The Las Vegas Valley, located in the arid southern Nevada region, has had an increasingly growing population in the past 15 years, with limited water resources. The area has also experienced a prolonged drought, spanning fifteen years from 2000 to 2014, and faces unique challenges in meeting its future water needs [1
]. The uncertainty of water resources is an important issue for the community due to climate change and its impacts on precipitation levels and spring runoff from the melting snow in the mountains [1
]. The water demands keep increasing because of the increasing population and the hydrological response. An example of a hydrological response is drought, which puts additional stress on water utilities. Because of these circumstances, valley water managers and planners require accurate depictions of water demand over medium and long-term forecasts to predict the water demand due to uncertain events that might affect water availability; additionally, this assists in planning for the needs of future investments and the infrastructure of water utilities.
The availability of water continues to be a critical issue in the valley, as is evident from the continuous drought from 2000 to 2014, which has affected its precipitation patterns due to climate change [2
]. Subsequently, the elevation of Lake Mead, the major water supply for the Las Vegas area, dropped to a historic low level of 1081 feet in 2010 [2
]. As a result, the Southern Nevada Water Authority (SNWA) initiated a drought plan and implemented effective conservation programs in the mid-1990s [3
For the planning, management, and development of water supply systems, the characteristics of water demand, together with uncertainties in natural phenomena, have caught the attention of many water resource researchers [4
]. Kenney et al. [7
] described that water consumption is mainly composed of three main factors: (1) socioeconomic factors, such as population distribution and sizes of homes and lots; (2) climate factors, such as air temperature, precipitation, and percent of humidity; and (3) policy factors, such as the cost of water utilities, regulations, and conservation programs. This study considers population, policy, and climate as factors in the modeling of water demand.
Due to the seasonal characteristics of water consumption and the complex stochastic and dynamic characteristics of external influences, such as climate systems and social and economic activities, it is challenging to develop appropriate models for accurate predictions of water consumption. There are a few previous studies on water demand modeling undertaken in Las Vegas [13
]. Trabia et al. [13
] used multiple linear regression to assess water use by several water demand related components (e.g., landscaping, showers, pools, etc.). Belsford et al. [14
] applied the log transform multiple regression method for decomposing multiple drivers of consumption using a dataset of neighborhood water consumption, home infrastructure characteristics, and vegetation in Las Vegas. Tchigriaeva et al. [15
] developed and estimated a random effects model using five years of monthly water use at the household level with four categories of factors that influence residential irrigation water demand in Las Vegas. These four categories of factors are exogenous factors, pricing policies, voluntary conservation incentives, and mandatory conservation regulations. Exogenous factors include precipitation, temperature, wind speed, household characteristics, and economic trends. Boulos et al. [16
] used a hydraulic-based model and a water network decision support system to forecast real-time water demand in Las Vegas. The real-time integration of supervisory control and data acquisition (SCADA) data was used as a boundary condition (e.g., tank water levels) and operational status (e.g., pump speeds or on/off status, valve settings) in the network model [16
]. Lott et al. [17
] used a mix-effected model (fix and random model), which includes independent variables such as the number of bedrooms, age of the house, yard size, monthly income, water price, a one-month lag of average temperature, days of precipitation per billing cycle, and average wind speed per billing cycle. These water demand models, except for Boulos’s real time hydraulic-based model, contain categorized components that describe characteristics of residential water demand, and include one or more weather variables to control for the influence of weather on the seasonality of residential water use.
As mentioned above, there are multiple demand-related variables, and those factors can be and often are interrelated. Moreover, water conservation practices and the availability of water strongly influence urban water demand [9
]. This demand can be controlled by adoption of a water conservation plan. For example, Las Vegas first initiated a conservation plan in 1995 [1
]. Once the goal was achieved, an additional water conservation plan was implemented to sustain the required per capita water supply. Since 1999, SNWA has formulated a new conservation plan every five years. During this period, the SNWA reviews its conservation plan efficiency at the one-year mark and makes subsequent changes as required [3
]. The currently implemented conservation measures in Las Vegas include: water pricing such as increasing block rates and water-waste fees, incentives such as water smart landscape rebate programs, rebate coupons, water efficient technologies, single-family indoor retrofits, regulation such as land-use codes and water-use ordinances, and education such as public-education outreach programs and demonstrations of water-efficient gardens [3
]. As a result of this additional conservation plan, the SNWA projects a reduction in total demand from 199 gallons per capita per day (GPCD) (753 liters per capita per day (LPCD)) in 2035 to 190 GPCD (719 LPCD) in 2055 [1
]. Between 1996 and 2007, Las Vegas’s trajectory of reduced water consumption rates was significantly lower. The average consumption during this period for an individual household declined by 55%, while that of the population increased by 63%. These results exhibit strong evidence of the success of Las Vegas’s policies [14
In this paper, we develop and test a model that does not isolate those effects (unlike the previous studies) but uses the historical water demand data to represent all of those factors that affect water demand in the region. The historical water demand data contains accumulated information that is a result of water demand related factors in the past, which are used in this paper’s model to be independent variables for predicting future water demand.
For residential water demand, variation happens mostly in summer where outdoor water use and irrigation account for the main uses. Water losses due to evapotranspiration are the reasons for consumptive use for outdoor and irrigation activities. These activities vary based on climate factors, such as temperature, radiation, percent of humidity, dew point temperature, and wind speed [18
]. Thus, seasonality and climate are also considered in this study’s model.
In general, outdoor and irrigation water demands are influenced by the amount of rainfall and temperature. For Las Vegas or semi-arid areas where there is minimal rainfall, the outdoor water demand is mainly influenced by the evapotranspiration process. This process is represented by evapotranspiration-related climate factors, such as dew point depression, diurnal temperature, average temperature, and wind speed. We assume that these climate factors have a minimal effect on indoor water use. This study’s model will be tested for the influence of precipitation and each evapotranspiration-related climate factor’s impact on water demand.
A time-series model has been introduced into the time pattern water consumption model, which can capture long-term trends, seasonal variation, autocorrelation, and random shocks that perturb the water demand. Maidment et al. [4
] and Tiwari et al. [20
] use a time-series model to describe monthly water use. Maidment et al. [4
] described that water consumption is mainly composed of four components: (1) a long-term trend due to policies and socio-economic variables, (2) seasonal variation from the annual cycle of weather, (3) autocorrelation due to perpetuation of past water use variation, and (4) climatic correlation due to rainfall, evaporation, and air temperature. Thus, a time-series approach has an intuitive potential in explaining the characteristics of water demand.
In order to accomplish water resource planning for efficient water management in the Las Vegas metropolitan area, the purposes of this study are: to develop a prediction model for mid- to long-term water demand, to consider the relationship between past water demand and local climate characteristics, and to identify the key climate factors impacting residential water consumption. Thus, our empirical model of residential water demand in the Las Vegas metropolitan area accounts for both seasonal and climatic impacts by using long-term historical water demand and climate data.
The final model for each climate factor results from the curve fitting of water demand among comparative transfer function with noise (ARIMAX) models. The 60-month water demand forecast is calculated from each of the best-fit ARIMAX models and the ARIMA (no climate input) model. The impact of the climate factor on water demand can be determined by improving the accuracy performance of the ARIMAX model from the ARIMA model.
This study is unique, because limited research has been conducted to address the impact of climatic factors on water demand modeling [5
]. Very few studies in the past have applied principal components as independent variables for water demand prediction to manage the issue of multicollinearity among the independent variables [9
]. Our study applies a principle component technique to combine the inter-related climate factors into a single index factor for the investigation of cumulative underlying climate effects on water demand. To determine the most influential climatic factors, this study tested nine meteorological factors and two climatic principle component indexes for their effects on long-term (25-year) water demand using ARIMAX (transfer function-noise models). Furthermore, none of the previous studies have developed ARIMAX equations specifying the number of lags on variables (for both deterministic and stochastic terms) to forecast monthly water demand. Additionally, time-series modeling has been predominately been used for short-term forecasting [5
], but this study could be utilized for medium- to long-term forecasting. Lastly, we simulate water demand from the ARIMAX equations to estimate the sensitivity of water demand due to climate change impact. The major contribution of this paper is not only that it addresses the influence of climatic factors on residential water demand in the semi-arid metropolitan area of Las Vegas, but also that it provides a long-term forecasting model for sensitivity tests of the effects of climate change on water demand in the area. Moreover, these ARIMAX models can be adapted to other regions to improve their water planning and conservation policies.
In this study, all climate time-series values were obtained from one reliable weather station (McCarran International Airport) that has continuously collected the data since 1949. We assume that these climate data represent the changing climate patterns in the Las Vegas metropolitan area. However, when using one weather station for the meteorological factors, the weather data may not account for spatial variations (latitude-longitude effect), and this could impact the accuracy of the findings. To be more precise, for the climate impact investigation, one could use climatic data from several stations, interpolate climate factors spatially, and use water demand data at the respective station neighborhoods for water demand modeling.
A log transformation of the data for both water consumption and the climate factor time-series provides those time-series with more uniform variability. The log transformation is suitable for non-negative variables and time-series data that has exponentially increasing/decreasing trends. Moreover, because the scales of the model’s variables significantly differ in magnitude, it necessitates the use of the log-log time-series regression model, which gives more stationary than absolute differences. The multicollinearity analysis of meteorological factors is conducted through principle component analysis. An investigation found that climatic variables, including maximum temperature, minimum temperature, average temperature, diurnal temperature, and dew point depression, influenced one another, which can be grouped as PCA1. Also, wind speed, wind direction, precipitation, and percent calm wind can be clustered together according to the principle component analysis to give another input, the PCA2 time-series, to test through the ARIMAX water consumption model.
Because per capita water use in Las Vegas was found to be decreasing, this declining trend was a result of the conservation program that was implemented in the 1990s in response to population growth and the impacts of a slow economy [2
]. Thus, the trending patterns in water consumption may be due to regulatory and economic factors. However, the variation of water consumption can be explained by the weather factor [4
]. Thus, in the time-series with the climate input model, the effects of non-meteorological factors, such as conservation policies and socioeconomics, may appear in the historical water demand data (autoregressive terms) as well as in stochastic noise (moving average terms).
After removing underlying trend and seasonality patterns for both the water and the climate time-series, the correlation of the random variation between climate factors and water demand can reveal the impact of climate factors on water demand. Table 1
gives the results of the correlation of random variation between climate factors and water demand. The random variation of water demand and climate factors can be referred to as the rate of yearly change of the logarithm of water consumption and the rate of yearly change of the logarithm of climate factors. The results show that dew point depression gives the highest positive significant correlation of 0.73, while precipitation gives the highest negative significant correlation of −0.55 (Table 1
The water demand model uses a time-series analysis to show that current water use is strongly influenced by past water use, as well as by current and past climate factors. The time-series model takes into account behavioral responses and time lags between policies and residents’ water consumption decisions [29
]. Based on the interview with the Southern Nevada Water Authority (SNWA), the SNWA closely monitored and controlled residential water consumption per capita following their water conservation plan in 2009. Thus, the water consumption trend and seasonal patterns would ordinarily be closely related to the previous water consumption record, except there were some unpredictable events, such as a storm (which rarely occurs in Las Vegas), which caused the outlier and irregular variation to the data.
The long-term water demand time-series model, in contrast to the short-term demand model, helps to examine water demand projection and to understand the effects of climate change [10
]. The monthly water demand model established the long-term relationships between the climate and water consumption variables. The ARIMAX model accounts for the autocorrelation in the water demand time-series by using the previous month and year and the following month and year of water use as an independent variable, and it also accounts for the cross lags of the climate factors as an independent variable [26
]. Thus, the ARIMAX model can be applied intuitively to forecast water demand. However, this ARIMA/ARIMAX methodology suggests that an investigator obtain at least 50 time steps (in this case 50 months) of a dataset to create the time-series model [26
]. For forecasting water demand, the model requires future meteorological factor values. Thus, a limitation of the proposed model is that we are required to obtain a predicted meteorological factor before forecasting water demand.
Since the impact of the climate factor on water demand is calculated by improving the accuracy performance (MAPE) from the no-climate input time-series model (ARIMA), we used actual climate inputs in the forecasting model in order to avoid adding a forecasting error from predicting the climate inputs. The evidence of the climate factor improves the forecasting of water demand as shown in Table 2
. Most R-Squared results of each ARIMAX model that has a climate factor as an independent variable are greater than the water demand time-series model without a climate factor, ARIMA. The best-fit model is the ARIMAX model of dew point depression, which gives the highest R-Squared value of 98.88 and the lowest AIC of −856.58 as compared with other competitive climate factors in ARIMAX models. High dew point depression (high temperature with low dew point temperature) reflects warm and dry weather. Thus, dew point depression can be an indirect indicator of water loss due to the evapotranspiration process in the Las Vegas region.
The fitting time-series model with the climate factor as an input series also has a considerably high R-Squared value, at about 98% excepting precipitation, and the prediction performance for the next 12 months has a low mean absolute percentage error (MAPE), at about 2–6% (Table 4
). Yet, there is a challenge to estimate climate factors accurately under future uncertainty. The forecasting reliability performance test was conducted and the results showed that the ARIMAX model with dew point depression and average temperature as input series gives a low predictive error of monthly water demand at 2.76% and 2.80% on the 5-year average and low average standard deviation at 1.79% and 1.63%, respectively (Table 5
). The results show, on the other hand, that the precipitation factor gives the least reliability in the forecasting, at 7.21% with the average standard deviation at 6.42%. The minimum MAPE results in Table 5
give the notation that in a monthly time frame, water demand can be highly influenced by many climate factors, such as average temperature, PCA1, PCA2, wind speed, percent calm wind, and precipitation, that show an MAPE of less than 0.10%. However, to evaluate the impact of climate change on water demand, we consider a climate factor that explains most of the water demand variation during a long-term period. The fitted model and forecasting results demonstrated that dew point depression is the significant climate factor that impacted water demand in Las Vegas from 1990 to 2014.
Because changing climates influence the increases or decreases in water demand, using the best forecasting ARIMAX model can determine the projected changes in water demand in Las Vegas. The sensitivity analysis results in Table 6
demonstrate the susceptibility of changes in water demand due to changes in dew point depression and average temperature. These results show that dew point depression and average temperature have positive impacts on water demand, and water consumption in the Las Vegas area is susceptible to changes of average temperature about three times more than changes of dew point depression. Based on our ARIMAX models’ simulations, the results suggest that the water demand in Las Vegas can be more vulnerable to changes in average temperature than changes in dew point depression.