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.     

AN ECONOMIC ANALYSIS OF WATER CONSERVATION POLICY1

Water conservation is a much emphasized policy of the Federal government. Discussion of water conservation proposals often involves confusion between a conservation “ethic,” which is an end in itself, and conservation as a means for attaining various economic objectives. Analysis indicates that outside of ground water “mining.” water is usually a renewable and reusable resource. During periods of normal precipitation, water conservation should be employed only when the value of the water saved exceeds the cost of effecting the savings. Water conservation is most valuable as a drought contingency tactic. Water conservation as a substitute for structural provision to meet normal water demand growth is apt to prove shortsighted.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

THE ENHANCED ROLE OF WATER CONSERVATION IN THE COST-BENEFIT ANALYSIS OF WATER PROJECTS1

The concept of water conservation has increased in importance because of revisions in the rules and procedures for performing cost-benefit analyses of federal water projects. These revisions include a requirement that nonstructural and water conservation measures be incorporated into economic assessments of projects. Project analyses will now proceed as if water supplies were allocated “most effectively,” that is, to their highest valued uses. A related requirement provides that the net benefits of any project should now be valued using willingness to pay measures. A specific cost-benefit methodology accommodating the revisions is constructed and discussed. Informational requirements for applying this methodology are identified. In addition to being consistent with federal mandates, this technique offers important advantages over the traditional “requirements” approach to water supply planning.     

CHAOTIC FORECASTING OF DISCHARGE TIME SERIES: A CASE STUDY1

ABSTRACT: This paper considers the problem of forecasting the discharge time series of a river by means of a chaotic approach. To this aim, we first check for some evidence of chaotic behavior in the dynamic by considering a set of different procedures, namely, the phase portrait of the attractor, the correlation dimension, and the largest Lyapunov exponent. Their joint application seems to confirm the presence of a nonlinear deterministic dynamic of chaotic type. Second, we consider the so‐called nearest neighbors predictor and we compare it with a classical linear model. By comparing these two predictors, it seems that nonlinear river flow modeling, and in particular chaotic modeling, is an effective method to improve predictions.     

DATA ANALYSIS OF WATER QUALITY TIME SERIES IN LAKE ERIE1

ABSTRACT: A comprehensive data analysis study is carried out for detecting trends and other statistical characteristics in water quality time series measured in Long Point Bay, Lake Erie. In order to glean an optimal amount of useful information from the available data, the exploratory and confirmatory data anslysis stages are adhered to. To test a range of hypotheses regarding the statistical properties of the time series, a wide variety of both parametric and nonparametric techniques are employed. A particularly useful nonparametric method for discovering trends is the seasonal Mann-Kendall test.     

CASE STUDIES OF AGRICULTURAL WATER CONSERVATION1

Farmers from four irrigation districts in Texas and California were questioned about water conservation practices they are now using, those they plan to adopt, and potential incentives that government might offer to induce still further water conservation on their part. While responses differed somewhat from place to place and among individual farmers, the general results were: a) farmers reported that “water conservation” is not new to them, it is something they practice regularly; b) recent innovations such as laser controlled land leveling devices have permitted some substantial water use reductions in recent years; and c) even greater incentive mechanisms that government could provide and that farmers would accept as useful incentives, such as long term low interest loans for water saving equipment, would probably not be able to reduce water use in agriculture much further than 15 percent below current levels. It is recommended nonetheless that Federal agencies and local water districts and individuals should nonetheless pursue water conservation training and education programs, demonstrations of conjunctive use and water banking opportunities for water saving, and increased loan programs for installation of water saving equipment.     

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.     

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.     

RESIDENTIAL WATER CONSERVATION: CASA DEL AGUA1

ABSTRACT: A single-family residence in Tucson, Arizona, was retrofitted with water-conserving fixtures, rainwater harvesting, and graywater reuse systems. During a four-year study, efficient use of water was shown to significantly decrease demand for domestic water at the house without reducing the residents' quality of life. The use of municipal water was reduced by 66 percent to 148 gallons per day (gpd) and total household use was reduced by 27 percent to 245 gpd. Graywater reuse averaged approximately 77 gpd or 32 percent of the total household water use. Evaporative cooling required about 15 gpd. Water use for toilet flushing was only 9 gallons per capita per day (gpcd) or 14 percent of interior water use.     

EFFECTS OF POTENTIAL WATER CONSERVATION EFFORTS IN EAST TENNESSEE1

ABSTRACT: The importance of water conservation was emphasized by a proposed National Water Policy which was established during the previous Carter Administration. This policy stressed water conservation on a national scale. Such a policy sought to apply one program to all water resources problems. Before implementation of this or another such policy, consideration must be given to those vast areas of the country which in reality do not have a shortage of water. One of these areas is the French-Broad River basin in Tennessee. This report was formulated in an effort to describe both the positive and negative effects of water policies which would bring about either a 10 percent or 30 percent reduction in water usage in this basically water rich area. The parameters used in the evaluation included selected economic, sociological, legal, and environmental impacts.     

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.     

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.     

INTERVENTION ANALYSIS OF WATER QUALITY RECORDS1

The impoundment of the Kootenai River by Libby Dam caused changes in discharge and water quality in the river downstream from Lake Koocanusa. The changes observed downsteam were largely attributable to the depth of withdrawal from the reservoir and the reservoir's ability to store and mix various influent water masses. The preimpoundment and postimpoundment time series of discharge and six water quality variables were autocorrelated and exhibited strong seasonality. Intervention analysis, a technique employing Box-Jenkins time series models, was used to quantify the nature and magnitude of the changes in water quality after the construction of Libby Dam. The models were developed with data from June 1967 through February 1981 and were able to satisfactorily forecast riverine conditions from March 1981 through January 1982.