), OLS
model: (a) Scenario 1, (b) Scenario 2, (c) Scenario 3, (d) Scenario 4.
6. Mean annual single-family residential housing unit water consumption (ccf),
GWR model: (a) Scenario 1, (b) Scenario 2, (c) Scenario 3, (d) Scenario 4.
7. Comparisons of mean housing unit water consumption: Scenario 3 minus
Scenario 1 (a) OLS model, (b) GWR model, Scenario 2 minus Scenario 1 (c) OLS
model, (d) GWR.
29
Table Captions
1. Four scenarios for future single-family residential development in the City of
Phoenix, Arizona and the Town of Paradise Valley, Arizona. Each scenario
combines one statistical distribution with one spatial distribution.
2. Ordinary least squares (OLS) regression coefficients with mean single-family
residential housing unit water consumption per census tract as the dependent
variable (measurement units reported in liters).
3. Geographically weighted regression (GWR) coefficients with mean single-family
residential housing unit water consumption per census tract as the dependent
variable (measurement units reported in liters).
4. Summary of statistical distributions of randomly generated new lots.
5. Forecasted single-family residential housing unit counts, City of Phoenix and
Town of Paradise Valley, Arizona.
6. Summary statistics of forecasted annual water consumption (ccf) for the City of
Phoenix and the Town of Paradise Valley, Arizona.
30
Figures
Figure 1
31
Figure 2
32
Figure 3
33
Figure 4
34
Figure 5
35
Figure 6
36
Figure 7
37
Tables
Table 1
Table 2
Table 3
38
Table 4
Table 5
Table 6
39
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