AN EVALUATION OF WEEKLY AND MONTHLY TIME SERIES FORECASTS OF MUNICIPAL WATER USE1

ABSTRACT: A cascade model for forecasting municipal water use one week or one month ahead, conditioned on rainfall estimates, is presented and evaluated. The model comprises four components: long term trend, seasonal cycle, autocorrelation and correlation with rainfall. The increased forecast accuracy obtained by the addition of each component is evaluated. The City of Deerfield Beach, Florida, is used as the application example with the calibration period from 1976–1980 and the forecast period the drought year of 1981. Forecast accuracy is measured by the average absolute relative error (AARE, the average absolute value of the difference between actual and forecasted use, divided by the actual use). A benchmark forecast is calculated by assuming that water use for a given week or month in 1981 is the same as the average for the corresponding period from 1976 to 1980. This method produces an AARE of 14.6 percent for one step ahead forecasts of monthly data and 15.8 percent for weekly data. A cascade model using trend, seasonality and autocorrelation produces forecasts with AARE of about 12 percent for both monthly and weekly data while adding a linear relationship of water use and rainfall reduces the AARE to 8 percent in both cases if it is assumed that rainfall is known during the forecast period. Simple rainfall predictions do not increase the forecast accuracy for water use so the major utility of relating water use and rainfall lies in forecasting various possible water use sequences conditioned on sequences of historical rainfall data.     

RESIDENTIAL WATER DEMAND: A POOLED,TIME SERIES,CROSS SECTION STUDY OF MALMÖ, SWEDEN1

Shortcoming associated with past water demand studies are evaluated. To overcome these shortcomings, pooled, time series, cross section data from -6, Sweden, are used in an ordinary Least squares analysis to estimate the demand for residential water. Elasticities for five variables, including price and income, are estimated. An approach for the conduct of future water demand studies is suggested.     

WATER CONSERVATION KITS: A TIME SERIES ANALYSIS OF A CONSERVATION POLICY1

ABSTRACT: The effect on water usage of installing water conservation kits in the city of Oxnard, California, is statistically evaluated. Using binary multiple regression analysis on a large sample of residential units, water consumption was compared before and after receipt of the kit. For this sample, installers reduced water consumption by 4.2 percent each billing period. Income (wealth) and household size elasticities are reported along with the Characteristics of the installing households.     

PAST AND FUTURE OF ANALYSIS OF WATER RESOURCES TIME SERIES1

ABSTRACT: water resources supply and demand time series consist of several or all of the four basic characteristics: tendency, intermittency, periodicity and stochasticity. Their importance changes from one type of variables to another. Historic developments of analysis of time series in hydrology have varied significantly over the past, from the stress on search for periodicities and persistence in annual series to the emphasis on the series stochastic properties. Supply and demand series are often highly interrelated, which fact is most often neglected in planning water resources systems in general, and water storage capacities in particular. The future of series analysis in water resources will likely be by a joint use of physically-based structural analysis and the use of advanced methods of treating data by stochastic processes, statistical estimation and inference techniques. The most intriguing challenge of the future of this analysis may be the treatment of nonnormal, nonlinear and in general nonstationary hydrologic and water use time series. The proper treatment of complex multivariate processes will also challenge the specialists, especially for the purposes of transfer of information between data on variables at given points, or between data at several points of a given variable, or both.     

DEVELOPING AND ASSESSING A MODEL OF RESIDENTIAL WATER CONSERVATION1

ABSTRACT: Relevant literature was reviewed from which a model of residential water conservation was developed. Four residential conservation program interventions were posited: 1) public education, 2) pricing variables, 3) water use restrictions, and 4) building code requirements. Four exogenous variables affecting residential water use were also posited: 1) temperature, 2) rainfall, 3) household income, and 4) household size. The impacts of these eight variables on residential per capita daily use were assessed by cross sectional and time series analysis. Study results generally supported the porposed model, with less consistent support obtained for pricing variables and conservation beliefs. The paper concludes with the hypothesis that an inclining block rate structure coupled with an informational program designed to inform consumers of their consumption under each block will have a synergistic impact.     

MUNICIPAL WATER CONSERVATION ALTERNATIVES1

ABSTRACT: The municipal water conservation options available to meet the goals of a national water conservation policy are evaluated. Water conservation with water conservation devices is shown to offer many significant advantages over education and pricing and metering as a method of accomplishing water conservation goals. Current constraints on the use of water conservation devices are outlined, and their elimination is suggested if the nation's water conservation goals are to be met.     

BAYESIAN MODELS OF FORECASTED TIME SERIES1

Bayesian Processor of Forecasts (BPF) combines a prior distribution, which describes the natural uncertainty about the realization of a hydrologic process, with a likelihood function, which describes the uncertainty in categorical forecasts of that process, and outputs a posterior distribution of the process, conditional upon the forecasts. The posterior distribution provides a means of incorporating uncertain forecasts into optimal decision models. We present fundamentals of building BPF for time series. They include a general formulation, stochastic independence assumptions and their interpretation, computationally tractable models for forecasts of an independent process and a first-order Markov process, and parametric representations for normal-linear processes. An example is shown of an application to the annual time series of seasonal snowmelt runoff volume forecasts.     

MUNICIPAL UTILIZATION OF WATER DEMAND MANAGEMENT: THE ONTARIO EXPERIENCE1

ABSTRACT: Managing the demand for municipal water supply has become a viable alternative or supplement to traditional supply management responses. Though senior governments in Canada are committed to the concept, there is a lack of knowledge concerning the level of use of the demand management concept and little promotion of water conservation. This paper assesses the extent of the use of this concept as it applies to municipal water supply across southern Ontario and examines factors that influence the variation in use of water conservation strategies. Information from 219 municipalities revealed that the concept is not in wide use in southern Ontario and that existing variation can be partially explained by the extent of problems experienced and the population size served by the municipal water supply system. Suggestions for increasing municipal use of the demand management concept are offered.     

IDENTIFICATION OF MONTHLY TRENDS IN URBAN WATER USE1

ABSTRACT: Monthly water use for the period 1960–1984 for the Columbus, Ohio, metropolitan area is analyzed to identify differential monthly trends in growth of water use. By associating water use activities with the identified trend months, inferences may be made as to the possible underlying causes of the observed trend in overall water use. Three methods were found useful in determining monthly trends: 1) regression analysis on the monthly percentage of annual use, 2) regression analysis on the monthly water use data itself, and 3) analysis of the slope of the monthly water use regression line. Agreement between the three methods is strong, but each provides some insight not found in the others. All three should be used in drawing final conclusions. For the case study, usage in the Winter months January-April has grown considerably relative to the other months, while the Summer-Fall months of June, August, September, and October show a relative decline. A possible explanation for the trend is aging of the distribution system, with consequent general leakage and increased water main breakage caused by freeze/thaw conditions. More research needs to be carried out linking water use activities to particular months or groups of months.     

EFFECTIVENESS OF DROUGHT POLICIES FOR MUNICIPAL WATER MANAGEMENT1

During the 1976–77 drought, three principal mechanisms were used to reduce water use in Utah communities: price increases, maximum monthly use restrictions, and restrictions on outdoor watering times. A regression model was developed to explain observed changes in water use, with price, type of restriction, household size, and summer rainfall as independent variables. For an average system, a 1 percent increase in price would reduce water use by 0.07 to 0.09 percent. A 1 percent increase in outdoor watering time restriction reduces use by 0.064 to 0.075 percent. A 1 percent increase in quantity restrictions leads to a reduction in water use of 0.014 to 0.054 percent. The effectiveness of rationing policies is influenced by system characteristics. For example, outdoor watering time restrictions were less effective in systems with above average household size and below average monthly use.     

MUNICIPAL WATER SUPPLY RESTRICTIONS AS URBAN GROWTH CONSTRAINTS1

ABSTRACT: Municipal water supply restrictions and/or conservation policies are widely believed to affect urban growth, at least in Western states. An analysis of this issue, drawing upon a wide array of empirical water use research, casts doubt upon the presumed connection. Water availability seems likely to have little effect upon the amenities which draw newcomers to Western cities. It also seems to have little effect upon the locational decisions of industries which affect growth by creating new jobs. Consequently, there is little reason to oppose municipal water restrictions as prejudicial to urban growth or to favor such restrictions in the hope of constraining growth.     

TREND ASSESSMENT OF WATER QUALITY TIME SERIES1

ABSTRACT A general methodology is described for identifying and statistically modeling trends which may be contained in a water quality time series. A range of useful exploratory data analysis tools are suggested for discovering important patterns and statistical characteristics of the data such as trends caused by external interventions. To estimate the entries in an evenly spaced time series when data are available at irregular time intervals, a new procedure based upon seasonal adjustment is described. Intervention analysis is employed at the confirmatory data analysis stage to rigorously model changes in the mean levels of a series which are identified using exploratory data analysis techniques. Furthermore, intervention analysis can be utilized for estimating missing observations when they are not too numerous. The effects of cutting down a forest upon various water quality variables and also the consequences of acid rain upon the alkalinity in a stream provide illustrative applications which demonstrate the effectiveness of the methodology.     

EFFECT OF PRICE ON THE RESIDENTIAL DEMAND FOR WATER WITHIN AN AGENCY1

ABSTRACT: This paper develops a model that can be used to forecast the residential elasticity of demand for water within a district. Long-term water conservation programs and revenue and cost decisions hinge crucially on a determination of this elasticity. This study then pools cross-sectional (census) and time series data to generate elasticity forecasts for the Oakland urban area.     

EFFECT OF PRICE STRUCTURE ON RESIDENTIAL WATER DEMAND1

ABSTRACT: Little is known about how different types of municipal water rate structures influence residential water use. Conventional wisdom suggests that increasing block rate structures promote conservation, but analysis of data from 85 Massachusetts communities does not support this view.     

SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES1

ABSTRACT: Simple models are presented for use in the modeling and generation of sequences of dependent discrete random variables. The models are essentially Markov Chains, but are structurally autoregressions, and so depend on only a few parameters. The marginal distribution is an intrinsic component in the specification of each model, and the Poisson, Geometric, Negative Binomial and Binomial distributions are considered. Details are also given for the introduction of time-dependence into the means of the sequences so that seaonality can be treated simply.     

TIME SERIES ANALYSIS IN PERSPECTIVE1

ABSTRACT: By employing a set of criteria for classifying the capabilities of time series models, recent developments in time series analysis are assessed and put into proper perspective. In particular, the inherent attributes of a wide variety of time series models and modeling procedures presented by the authors of the 18 papers contained in this volume are clearly pointed out. Additionally, it is explained how these models can address many of the time series problems encountered when modeling hydrologic, water quality and other kinds of time series. For instance, families of time series models are now available for modeling series which may contain nonlinearities or may follow nonGaussian distributions. Based upon a sound physical understanding of a problem and results from exploratory data analyses, the most appropriate model to fit to a data set can be found during confirmatory data analyses by following the identification, estimation and diagnostic check stages of model construction. Promising future research projects for developing flexible classes of time series models for use in water resources applications are suggested.     

ACHIEVING URBAN WATER CONSERVATION1

ABSTRACT: Increasing costs and competition for water have resulted in pressure to manage urban water demand through conservation programs. Metering, pricing, devices, restrictions, building code changes, and horticultural practices have all been effective in reducing average residential water use. Some conservation means are specifically aimed at reducing peak demands but these usually reduce average usage as well. Combined programs of conservation can be expected to reduce urban demand by as much as 25–30 percent over the long term. Restrictions can reduce water usage on the short term even further. The success of conservation programs is as dependent on the effectiveness of public education and information dissemination as on the conservation practices themselves.     

Residential Demand for Water in the Chicago Metropolitan Area1

Mieno, Taro and John B. Braden, 2011. Residential Demand for Water in the Chicago Metropolitan Area. Journal of the American Water Resources Association (JAWRA) 47(4):713‐723. DOI: 10.1111/j.1752‐1688.2011.00536.x Abstract: This paper provides the first contemporary analysis of residential water demand in humid Northeastern Illinois, in the vicinity of Chicago, and explores seasonal and income‐based differentials in the responsiveness of water use to water prices. Using a panel of system‐level data for eight water systems and controlling for seasons, weather, incomes, and community characteristics, the analysis yields low estimates of price elasticity of demand for water in line with other studies. Furthermore, price response is greater in summer and less in higher income communities. We suggest that use of seasonal pricing can help mitigate equity issues arising from differential income elasticities while taking advantage of the greater price responsiveness of summertime water use.     

WATER SAVINGS FROM LAWN WATERING RESTRICTIONS DURING A DROUGHT YEAR,FORT COLLINS,COLORADO1

ABSTRACT: During the drought year of 1977, unusually low river flows during the summer caused the City of Fort Collins, Colorado, to institute lawn watering restrictions for six weeks as a conservation measure. Water use during the restriction period decreased 41 percent below the previous year. The effectiveness of the restrictions, however, has been unclear because abnormally wet weather also appeared to reduce evapotranspiration rates during the period the restrictions were in effect. The statistical analysis indicates that the reduction in water use due to lawn watering restrictions was 603 acre-feet and that abnormal weather reduced use by an additional 659 acre-feet during the same period. During a period of normal evapotranspiration rates, such restrictions would be expected to reduce Fort Collins municipal water usage by 19.7 percent.     

DEMAND PROJECTIONS CONSIDERING CONSERVATION1

ABSTRACT: Prediction of future water demands depends on the degree to which conservation effects can be anticipated. A model developed for the Corps of Engineers shows that choosing a numerical conservation target to be achieved is more meaningful and yields more predictable results than price or price elasticity manipulations. The method developed and then applied to the Kaneohe Bay region of Oahu considers the following determinants of demand: geographic distribution of the users, indoor and outdoor requirements, time - by year and month of the year, precipitation, historical unit usage rates, gross and irrigable acreage of land uses, price for water, elasticity of demand with respect to price, source of the water supply (local private supplies vs. agency supplies), and the percentage conservation savings anticipated in each future period in indoor and outdoor uses of water in each of 40 possible land uses. While developed for use in Hawaii, the model is applicable generally.