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.     

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.     

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.     

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.     

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.     

FOURIER INFERENCE: SOME METHODS FOR THE ANALYSIS OF ARRAY AND NONGAUSSIAN SERIES DATA1

Fourier inference is a collection of analytic techniques and philosophic attitudes, for the analysis of data, wherein essential use is made of empirical Fourier transforms. This paper sets down some basic results concerning the finite Fourier transforms of stationary process data and then, to illustrate the approach, uses those results to develop procedures for: 1) estimating cloud and storm motion, 2) passive sonar and 3) fitting finite parameter models to nonGaussian time series via bispectral fitting. This last procedure is illustrated by an analysis of a stretch of Mississippi River runoff data. Examples 1), 2) refer to data having the form Y(x_j, y_j, t) for j = 1, …, J and t = 0, …, T-l say, and view that data as part of a realization of a spatial-temporal process. Such data has become common in geophysics generally and in hydrology particularly. The goal of this paper is to present some new statistical procedures pertinent to problems in the water sciences, equally it is to illustrate the genesis of those procedures and how their properties may be approximated.     

FILTERING OF DISSOLVED OXYGEN DATA IN STREAM WATER QUALITY ANALYSIS1

ABSTRACT: In this study a set of equations was developed which can be used to separate the time varying effects from observed dissolved oxygen (DO) data. A steady state DO profile thus derived allows a reasonable stream stimulation such that both the model and the data used in its formulation do not contain DO due to biological activities. Biological DO production and consumption are complex phenomena. By excluding these highly variable processes, this method simplifies stream DO modeling considerably. The net oxygen input due to these processes exist only part of the day, but, in the stream waste assimilative capacity analysiis and waste load allocation, one would focus his attention on critical condition. Hence, unless the change of stream ecology is the main concern, it is desirable to formulate a stream water quality model without this time varying term.     

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.     

THRESHOLD TIME SERIES MODELING OF TWO ICELANDIC RIVERFLOW SYSTEMS1

ABSTRACT: This paper reports our experience in building time series models which connect the flows in two Icelandic rivers with the meteorological variables of precipitation and temperature. Two rivers with different hydrological characteristics were studied. In areas where precipitation may be either in the form of rain or snow linear models are inadequate to describe the relationship between the river and the meteorological variables. The methodology of threshold models recently developed seems to be well suited for taking into account the sharp difference in the relationship according to whether it is freezing or not. The possibility of identifying an alternative threshold variable is also explored.     

CONSIDERATIONS OF SCALE IN WATER QUALITY MONITORING AND DATA ANALYSIS1

ABSTRACT: An assumption of scale is inherent in any environmental monitoring exercise. The temporal or spatial scale of interest defines the statistical model which would be most appropriate for a given system and thus affects both sampling design and data analysis. Two monitoring objectives which are strongly tied to scale are the estimation of average conditions and the evaluation of trends. For both of these objectives, the time or spatial scale of interest strongly influences whether a given set of observations should be regarded as independent or serially correlated and affects the importance of serial correlation in choosing statistical methods. In particular serial correlation has a much different effect on the estimation of long-term means than it does on the estimation of specific-period means. For estimating trends, a distinction between serial correlation and trend is scale dependent. An explicit consideration of scale in monitoring system design and data analysis is, therefore, most important for producing meaningful statistical information.     

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.     

GENERATION OF SYNTHETIC AND MISSING CLIMATIC DATA FOR PUERTO RICO1

ABSTRACT: Climatic data such as temperature, solar radiation, relative humidity, and wind speed have been widely used to estimate evapotranspiration. Moat of the solar radiation data and portions of the relative humidity data are either not available or missing from the records in Puerto Rico. Depending upon the availability and data characteristics of records, three methods (including a regression technique, an averaging of historical data, and a regional average) were used to generate missing data, and a time series analysis was used to synthesize a series of climatic data. The limitations and applicability of each method are discussed. The results showed that the time series analysis method can be successfully used to synthesize a series of monthly solar radiations for several stations. The regression technique and the regional average can be successfully applied to generate missing monthly solar radiation data. The regression technique and the averaging of historical data have been satisfactorily used to interpolate missing monthly relative humidity. The explained variance (R²) varied from 0.68 to 0.88, which are both significant at the 0.05 level of significance.     

STOCHASTIC ANALYSIS OF TIME-AGGREGATED HYDROLOGIC DATA1

Stochastic models fitted to hydrologic data of different time scales are interrelated because the higher time scale data (aggregated data) are derived from those of lower time scale. Relationships between the statistical properties and parameters of models of aggregated data and of original data are examined in this paper. It is also shown that the aggregated data can be more accurately predicted by using a valid model of the original data than by using a valid model of the aggregated data. This property is particularly important in forecasting annual values because only a few annual values are usually available and the resulting forecasts are relatively inaccurate if models based only on annual data are used. The relationships and forecasting equations are developed for general aggregation time and can be used for hourly and daily, daily and monthly or monthly and yearly data. The method is illustrated by using monthly and yearly streamflow data. The results indicate that various statistical characteristics and parameters of the model of annual data can be accurately estimated by using the monthly data and forecasts of annual data by using monthly models have smaller one step ahead mean square error than those obtained by using annual data models.     

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.     

MODELING HYDROLOGIC TIME SERIES FROM THE ARCTIC1

The general intervention model is applied to hydrologic and meteorologjc time series from the Canadian Arctic. The authors show how the model is able to account for environmental interventions, missing observations in the data, changes in data collection procedures, the effects of external inputs, as well as seasonality and autocorrelation. Methods for identifying transfer functions by making use of a physical understanding of the processes involved are demonstrated and sample applications of the general intervention model to Arctic data are shown.     

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.     

STATISTICAL ANALYSIS OF DAILY WATER QUALITY DATA1

ABSTRACT. The stochastic nature of some water quality time series were examined. These time series include nine years of daily observations in: (1) the stream flow (Q), (2) the water temperature (T), (3) the dissolved oxygen (DO), and (4) the biochemical oxygen demand (BOD) of the Passaic River at Little Falls, New Jersey. It was found that the random component contributes more than 60 per cent of the variance in the BOD series, but only 30 per cent or less in the DO series. Autocorrelation analysis suggest that DO and BOD residual series have a persistence of about 30 days. Significant crosscorrelation between DO and temperature T was found when DO lags T for up to 30 days, which indicates that the critical DO probably lags the critical temperature. Also, spectral anlaysis shows multiple peaks in the BOD series, reflecting effects of storm runoff and other non-point source pollution on river water quality.     

ROLE OF MODELS IN GROUNDWATER MANAGEMENT1

To answer the difficult question of how to integrate operation of ground and surface water supplies into their management plans, the decision-makers must be able to predict the effects of various alternative modes of operation and meteorological conditions on the groundwater basin. Many types of models have been used for simulating the behavior of groundwater basins under these changes. Analog simulators, analog computers, and digital computers have been employed for model development. To achieve plausible models, detailed hydraulic and hydrologic characteristics are required, such as data on transmissivity, storage, and net deep percolation. These data are used in the equations that form the model. Water quality, which cannot be separated from quantity, deserves equal consideration. Recently, considerable efforts have been made to develop water quality prediction tools through the use of modeling techniques.     

THE DEVELOPMENT OF THE NILE HYDROMETEOROLOGICAL FORECAST SYSTEM1

ABSTRACT: The National Oceanic and Atmospheric Administration is developing a river forecast system for the Nile River in Egypt. The river forecast system operates on scientific work stations using hydrometeorological models and software to predict inflows into the high Aswan Dam and forecast flow hydrographs at selected gaging locations above the dam The Nile Forecasting System (NFS) utilizes satellite imagery from the METEOSAT satellite as the input to the forecast system. Satellite imagery is used to estimate precipitation over the Blue Nile Basin using five different techniques. Observed precipitation data and climatic statistics are used to improve precipitation estimation. Precipitation data for grid locations are input to a distributed water balance model, a hill slope routing model, and a channel routing model. A customized Geographic Information System (GIS) was developed to show political boundaries, rivers, terrain elevation, and gaging network. The GIS was used to develop hydrologic parameters for the basin and is used for multiple display features.