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.     

SHORT-TERM FORECASTING OF SNOWMELT RUNOFF USING ARMAX MODELS1

ABSTRACT: Time series models of the ARMAX class were investigated for use in forecasting daily riverflow resulting from combined snowmelt/rainfall. The Snowmelt Runoff Model (Martinec-Rango Model) is shown to have a form similar to the ARMAX model. The advantage of the ARMAX approach is that analytical model identification and parameter estimation techniques are available. In addition, previous forecast errors can be included to improve forecasts and confidence limits can be estimated for the forecasts. Diagnostic checks are available to determine if the model is performing properly. Finally, Kalman filtering can be used to allow the model parameters to vary continuously to reflect changing basin runoff conditions. The above advantages result in improved flow forecasts with fewer model parameters.     

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.     

ANALYSIS AND MODELING OF LONG-TERM STREAM TEMPERATURES ON THE STEAMBOAT CREEK BASIN,OREGON: IMPLICATIONS FOR LAND USE AND FISH HABITAT1

ABSTRACT: Steamboat Creek basin is an important source of timber and provides crucial spawning and rearing habitat for anadromous steelhead trout (Oncorhynchus mykiss). Because stream temperatures are near the upper limit of tolerance for the survival of juvenile steelhead, the possible long-term effect of clear-cut logging on stream temperatures was assessed. Twenty-year (1969–1989) records of summer stream temperature and flow from four tributaries and two reaches of Steamboat Creek and Boulder Creek (a nearby unlogged watershed) were analyzed. Logging records for the Steamboat Creek basin and air temperature records also were used in the analysis. A time-series model of the components of stream temperature (seasonal cycle of solar radiation, air temperature, streamflow, an autoregressive term of order 1, and a linear trend variable) was fitted to the water-temperature data. The linear trend variable was significant in all the fitted models except Bend Creek (a tributary fed by cool ground-water discharge) and Boulder Creek. Because no trends in either climate (i.e., air temperature) or streamflow were found in the data, the trend variable was associated with the pre-1969 loss and subsequent regrowth of riparian vegetation and shading canopies.     

PROBLEMS IN FORECASTING WATER REQUIREMENTS1

ABSTRACT. Methodological problems associated with forecasting water requirements by use of regression analysis are examined. Problems occurring when long-range forecasts are based on linear and nonlinear extrapolation of time series models include possible changes in socioeconomic conditions, water allocation system structure, and limits to growth. Problems arising in forecasting based on multiple regression models are likely to involve serially dependent errors, multicollinear explanatory variables, and difficulties inherent to the presence of explanatory variables that must themselves be predicted.     

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.     

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.     

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.     

A HYDROCLIMATIC APPLICATION STRATEGY FOR THE POISSON PARTIAL DURATION MODEL1

ABSTRACT: A strategy for formulating and testing the Poisson partial duration extreme value model is presented. The procedure is demonstrated using recorded Streamflow series from a humid subtropical region of the southern United States. The observed data series are partitioned by climatic causes and tested for both the Poisson assumption and the validity of the exponential as marginal distributions. Several statistical tests are utilized in making these determinations. Some important aspects of the model as applied to humid climates are demonstrated. It was found that a majority of Streamflow series could be represented by the model and that significant differences do exist between the arrival structures of floods resulting from different climatic mechanisms. However, these differences generally do not exist in the distribution of the flood magnitudes. In addition, it is possible that model validity is restricted by drainage basin size.     

USABILITY ASSESSMENTS FOR HYDROLOGIC FORECASTING DSS1

ABSTRACT: Usability assessments were used to obtain feedback on the development of a flood forecasting decision support system. The feedback was used to guide design of system functionality, interface, training, implementation, and operations. The usability process was user focused and was dependent upon implementation of a prototype system in an operational setting. This paper describes concepts and methods applied to collect reflective and objective data on DSS components and information outputs. The general structure of the usability assessments is discussed and results of assessments are summarized.     

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.     

EVALUATION OF PRACTICES IN WATER SUPPLY FORECASTING1

ABSTRACT: Snowmelt runoff is a primary source of water supply in much of the Western United States. Multipurpose planning requires long-range forecasts and the accuracy of the forecasts has a significant effect on economic benefits. In an effort to increase the accuracy of snowrnelt runoff forecasts, selected practices in water supply forecasting were evaluated. These practices include 1) using multiple regression in developing forecasting models;2) using a model that was calibrated to make forecasts an April 1 for making forecasts at other times;3) using maximum snow water equivalent measurements in forecast equations; and 4) using weighted snow water equivalent measurements for making forecasts. The results of a case study indicate that forecasting accuracy is significantly affected by these practices. Goodness-of-fit statistics may not be indicative of the accuracy of forecasts when the prediction equations are used to make forecasts for dates other than that used in calibration. The use of maximum snow water equivalentmeasurements and weighted averages did not improve forecast accuracy.     

INDEXED SEQUENTIAL HYDROLOGIC MODELING FOR HYDROPOWER CAPACITY ESTIMATION1

ABSTRACT: The indexed sequential hydrologic modeling (ISM) methodology is utilized by the Western Area Power Administration as the basis for risk-based estimation of project-dependable hydropower capacity for several federally owned/operated projects. ISM is a technique based on synthetic generation of a series of overlapping short-term inflow sequences obtained directly from the historical record. The validity of ISM is assessed through application to the complex multireservoir hydropower system of the Colorado River basin for providing risk estimates associated with determination of reliable hydrogeneration capacity. Performance of ISM is compared with results from stochastically generated streamflow input data to the Colorado River Simulation System (CRSS). Statistical analysis and comparison of results are based on monthly power capacity, energy generation, and downstream water deliveries. Results indicate that outputs generated from ISM synthetically generated sequences display an acceptable correspondence with those obtained from stochastically generated hydrologic data for the Colorado River Basin.     

MODEL ACCURACY IN SNOWMELT-RUNOFF FORECASTS EXTENDING FROM 1 TO 20 DAYS1

ABSTRACT: This paper examines the performance of snowmelt-runoff models in conditions approximating real-time forecast situations. These tests are one part of an intercomparison of models recently conducted by the World Meteorological Organization (WMO). Daily runoff from the Canadian snowmelt basin Illecille. waet (1155 km², 509–3150 m a.s.l.) was forecast for 1 to 20 days ahead. The performance of models was better than in a previous WMO project, which dealt with runoff simulations from historical data, for the following reasons: (1) conditions for models were more favorable than a real-time forecast situation because measured input data and not meteorological forecast inputs were distributed to the modelers; (2) the selected test basin was relatively easy to handle and familiar from the previous WMO project; and (3) all kinds of updating were allowed so that some models even improved their accuracy towards longer forecast times. Based on this experience, a more realistic follow-up project can be imagined which would include temperature forecasts and quantitative precipitation forecasts instead of measured data.     

THE ARMA MODELS APPLIED TO THE FLOW OF KARSTIC SPRINGS1

ABSTRACT: Autoregressive moving average (ABMA) models have been applied to study the flow series of the karstic springs of La Villa, Fuente Mayor (Spain), and Aliou (France). The theoretical meaning of the parameters involved in the model upon applying it to a simplified scheme of the emptying of a karstic aquifer is first analyzed. The types of transformations necessary to apply these models to the flow series that lack normality and have strong periodic components are also indicated, as are the advantages of this type of model and the physical significance of the parameters obtained, with respect to the standpoint of hydraulics, ranging from rather homogeneous aquifers (La Villa) to extremely karstic (Aliou), including aquifers with intermediate characteristics (Fuente Mayor).     

Karst Hydrological Processes and Grey System Model1

Hao, Yonghong, Jiaojuan Zhao, Huamin Li, Bibo Cao, Zhongtang Li, and Tian‐Chyi J. Yeh, 2012. Karst Hydrological Processes and Grey System Model. Journal of the American Water Resources Association (JAWRA) 48(4): 656‐666. DOI: 10.1111/j.1752‐1688.2012.00640.x Abstract: The karst hydrological processes are the response of karst groundwater system to precipitation. This study provided a concept model of karst hydrological processes. The hydraulic response time of spring discharge to precipitation includes the time that precipitation penetrates through the vadose zone, and the subsequent groundwater pressure wave propagates to a spring outlet. Due to heterogeneities in karst aquifers, the hydraulic response time is different in different areas. By using grey system theory, we proposed a karst hydrological model that offers a calculation of hydraulic response time, and a response model of spring discharge to precipitation. Then, we applied the models to the Liulin Springs Basin, China. In the south part of the Liulin Springs Basin, where large fields of carbonate rocks outcrop with intensive karstification, the hydraulic response time is one year. In the north, where the Ordovician karst aquifer is covered by Quaternary loess sediments, the response time is seven years. The grey system GM(1,3) response model of spring discharge to precipitation was applied in consideration of the hydraulic response time. The model calibration showed that the average error was 6.55%, and validation showed that the average error was 12.19%.     

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.     

SPATIAL ANALYSIS FOR MONTHLY RAINFALL IN SOUTH FLORIDA1

ABSTRACT: Several methods have been developed to interpolate point rainfall data and integrate areal rainfall data from any network of stations. From previous studies, it can be concluded that models for spatial analysis of rainfall are dependent on topography, area of analysis, type of rainfall, and density of gauging network. The purpose of this study is to evaluate a set of six appropriate models for point and areal rainfall estimations over a 4000 square mile area in South Florida. In this study, a case of developing spatial continuity model for monthly rainfall from a database that had various lengths of records and missing data is documented. The spatial correlation and variogram models for monthly rainfall were developed. Six methods of spatial interpolation were applied and the results validated with historical observations. The results of the study indicate that the multiquadric, kriging, and optimal interpolation schemes are the best three methods for interpolation of monthly rainfall within the study area. The optimal and kriging methods have the advantage of providing estimates of the error of interpolation. The optimal interpolation method uses the spatial correlation function and the kriging method uses the variogram function. The two spatial functions are related. Either of the two methods provide good estimates of monthly point and areal rainfall in the study area.