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.     

System dynamics modeling for municipal water demand estimation in an urban region under uncertain economic impacts

Accurate prediction of municipal water demand is critically important to water utilities in fast-growing urban regions for drinking water system planning, design, and water utility asset management. Achieving the desired prediction accuracy is challenging, however, because the forecasting model must simultaneously consider a variety of factors associated with climate changes, economic development, population growth and migration, and even consumer behavioral patterns. Traditional forecasting models such as multivariate regression and time series analysis, as well as advanced modeling techniques (e.g., expert systems and artificial neural networks), are often applied for either short- or long-term water demand projections, yet few can adequately manage the dynamics of a water supply system because of the limitations in modeling structures. Potential challenges also arise from a lack of long and continuous historical records of water demand and its dependent variables. The objectives of this study were to (1) thoroughly review water demand forecasting models over the past five decades, and (2) propose a new system dynamics model to reflect the intrinsic relationship between water demand and macroeconomic environment using out-of-sample estimation for long-term municipal water demand forecasts in a fast-growing urban region. This system dynamics model is based on a coupled modeling structure that takes into account the interactions among economic and social dimensions, offering a realistic platform for practical use. Practical implementation of this water demand forecasting tool was assessed by using a case study under the most recent alternate fluctuations of economic boom and downturn environments.     

RECYCLING INPUT DATA DURING ANALYTIC ELEMENT MODELING NEAR INDIANAPOLIS,INDIANA1

ABSTRACT: Overlapping and adjacent ground water investigations are common in areas where aquifers are threatened by industrial development. In the Indianapolis area in Marion County, Indiana, a patchwork of ground water flow models have been used during the past 20 years to evaluate ground water resources and to determine the effects of local contamination. In every case these ground water models were constructed from scratch. Site specific finite difference grids or finite element meshes inhibit the direct reuse of input data when the area of interest shifts. Because the aquifer is not discretized into a grid or mesh with analytic element models, there are unique opportunities for direct reuse of model input data. In two applications of this principle we illustrate how the newly emerging analytic element method allows a fairly straightforward reuse of model input data from previous models in the same general area. In analytic element models of Central Indiana, streams and their tributaries are represented in different resolutions. Input data items of several modeling studies are stored and cataloged on disk in such a manner that they can be selectively retrieved by a data management program PREPRO. In this manner, a new ground water model can be set up quickly with input data which have been previously defined and tested during model calibration.     

IMPACT OF VARIED DATA RESOLUTION ON HYDRAULIC MODELING AND FLOODPLAIN DELINEATION1

ABSTRACT: Current data collection technologies such as light detection and ranging (LIDAR) produce dense digital terrain data that result in more accurate digital terrain models (DTMs) for engineering applications. However, such data are redundant and often cumbersome for hydrologic and hydraulic modeling purposes. Data filtering provides a means of eliminating redundant points and facilitates model preparation. This paper demonstrates the impact of varied data resolution on a case study completed for a 2.3 mi² area with mild slopes (about 001 ft/ft) along Leith Creek near Laurinburg, North Carolina. For the original data set and seven filtered data sets, filtering induced changes in elevation, area, and hydraulic radius were determined for 10 water depths at 23 cross sections. Water surface elevations resulting from HEC‐RAS (Hydrologic Engineering Center‐River Analysis System) models for each data set were then compared. A hydraulic model sensitivity analysis was also conducted to compare filtering error to error introduced by variation in flow rates and roughness values. Finally, automated floodplain delineation was performed for each filter level based on the computed hydraulic model results and the filtered LIDAR elevations. Data filtering results indicate that significant time savings are achieved throughout the modeling process and that filtering to four degrees can be performed without compromising cross‐sectional geometry, hydraulic model results, or floodplain delineation results.     

VELOCITY EQUATION FOR WATER QUALITY MODELING IN GEORGIA1

ABSTRACT: Tabletop water quality modeling still plays an important role in the water pollution control activities of the Georgia Environmental Protection Division. Tabletop models are those developed with out the aid of extensive field data. One important component of GEORGIA DOSAG, our basic water quality model, is the equation used to predict flow through velocity. However, Georgia is characterized by wide physiographic diversity which reduces the effectiveness of uncalibrated velocity equations. Using 15 years of accumulated time-of-travel studies, a series of empirical velocity equations were developed and calibrated to various physiographic conditions in Georgia. Equations are available for each major soil province and for three stream flow ranges within each province - Q<100 cfs, 100<Q<1000 cfs, and Q>1000 cfs. Now, in the absence of extensive field data, we have data based velocity equations which can be tailored to each site under study.     

CHALLENGES IN MODELING HYDROLOGIC AND WATER QUALITY PROCESSES IN RIPARIAN ZONES1

This paper presents key challenges in modeling water quality processes of riparian ecosystems: How can the spatial and temporal extent of water and solute mixing in the riparian zone be modeled? What level of model complexity is justified? How can processes at the riparian scale be quantified? How can the impact of riparian ecosystems be determined at the watershed scale? Flexible models need to be introduced that can simulate varying levels of hillslope‐riparian mixing dictated by topography, upland and riparian depths, and moisture conditions. Model simulations need to account for storm event peak flow conditions when upland solute loadings may either bypass or overwhelm the riparian zone. Model complexity should be dictated by the level of detail in measured data. Model algorithms need to be developed using new macro‐scale and meso‐scale experiments that capture process dynamics at the hillslope or landscape scales. Monte Carlo simulations should be an integral part of model simulations and rigorous tests that go beyond simple time series, and point‐output comparisons need to be introduced. The impact of riparian zones on watershed‐scale water quality can be assessed by performing simulations for representative hillsloperiparian scenarios.     

DECISION SUPPORT FOR ALLOCATION OF WATERSHED POLLUTION LOAD USING GREY FUZZY MULTIOBJECTIVE PROGRAMMING1

ABSTRACT: This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water quality models, water quality standards, wastewater treatment costs, and potential benefits gained via in‐stream water quality improvement. While fuzzy sets are characterized based on semantic and cognitive vagueness in decision making, grey numbers can delineate measurement errors in data collection. By employing three distinct set theoretic fuzzy operators, the synergy of grey and fuzzy implications may smoothly characterize the prescribed management complexity. With the aid of genetic algorithm in the solution procedure, the modeling outputs contribute to the development of an effective waste load allocation and reduction scheme for tributaries in this subwatershed located in the lower Tseng‐Wen River Basin, South Taiwan. Research findings indicate that the inclusion of three fuzzy set theoretic operators in decision analysis may delineate different tradeoffs in decision making due to varying changes, transformations, and movements of waste load in association with land use pattern within the watershed.     

UTILIZATION OF MODELS IN WATER RESOURCES1

ABSTRACT: A 1984 survey of water resources personnel was conducted to determine the current and future uses of mathematical models in planning, design and operations of water resources systems. Eighty-six percent of those responding indicated they have used mathematical models in the last year. Lack of appropriate data, inadequate time and funding to do the modeling and lack of models that represent the “real world” situation were the most frequently mentioned constraints to model use. Microcomputers were seen as having a positive influence on mathematical model use in water resources.     

Time Series Forecasting of Cyanobacteria Blooms in the Crestuma Reservoir (Douro River, Portugal) Using Artificial Neural Networks

In this work, time series neural networks were used to predict the occurrence of toxic cyanobacterial blooms in Crestuma Reservoir, which is an important potable water supply for the Porto region, located in the north of Portugal. These models can potentially be used to provide water treatment plant operators with an early warning for developing cyanobacteria blooms. Physical, chemical, and biological parameters were collected at Crestuma Reservoir from 1999 to 2002. The data set was then divided into three independent time series, each with a fortnightly periodicity. One training series was used to “teach” the neural networks to predict results. Another series was used to verify the results, and to avoid over-fitting of the data. An additional independently collected data series was then used to test the efficacy of the model for predicting the abundance of cyanobacteria. All of the models tested in this study incorporated a prediction time (look-ahead parameter) equal to the sampling interval (two weeks). Various lag periods, from 2 to 52 weeks, were also investigated. The best model produced in this study provided the following correlations between the target and forecast values in the training, verification, and validation series: 1.000 (P = 0.000), 0.802 (P = 0.000), and 0.773 (P = 0.001), respectively. By applying this model to the three-year data set, we were able to predict fluctuations in cyanobacteria abundance in the Crestuma Reservoir, with a high level of precision. By incorporating a lag-period of eight weeks, we were able to detect secondary fluctuations in cyanobacterial abundance over the annual cycle.     

A Sensitivity and Error Analysis Framework for Lake Eutrophication Modeling1

ABSTRACT: A framework for sensitivity and error analysis in mathematical modeling is described and demonstrated. The Lake Eutrophication Analysis Procedure (LEAP) consists of a series of linked models which predict lake water quality conditions as a function of watershed land use, hydrolgic variables, and morphometric variables. Specification of input variables as distributions (means and standard errors) and use of first-order error analysis techniques permits estimation of output variable means, standard errors, and confidence ranges. Predicted distributions compare favorably with those estimated using Monte-Carlo simulation. The framework is demonstrated by applying it to data from Lake Morey, Vermont. While possible biases exist in the models calibrated for this application, prediction variances, attributed chiefly to model error, are comparable to the observed year-to-year variance in water quality, as measured by spring phosphorus concentration, hypolimnetic oxygen depletion rate, summer chlorophyll-a, and summer transparency in this lake. Use of the framework provides insight into important controlling factors and relationships and identifies the major sources of uncertainty in a given model application.     

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.     

LAKE WATER QUALITY ASSESSMENT FROM LANDSAT THEMATIC MAPPER DATA USING NEURAL NETWORK: AN APPROACH TO OPTIMAL BAND COMBINATION SELECTION1

Abstract: The concern about water quality in inland water bodies such as lakes and reservoirs has been increasing. Owing to the complexity associated with field collection of water quality samples and subsequent laboratory analyses, scientists and researchers have employed remote sensing techniques for water quality information retrieval. Due to the limitations of linear regression methods, many researchers have employed the artificial neural network (ANN) technique to decorrelate satellite data in order to assess water quality. In this paper, we propose a method that establishes the output sensitivity toward changes in the individual input reflectance channels while modeling water quality from remote sensing data collected by Landsat thematic mapper (TM). From the sensitivity, a hypothesis about the importance of each band can be made and used as a guideline to select appropriate input variables (band combination) for ANN models based on the principle of parsimony for water quality retrieval. The approach is illustrated through a case study of Beaver Reservoir in Arkansas, USA. The results of the case study are highly promising and validate the input selection procedure outlined in this paper. The results indicate that this approach could significantly reduce the effort and computational time required to develop an ANN water quality model.     

GROUND WATER SIMULATION USING A ONE DIMENSIONAL FLOW MODEL1

ABSTRACT: In projects involving ground water problems, dependence on the mathematical modeling of the ground water flow phenomena is inescapable. At present, two dimensional flow models, which require tremendous amounts of computer time and storage, are generally used. When such bulky models are used for planning purposes, the two requirements (computer time and storage) can severely limit the number of alternatives that can be considered. A simple quantity and quality simulation model is developed here which requires considerably less computer time and storage and gives reasonably accurate results. The model was applied to simulate a ground water basin in San Luis Rey River in Southern California. The results were compared with those obtained by a USGS model. It was found that the simple model gave results which were consistentaly within five percent of the USGS model results, while the requirements on computer time and storage were drastically reduced.     

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.     

MULTIPLICATIVE,SEASONAL ARIMA MODELS FOR LAKE ERIE AND LAKE ONTARIO WATER LEVELS1

ABSTRACT: Federal agencies in the U.S. and Canada continuously examine methods to improve understanding and forecasting of Great Lakes water level dynamics in an effort to reduce the negative impacts of fluctuating levels incurred by interests using the lakes. The short term, seasonal and long term water level dynamics of lakes Erie and Ontario are discussed. Multiplicative, seasonal ARIMA models are developed for lakes Erie and Ontario using standardized, monthly mean level data for the period 1900 to 1986. The most appropriate model identified for each lake had the general form: (1 0 1)(0 1 1)₁₂. The data for each lake were subdivided by time periods (1900 to 1942;1 943 to 1986) and the model coefficients estimated for the subdivided data were similar, indicating general model stability for the entire period of record. The models estimated for the full data sets were used to forecast levels 1,2,3, and 6 months ahead for a period of high levels (1984 to 1986). The average absolute forecast error for Lake Erie was 0.049m, 0.076m, 0.091 m and 0.128m for the 1, 2,3, and 6 month forecasts, respectively. The average absolute forecast error for Lake Ontario was 0.058m, 0.095m, 0.120m and 0.136m for the 1,2,3, and 6 month forecasts, respectively. The ARIMA models provide additional information on water level time series structure and dynamics. The models also could be coordinated with current forecasting methods, possibly improving forecasting accuracy.     

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 Stochastic Modeling Approach to Address Hydrogeologic Uncertainties in Modeling Wellhead Protection Boundaries in Karst Aquifers1

Abstract: Development of any numerical ground‐water model is dependent on hydrogeologic data describing the subsurface. These data are obtained from geologic core analyses, stratigraphic analyses, aquifer performance tests, and geophysical studies. But typically in remote areas, these types of data are very sparse and site‐specific in terms of the aerial extent of the resource to be modeled. Uncertainties exist as to how well the available data from a few locations defines a heterogeneous surficial aquifer such as the Biscayne Aquifer in Miami‐Dade County, Florida. This is particularly the case when an exceptionally conductive horizontal flow zone is detected at one site due to specialized testing that was not historically conducted at the other at sites that provided data for the model. Not adequately accounting for the potential effect of the high flow zone in the aquifer within a ground‐water numerical model, even though the zone may be of very limited thickness, might underpredict the well field protection capture boundaries. Applied Stochastic ground‐water modeling in determining well field protection zones is steadily becoming important in addressing the uncertainty of the hydrogeologic subsurface parameters, specifically in karstic heterogeneous aquifers. This is particularly important in addressing the uncertainty of a 60‐day travel time capture zone in the Northwest Well Field, Miami‐Dade County, where a predominantly high flow zone controls much of the flow in the production wells. A stochastic ground‐water modeling application along with combination of pilot points and regularization technique is presented to further consolidate the uncertainty of the subsurface.