A MONTHLY TIME SERIES MODEL OF MUNICIPAL WATER DEMAND1

A multivariate time series model is formulated to study monthly variations in municipal water demand. The left hand side variable in the multivariate regression model is municipal water demand (gallons per connection per day) and the right hand side contains (explanatory) variables which include price (constant dollars), average temperature, total precipitation, and percentage of daylight hours. The application of the regression model to Salt Lake City Water Department data produced a high multiple correlation coefficient and F-statistic. The regression coefficients for the right hand side variables all have the appropriate sign. In an ex post forecast, the model accurately predicts monthly variations in municipal water demand. The proposed monthly multivariate model is not only found useful for forecasting water demand, but also useful for predicting and studying the impact of nonstructural management decisions such as the effect of price changes, peak load pricing methods, and other water conservation programs.     

THE ACCURACY OF WATER USE FORECASTS: EVALUATION AND IMPLICATIONS1

ABSTRACT: Forecasts of 1980 river basin water use presented in the reports of the 1960 Senate Select Committee on National Water Resources and in the Water Resources Council's First National Water Assessment of 1968 were compared to estimates of actual use in 1980 to assess the accuracy of efforts to forecast future water use. Results show that the majority of the forecasts were substantially in error. In general, the First National Assessment forecasts erred by a smaller margin, but tended to repeat the regional patterns of overestimation (underestimation) exhibited in the Senate Select Committee forecasts. Moreover, forecasts of the two groups that came within 20 percent of the 1980 withdrawals, in general were accurate, not because of superior prediction, but because of offsetting errors in forecast components. This performance leads us to conclude that water use forecasts, regardless of the time-frame or the forecast method employed, are likely to always be highly inaccurate. Accordingly, if such forecasting efforts are to be of value in contemporary water resources planning, forecasters should direct their attention toward methods which will illuminate the determinants of the demand for water.     

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.     

A COMPARATIVE STUDY OF LINEAR AND NONLINEAR TIME SERIES MODELS FOR WATER QUALITY1

ABSTRACT: Surface water quality data are routinely collected in river basins by state or federal agencies. The observed quality of river water generally reflects the overall quality of the ecosystem of the river basin. Advanced statistical methods are often needed to extract valuable information from the vast amount of data for developing management strategies. Among the measured water quality constituents, total phosphorus is most often the limiting nutrient in freshwater aquatic systems. Relatively low concentrations of phosphorus in surface waters may create eutrophication problems. Phosphorus is a non-conservative constituent. Its time series generally exhibits nonlinear behavior. Linear models are shown to be inadequate. This paper presents a nonlinear state-dependent model for the phosphorous data collected at DeSoto, Kansas. The nonlinear model gives significant reductions in error variance and forecasting error as compared to the best linear autoregressive model identified.     

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.     

APPROACHES TO MULTIVARIATE MODELING OF WATER RESOURCES TIME SERIES1

ABSTRACT: Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three-stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer-function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.     

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.     

THE ADOPTION OF MUNICIPAL WATER CONSERVATION: AN UNLIKELY EVENT?1

ABSTRACT: It is contended that water conservation measures that reduce a water system's net revenues are unlikely to be adopted. Pricing policies that induce conservation can be designed to increase net revenues. Management practices that lead to conservation and pure conservation measures may reduce net revenues; consequently, they are unlikely to be adopted. Recent experience in five southwestern cities supports these contentions. It is argued that the managers of a municipal water enterprise are particularly sensitive to short term variation in revenues. Consequently, to increase the likelihood of the adoption of measures that reduce net revenues it is necessary to remove either the decision to adopt measures that reduce net revenue or the adverse revenue effect from the water enterprise. Finally, to make higher rates for conservation palatable, imaginative use for the funds generated must be developed.     

FORECASTING URBAN WATER USE: THE IWR-MAIN MODEL1

ABSTRACT: In the current forecasting practice, future water requirements of a growing urban area are often represented as the product of the number of people to be served by the water system and an assumed quantity of gross per capita water use. This paper describes a forecasting approach that differs from the per capita method in two important aspects. First, it disaggregates urban water use into a large number of categories, each consisting of a relatively homogeneous group of water users. Second, it links water use in each category to factors that determine both the need for water as well as the intensity of water use. This approach is incorporated into a computerized forecasting system referred to as IWR-MAIN. The advantages of the IWR.MAIN model over the traditional per capita method are illustrated in a case study of Anaheim, California.     

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.     

PROTECTING BEIJLNG'S MUNICIPAL WATER SUPPLY THROUGH WATERSHED MANAGEMEN AN ECONOMIC ASSESSMENT1

ABSTRACT: Watersheds above the Miyun reservoir, a principal source of surface water for Beijing, are designated to be managed for water production, but under the principle of multiple use. Because of the scarcity of arable land, these watersheds cannot be managed only for drinking water. Efforts are under way to reduce sediment delivery, improve the quality of water entering Miyun reservoir, and improve the welfare of watershed inhabitants. An economic appraisal of a watershed management project for the 3,298‐ha Shixia watershed above the Miyun reservoir, indicates a 24 percent economic rate of return on the investment made in the project. The net present value (NPV) of the project, calculated at a discount rate of 10 percent, is approximately US$3.49 million. Sensitivity analyses indicate that a doubling of labor costs lowers the NPV to US$2.07 million and a 10 percent decrease in benefits lowered the NPV to US$2.87. It is concluded that the implementation of conservation practices on the Shixia Demonstration Watershed represent an economically efficient use of resources.     

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.     

TESTING FOR TREND IN LAKE AND GROUND WATER QUALITY TIME SERIES1

ABSTRACT: The detection of gradual trends in water quality time series is increasing in importance as concern grows for diffuse sources of pollution such as acid precipitation and agricultural non-point sources. A significant body of literature has arisen dealing with trend detection in water quality variables that exhibit seasonal patterns. Much of the literature has dealt with seasonality of the first moment. However, little has been mentioned about seasonality in the variance, and its effect upon the performance of trend detection techniques. In this paper, eight methods of trend detection that arise from both the statistical literature as well as the water quality literature have been compared by means of a simulation study. Varying degrees of seasonality in both the variances and the means have been introduced into the artificial data, and the performances of these procedures are analyzed. Since the focus is on lake and ground water quality monitoring, quarterly sampling and short to moderate record lengths are examined.     

USE AND EFFECTIVENESS OF MUNICIPAL WATER RESTRICTIONS DURING DROUGHT IN COLORADO1

ABSTRACT: Drought conditions in the summer of 2002 prompted several cities along Colorado's Front Range to enact restrictions on outdoor water use, focusing primarily on limiting the frequency of lawn watering. The different approaches utilized by eight water providers were tracked to determine the level of water savings achieved, measured as a comparison of 2002 usage to 2000 to 2001 average usage, and also based on a statistical estimate of 2002 “expected use” that accounts for the impact of drought conditions on demand. Mandatory restrictions were shown to be an effective tool for drought coping. During periods of mandatory restrictions, savings measured in expected use per capita ranged from 18 to 56 percent, compared to just 4 to 12 percent savings during periods of voluntary restrictions. As anticipated, providers with the most stringent restrictions achieved the greatest savings.     

USE AND MISUSE OF COMPLEX MODELS: EXAMPLES FROM WATER DEMAND MANAGEMENT1

ABSTRACT: The power of computers has increased in recent decades, and one might expect improved management to result because decisions can be made with understanding available only via models. However, there is potential for quite the opposite: poor decisions due to unrealistic model output generated by users without access to appropriate training in the use of models. We discuss and, by reference to water demand models (IWR-MAIN, MWD-MAIN), illustrate three areas in which unintended errors of judgment by untrained personnel may cause difficulty:

• * Attributes of management models; if output from any type of model has no measure of confidence, then results may be over- or undervalued
• * Input data; with complex models, problems here typically will be difficult to detect.
• * Calibration and history-matching (verification); if these steps or data are combined, then users should be less trustful of model output than otherwise.

Because all models have weaknesses and because there always is uncertainty about output from any model, we end with suggestions for coping with complex models. Monitoring programs play a central role in such efforts because they can identify discrepancies between model predictions and actual events and because they can ensure time is available to develop solutions for problems unanticipated in the modeling effort.     

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.     

STATISTICAL ANALYSIS OF WATER CONSUMPTION1

The purpose of this study was to determine the degree of influence of various factors on municipal water consumption in Illinois. For the collection of basic data, questionnaires were sent to all public water works of incorporated towns. The questionnaire was designed to obtain information on factors which may have any effect on water use. The effects of the different parameters on water consumption were based on several correlation and regression combinations of predictands and predictors. It was found that in the Chicago region the percent of services and water used for commercial and industrial purposes and the age of the water works were the most important parameters influencing water consumption (gallons per capita per day) when pumpage is metered at the water works as well as at the customers. For the State, excluding the Chicago region, percent of public water use, persons per service, population and commercial and industrial water use were the most important parameters. It has been recommended that similar statistical analysis be conducted periodically to establish a trend or law of change from the influencing parameters.     

EVALUATION OF GREAT LAKES NET BASIN SUPPLY FORECASTS1

ABSTRACT: Evaluation of the Great Lakes Environmental Research Laboratory's (GLERL's) physically-based monthly net basin supply forecast method reveals component errors and the effects of model improvements for use on the Laurentian Great Lakes. While designed for probabilistic outlooks, it is assessed for giving deterministic outlooks along with other net basin supply forecast methods of the U.S. Army Corps of Engineers and Environment Canada, and with a stochastic approach commissioned by the Corps. The methods are compared to a simple clima-tological forecast and to actual time series of net basin supplies. Aetual net basin supplies are currently determined by estimating all components directly, instead of as water-balance residuals. This is judged more accurate and appropriate for both forecasting and simulation. GLERL's physically-based method forecasts component supplies while the other methods are based on residual supplies. These other methods should be rederived to be based on component supplies. For each of these other methods, differences between their outlooks and residual supplies are used as error estimates for the rederived methods and component supplies. The evaluations are made over a recent period of record high levels followed by a record drought. Net basin supply outlooks are better than climatology, and GLERL's physically-based method performs best with regard to either component or residual net basin supplies. Until advances are made in long-range climate outlooks, deterministic supply outlooks cannot be improved significantly.     

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.