Temporal variation and persistence of bacteria in streams

Better understanding of bacterial fate and transport in watersheds is necessary for improved regulatory management of impaired streams. Novel statistical time series analyses of coliform data can be a useful tool for evaluating the dynamics of temporal variation and persistence of bacteria within a watershed. For this study, daily total coliform data for the Little River in East Tennessee from 1 Oct. 2000 to 31 Dec. 2005 were evaluated using novel time series techniques. The objective of this study was to analyze the total coliform concentration data to: (i) evaluate the temporal variation of the total coliform, and (ii) determine whether the total coliform concentration data demonstrated any long-term or short-term persistence. For robust analysis and comparison, both time domain and frequency domain approaches were used for the analysis. In the time domain, an autoregressive moving average approach was used; whereas in the frequency domain, spectral analysis was applied. As expected, the analyses showed that total coliform concentrations were higher in summer months and lower in winter months. However, the more interesting results showed that the total coliform concentration exhibited short-term as well as long-term persistence ranging from about 4 wk to approximately 1 yr, respectively. Comparison of the total coliform data to hydrologic data indicated both runoff and baseflow are responsible for the persistence.     

SEASONAL ARIMA INFLOW MODELS FOR RESERVOIR SIZING1

ABSTRACT: The reliable sizing of reservoirs is a very important task of hydraulic engineering. Although many reservoirs throughout the world have been designed using Rippl's mass curves with historical inflow volumes at the dam site, this technique is now considered outdated. In this paper, synthetic series of monthly inflows are used as an alternative to historical inflow records. These synthetic series are generated from stochastic SARIMA (Seasonal Autoregressive Integrated Moving Average) models. The analyzed data refer to the planned Almopeos Reservoir on the Almopeos River in Northern Greece with 19‐year monthly inflow series. The analysis of this study demonstrates the ability of SARIMA models, in conjunction with the adequate transformation, to forecast monthly inflows of one or more months ahead and generate synthetic series of monthly inflows that preserve the key statistics of the historical monthly inflows and their persistence Hurst coefficient K. The forecasted monthly inflows would be of help in evaluating the optimal real time reservoir operation policies and the generated synthetic series of monthly inflows can be used to provide a probabilistic framework for reservoir design and to cope with the situation where the design horizon of interest exceeds the length of the historical inflow record.     

MULTIFRACTAL SCALING OF DAILY RUNOFF TIME SERIES IN AGRICULTURAL WATERSHEDS1

Abstract: Multifractal scaling behavior of long-term records of daily runoff time series in 32 subwatersheds covering a wide range of sizes was examined. These subwatersheds were associated with four agricultural watersheds with different climates and topography. The empirical moment scaling curves obtained using the trace moment method showed that the runoff time series exhibited a multifractal behavior, which was valid over a time scale range from one day to about three years. The multi-fractal scaling of the runoff time series was well described by the Universal Multifractal Model. The spectral analysis (β < 1) and the order of fractional integration (H ⋍; 0) indicated that the runoff time series were conservative. The multifractal parameters, α (multifractal index) and C₁ (co-dimension), were reasonably close to each other for subwatersheds within each of the watersheds and were generally similar among the four watersheds. The α values of the four watersheds were 1.10 ± 0.13, 1.61 ± 0.06,1.61 ± 0.24, and 1.63 ± 0.19. The C₁ values of four watersheds were 0.19 ± 0.01, 0.17 ± 0.01, 0.17 ± 0.04, and 0.11 ± 0.02. The multifractal analyses provided useful insight into the runoff time series, especially the occurrence and distribution of extreme events.     

COMPARING THE PALMER DROUGHT INDEX AND THE STANDARDIZED PRECIPITATION INDEX1

ABSTRACT: The Palmer Drought Index (PDI) is used as an indicator of drought severity, and a particular index value is often the signal to begin or discontinue elements of a drought contingency plan. The Standardized Precipitation Index (SPI) was recently developed to quantify a precipitation deficit for different time scales. It was designed to be an indicator of drought that recognizes the importance of time scales in the analysis of water availability and water use. This study compares historical time series of the PDI with time series of the corresponding SPI through spectral analysis. Results show that the spectral characteristics of the PDI vary from site to site throughout the U.S., while those of the SPI do not vary from site to site. They also show that the PDI has a complex structure with an exceptionally long memory, while the SPI is an easily interpreted, simple moving average process.     

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.     

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.     

SAMPLING FREQUENCY SELECTION FOR REGULATORY WATER QUALITY MONITORING1

ABSTRACT: The selection of sampling frequencies in order to achieve reasonably small and uniform confidence interval widths about annual sample means or sample geometric means of water quality constituents is suggested as a rational approach to regulatory monitoring network design. Methods are presented for predicting confidence interval widths at specified sampling frequencies while considering both seasonal variation and serial correlation of the quality time series. Deterministic annual cycles are isolated and serial dependence structures of the autoregressive, moving average type are identified through time series analysis of historic water quality records. The methods are applied to records for five quality constituents from a nine-station network in Illinois. Confidence interval widths about annual geometric means are computed over a range of sampling frequencies appropriate in regulatory monitoring. Results are compared with those obtained when a less rigorous approach, ignoring seasonal variation and serial correlation, is used. For a monthly sampling frequency the error created by ignoring both seasonal variation and serial correlation is approximately 8 percent. Finally, a simpler technique for evaluating serial correlation effects based on the assumption of AR(1) type dependence is examined. It is suggested that values of the parameter p₁, in the AR(1) model should range from 0.75 to 0.90 for the constituents and region studied.     

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.     

Automated Algorithms for Heuristic Base‐Flow Separation1

Abstract: The subjective nature of graphical base‐flow separation combined with the many applications of base‐flow time series derived from continuous streamflow data, motivates the development and application of automated algorithms for heuristic base‐flow separation. Base‐flow time series derived from gauged streamflow support diverse applications in engineering hydrology, catchment analysis, hydrogeologic investigations, regional low‐flow analysis, and recharge estimation. Whether based on graphical procedures for recession analysis or analytical expressions derived from fundamental equations of ground‐water flow, the variety of base‐flow separation algorithms belies the array of base‐flow definitions and interpretations that variously refer to dominant process, source, flow path, and characteristic response time. Algorithms that are invariant in their consistent – though heuristic – characterization of base‐flow response are particularly useful for interbasin comparisons of low‐flow characteristics and hydrologic regionalization. More adaptable algorithms provide application‐specific flexibility in allocating flow components like interflow to either quickflow or slowflow. Four widely used algorithms that produce consistent base‐flow time series using only gauged streamflow records are compared and contrasted with a complementary heuristic algorithm that incorporates hydrologic judgment explicitly, through manual parameterization. The utility of these inherently subjective algorithms is illustrated through a simple example of flow phase separation in a two‐component end‐member mixing model of dissolved chlorides in the Cuyahoga River.     

Global Warming and Global Dioxide Emission: An Empirical Study

In this paper, the dynamic relationship between global surface temperature (global warming) and global carbon dioxide emission (CO₂) is modelled and analyzed by causality and spectral analysis in the time domain and frequency domain, respectively. Historical data of global CO₂emission and global surface temperature anomalies over 129 years from 1860–1988 are used in this study. The causal relationship between the two phenomena is first examined using the Sim and Granger causality test in the time domain after the data series are filtered by ARIMA models. The Granger causal relationship is further scrutinized and confirmed by cross-spectral and multichannel spectral analysis in the frequency domain. The evidence found from both analyses proves that there is a positive causal relationship between the two variables. The time domain analysis suggests that Granger causality exists between global surface temperature and global CO₂emission. Further, CO₂emission causes the change in temperature. The conclusions are further confirmed by the frequency domain analysis, which indicates that the increase in CO₂emission causes climate warming because a high coherence exists between the two variables. Furthermore, it is proved that climate changes happen after an increase in CO₂emission, which confirms that the increase in CO₂emission does cause global warming.     

USING A CHOICE MODELLING APPROACH FOR CUSTOMER SERVICE STANDARDS IN URBAN WATER1

ABSTRACT: A series of reforms in the water industry in Australia has created a demand from the industry and regulators for objective methodologies to evaluate incremental changes in the customer service standards. In this paper, the use of choice modeling for estimating implicit prices associated with urban water supply attributes is explored. Results from multinomial logit (MNL) and random parameters logit (RPL) models show that increases in annual water bills and the frequency of future interruptions were the most important attributes. Implicit price confidence intervals based on the best models suggest that people are willing to pay positive amounts to achieve a water supply that is less frequently interrupted. The provision of alternative water supplies during an interruption and notification of the interruption were found to be unimportant to respondents. Choice modeling proved to be a useful technique and provided the industry and regulators with additional information for standard setting.     

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.     

VISUALIZATION OF TRENDS AND FLUCTUATIONS IN CLIMATIC RECORDS1

ABSTRACT: Small systematic changes in climatic records are often poorly visualized by standard time series plots because they are usually hidden by the magnitude and variability of the data values themselves. A visualization approach based on the rescaled adjusted partial sums (RAPS) which overcomes the above-stated shortcomings is presented. This visualization highlights trends, shifts, data clustering, irregular fluctuations, and periodicities in the record. Additional information on the number, magnitude, shape, frequency, and timing of fluctuations and trends can also be inferred. The visualization approach can be used for preliminary visual inspection of a time series, to gain a feel for the data, and/or to guide and focus subsequent statistical tests and analyses. It is not intended as a substitute for standard statistical analysis. Alternatively, the visualization approach can be used to display findings of a time series analysis. The capabilities and limitations of the approach are discussed and illustrated for two time series of annual rainfall values.     

FOREST HYDROLOGY AND EXTREME RAINFALL FREQUENCY1

Extreme rainfall frequency analysis provides one means to predict, within certain limits of probability, the average time interval between the recurrences of storms of a specified duration and magnitude. This in turn furnishes the forest hydrologist a valuable tool for engineering design and runoff and erosion forecast. A modification in the application of the annual maximum and annual exceedance series analysis described by V. T. Chow can, for special purposes, lead to an even more useful estimate of extreme events on a seasonal basis. This can be particularly important on small forested headwater watersheds where the runoff response to extreme rainfall may vary considerably with seasonal changes in canopy cover and soil moisture characteristics. Although the application of data covering a relatively short period of record has produced some inconsistencies among the frequency diagrams, under certain circumstances for short-term recurrence interval forecast and for non-critical application the analysis of extreme rainfall frequency from less than 20 years data seems justified.     

MULTIRESERVOIR ANALYSIS TECHNIQUES IN WATER QUANTITY STUDIES1

ABSTRACT. This paper deals with the subject of applying different types of systems analysis tools to water quantity studies of multireservoir networks of increasing degrees of complexity. The object is to show how each tool can be used, modified and combined with other tools to solve specific problems and to indicate the degrees of complexity at which more sophisticated tools should be applied. Firstly, several applications and limitations of linear programming and dynamic programming are discussed. Secondly, it is shown that mass curve analysis is useful, can be extended to serve in computing reservoir rules for conventional multireservoir simulation models, and can be applied in conjunction with either historic or generated sequences of hydrologic input data. Thirdly, extended and limiting features of conventional time-interval-by-time-interval multireservoir simulation models are analyzed. And fourthly, a two-model series for problems which defy analysis by more basic tools is described in detail, the first model using network analysis (Out-of-Kilter Algorithm) for all space and time arcs simultaneously and providing data for the second general-purpose model using network analysis each time interval. The importance of efficient computer procedures is stressed. The background for the paper includes systems analysis of water availability and hydro-thermal power studies carried out during the past six years in that part of Canada lying between the Great Lakes and the Rocky Mountain Divide.     

Validation of spectral gas radiation models under oxyfuel conditions—Part B: Natural gas flame experiments

Combustion of hydrocarbon fuels with pure oxygen results in a different flue gas composition as combustion with air. Standard CFD spectral gas radiation models for air blown combustion are out of their validity range. The series of three articles provides a common spectral basis for the validation of new developed models. Part B of the series presents spectral measurements in the spectral range of 2.4–5.4 μm of a 70 kW turbulent natural gas flame in air blown combustion and in wet and dry oxyfuel combustion. The experimentally measured intensity spectra were compared with simulated spectra based on measured gas atmospheres. The line-by-line database HITEMP2010 and the two statistical-narrow-band models EM2C and RADCAL were used for the numerical simulation. The measured spectra showed large fluctuations due to turbulence. The up to 75% increased averaged experimental intensity compared to the simulated intensity pointed out the importance of the effect of turbulence-radiation-interaction in combustion simulations.     

Nonlinear time series analysis of ground-level ozone dynamics in Southern Taiwan

The ozone pollution at ground level in rural and urban areas has been a long-standing problem in the world. This paper focuses on estimating self-affined nature of nonlinearity of ground-level peak ozone time series, which is analyzed by two nonlinear fractal statistical methods, including R/S analysis and BDS test. To explore the underlying structure of ozone observations at ground level and improve the forecasting capacity in urban region, practical implementation was assessed by a case study via collecting and analyzing the monitoring data at Chaojhou and Zenwu in the Kaohsiung metropolitan region, Taiwan. Based on R/S analysis, the time series can be identified as persistent and long-memory processes with Hurst exponents of both about 0.75. In addition, the V statistics specifies possible fluctuation cycle lengths of 32, 170, and 420 day simultaneously. Such results are consistent with the regional meteorological conditions leading to help characterize the regional scale ozone behavioral trend. Furthermore, the BDS test results confirm a strong nonlinearity of both time series associated with these two cities. Yet in both cases, nonlinearity implies chaos. The R/S analysis and BDS test provide strong evidence for nonlinearity and fractality of ozone time series due to noisy chaos, and we could not rule out the possibility of deterministic chaos in tropospheric ozone system.     

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.     

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.     

SIMULATION AS AN AID TO DECISION MAKING IN A WATER UTILITY1

ABSTRACT. Middle and high management levels within water utilities would find their decision making activities greatly enhanced if provided with a set of techniques having the following characteristics: (1) the ability to procure information and knowledge about real-life systems, (2) the ability to promote analysis of the real life system and (3) the capacity to gauge the impact of decisions. A model/simulation is presented, having the capability to mime operational aspects of water supply systems. The simulation produces time series of what are considered relevant operational variables. These series are amenable to analysis of both static and dynamic effects of alternative policies, changing environmental conditions and varying parametric specifications. Because of its modular structure and the ad hoc programming language utilized, it offers great flexibility. The model/simulation allows extensions, deletions and modifications without consequent reformulation or extensive reprogramming. It performs a number of statistical tests useful for its own verification and validation. Also available are a suggested methodology and procedures for model use, possible difficulties with data gathering and operation, plus an idea of what cannot be done with the currently extant model version.