FRACTIONAL DIFFERENCING MODELING IN HYDROLOGY1

ABSTRACT: Fractional differencing is a tool for modeling time series which have long-term dependence; i.e., series in which the correlation between distant observations, though small, is not negligible. Fractionally differenced ARIMA models are formed by permitting the differencing parameter d in the familiar Box-Jenkins ARIMA(p, d, q) models to take nonintegral values; they permit the simultaneous modeling of the long-term and short-term behavior of an observed time series. This paper discusses the usefulness of fractional differencing to time-series modeling, with emphasis on hydrologic applications. A methodology for fitting fractionally differenced ARIMA models is described, and examples are presented.     

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES1

Results involving correlation properties and parameter estimation for autoregressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.     

KALMAN FILTER ESTIMATION AND PREDICTION OF DAILY STREAM FLOWS: I. REVIEW,ALGORITHM, AND SIMULATION EXPERIMENTS1

An important class of models, frequently used in hydrology for the forecasting of hydrologic variables one or more time periods ahead, or for the generation of synthetic data sequences, is the class of autoregressive(AR) models. As the AR models belong to the family of linear stochastic difference equations, they have both a deterministic and a stochastic component. The stochastic component is often assumed to have a Gaussian distribution. It is well known that hydrologic observations (e.g., stream flows) are heavily affected by noise. To account explicitly for the observation noise, the linear stochastic difference equation is expressed in state variable form and an observation model is introduced. The discrete Kalman filter algorithm can then be used to obtain estimates of the state variable vector. Typically, in hydrologic systems, model parameters, system noise statistics and measurement noise statistics are unknown, and have to be estimated. In this study an adaptive algorithm is discussed which estimates these quantities simultaneously with the state variables. The performance of the algorithm is evaluated by using simulated data.     

Multi-objective optimization of waste and resource management in industrial networks – Part I: Model description

This article presents a general multi-objective mixed-integer linear programming (MILP) optimization model aimed at providing decision support for waste and resources management in industrial networks. The MILP model combines material flow analysis, process models of waste treatments and other industrial processes, life cycle assessment, and mathematical optimization techniques within a unified framework. The optimization is based on a simplified representation of industrial networks that makes use of linear process models to describe the flows of mass and energy. Waste-specific characteristics, e.g. heating value or heavy metal contamination, are considered explicitly along with potential technologies or process configurations. The systems perspective, including both provision of waste treatment and industrial production, enables constraints imposed upon the systems, e.g. available treatment capacities, to be explicitly considered in the model. The model output is a set of alternative system configurations in terms of distribution of waste and resources that optimize environmental and economic performance. The MILP also enables quantification of the improvement potential compared to a given reference state. Trade-offs between conflicting objectives are identified through the generation of a set of Pareto-efficient solutions. This information supports the decision making process by revealing the quantified performance of the efficient trade-offs without relying on weighting being expressed prior to the analysis. Key features of the modeling approach are illustrated in a hypothetical case. The optimization model described in this article is applied in a subsequent paper (Part II) to assess and optimize the thermal treatment of sewage sludge in a region in Switzerland.     

Streamflow Forecasting Using Singular Value Decomposition and Support Vector Machine for the Upper Rio Grande River Basin

The current study improves streamflow forecast lead‐time by coupling climate information in a data‐driven modeling framework. The spatial–temporal correlation between streamflow and oceanic–atmospheric variability represented by sea surface temperature (SST), 500‐mbar geopotential height (Z₅₀₀), 500‐mbar specific humidity (SH₅₀₀), and 500‐mbar east–west wind (U₅₀₀) of the Pacific and the Atlantic Ocean is obtained through singular value decomposition (SVD). SVD significant regions are weighted using a nonparametric method and utilized as input in a support vector machine (SVM) framework. The Upper Rio Grande River Basin (URGRB) is selected to test the applicability of the proposed model for the period of 1965–2014. The April–August streamflow volume is forecasted using previous year climate variability, creating a lagged relationship of 1–13 months. SVD results showed the streamflow variability was better explained by SST and U₅₀₀ as compared to Z₅₀₀ and SH₅₀₀. The SVM model showed satisfactory forecasting ability with best results achieved using a one‐month lead to forecast the following four‐month period. Overall, the SVM results showed excellent predictive ability with average correlation coefficient of 0.89 and Nash–Sutcliffe efficiency of 0.79. This study contributes toward identifying new SVD significant regions and improving streamflow forecast lead‐time of the URGRB.     

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.     

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.     

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.     

Optimizing organic fertilizer applications under steady-state conditions

Because organic N fertilizers must be mineralized before they become plant-available, application designs should consider time and temperature effects on N release as well as crop N requirements. This study presents deterministic (DOpt) and stochastic (SOpt) linear optimization models to determine sustainable land application schedules. The easily solved models minimize the amount of N that is applied while assuring than crop N demands are met as they develop. Temperature effects on N mineralization were included by using the Arrhenius equation to create a temperature-adjusted time series. Uncertainties associated with mineralization rates and the temperature-adjustment (Q10) factor are considered by SOpt. Examples are presented for a summer maize (Zea mays L.) and winter triticale (Triticum aestivum L. x Secale cereale L.) rotation operated by a hypothetical dairy operation in Stanislaus County, California. Monte Carlo simulations were used to test the models. A closed-form solution for estimating the time until steady state is presented and steady-state conditions were reached within 7 yr after applications were initiated. Because of temperature effects, DOpt solutions were 12% greater during the winter and 29% lower during the summer than a reference approach that applied liquid manure at 130% of the crop N demand. Stochastic linear optimization values were 1.7% greater than DOpt values in the summer and 6.2% greater in the winter. Surplus N estimates from Monte Carlo simulations averaged 104 kg ha(-1) for DOpt and 126 ka ha(-1) for SOpt, but SOpt was much less likely to result in crop N deficits. Linear optimization is a viable tool for scheduling organic N applications.     

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.     

Short-term wind speed forecasting: Application of linear and non-linear time series models

This study forecasts day-ahead wind speed at 15 minute intervals at the site of a wind turbine located in Maharashtra, India. Wind speed exhibits non-stationarity, seasonality and time-varying volatility clustering. Univariate linear and non-linear time series techniques namely MSARIMA, MSARIMA-GARCH and MSARIMA-EGARCH have been employed for forecasting wind speed using data span ranging from 3 days to 15 days. Study suggests that mean absolute percentage error (MAPE) values first decrease with the increase in data span, reaches its minima and then start increasing. All models provide superior forecasting performances with 5 days data span. It is further evident that ARIMA-GARCH model generates lowest MAPE with 5 days data span. All these models provide superior forecasts with respect to current industry practices. This study establishes that employing various linear and non-linear time series techniques for forecasting day-ahead wind speed can benefit the industry in terms of better operational management of wind turbines and better integration of wind energy into the power system, which have huge financial implications for wind power generators in India.     

Statistical Models to Predict and Assess Spatial and Temporal Low‐Flow Variability in New England Rivers and Streams

In the northern hemisphere, summer low flows are a key attribute defining both quantity and quality of aquatic habitat. I developed one set of models for New England streams/rivers predicting July/August median flows averaged across 1985–2015 as a function of weather, slope, % imperviousness, watershed storage, glacial geology, and soils. These models performed better than most United States Geological Survey models for summer flows developed at a statewide scale. I developed a second set of models predicting interannual differences in summer flows as a function of differences in air temperature, precipitation, the North Atlantic Oscillation (NAO) index, and lagged NAO. Use of difference equations eliminated the need for transformations and accounted for serial autocorrelations at lag 1. The models were used in sequence to estimate time series for monthly low flows and for two derived flow metrics (tenth percentile [Q10] and minimum 3‐in‐5 year average flows). The first metric is commonly used in assessing risk to low‐flow conditions over time, while the second has been correlated with increased probability of localized extinctions for brook trout. The flow metrics showed increasing trends across most of New England for 1985–2015. However, application of summer flow models with average and extreme climate projections to the Taunton River, Massachusetts, a sensitive watershed undergoing rapid development, projected that low‐flow metrics will decrease over the next 50 years.     

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.     

Removal of Pb(II) ions from aqueous solution using activated tea waste: Adsorption on a fixed-bed column

An inexpensive and effective adsorbent was developed from waste tea leaves for the dynamic uptake of Pb(II). Characterization of the adsorbents showed a clear change between physico-chemical properties of activated tea waste and simply tea waste. The purpose of this work was to evaluate the potential of activated tea waste in continuous flow removal of Pb(II) ions from synthetic aqueous effluents. The performance of the system was evaluated to assess the effect of various process variables, viz., of bed height, hydraulic loading rate and initial feed concentration on breakthrough time and adsorption capacity. The shape of the breakthrough curves was determined for the adsorption of Pb(II) by varying different operating parameters like hydraulic loading rate (2.3–9.17 m³/h m²), bed height (0.3–0.5 m) and feed concentration (2–10 mg/l). An attempt has also been made to model the data generated from column studies using the empirical relationship based on the Bohart–Adams model. There was an acceptable degree of agreement between the data for breakthrough time calculated from the Bohart–Adams model and the present experimental study with average absolute deviation of less than 5.0%. The activated tea waste in this study showed very good promise as compared with the other adsorbents available in the literature. The adsorbent could be suitable for repeated use (for more than four cycles) without noticeable loss of capacity.     

Long-term trends in the Real real prices of primary commodities: Inflation bias and the Prebisch–Singer hypothesis

In his recent article on measuring the long-term trends in the real prices of primary commodities, Cuddington (2010) extends in several important respects our earlier efforts (Svedberg and Tilton, 2006) to correct real commodity price trends for biases in the Consumer Price Index and other deflators. First, he argues for a log-linear relationship between prices and time. Second, he proposes a simple and quick method for obtaining corrected price trends from the published but uncorrected estimates. Finally, he illustrates, for the case of copper and presumably for many other commodities as well, the difficulties of obtaining real price trends significantly different from zero when the log values of the price data contain a unit root, requiring the use of difference stationary models.We welcome these insights, which should improve and make easier efforts to estimate correctly real commodity price trends over the long run. We would stress, however, that it is still important to correct for the biases in inflation indices, notwithstanding the failure of difference stationary models to obtain long-run real price trends (both corrected and uncorrected) significantly different from zero.     

Determination of model parameters for zinc (II) ion biosorption onto powdered waste sludge (PWS) in a fed-batch system

Biosorption of zinc (II) ions onto pre-treated powdered waste sludge (PWS) was investigated using a completely mixed tank operating in fed-batch mode instead of an adsorption column. Experiments with variable feed flow rate (0.05-0.5 L h(-1)), feed Zn(II) ion concentrations (37.5-275 mg L(-1)) and amount of adsorbent (1-6 g PWS) were performed using fed-batch operation at pH 5 and room temperature (20-25 degrees C). Break-through curves describing variations of aqueous (effluent) zinc ion concentrations with time were determined for different operating conditions. Percent zinc removal from the aqueous phase decreased, but the biosorbed (solid phase) zinc ion concentration increased with increasing feed flow rate and zinc concentration. A modified Bohart-Adams equation was used to determine the biosorption capacity of PWS (q'(s)) and the rate constant (K) for zinc ion biosorption. Biosorption capacity (q'(s)=57.7 g Zn kg(-1) PWS) of PWS in fed-batch operation was found to be comparable with powdered activated carbon (PAC) in column operations. However, the adsorption rate constant (K=9.17 m(3) kg(-1) h(-1)) in fed-batch operation was an order of magnitude larger than those obtained in adsorption columns because of elimination of mass transfer limitations encountered in the column operations. Therefore, a completely mixed tank operated in fed-batch mode was proven to be more advantageous as compared to adsorption columns due to better contact between the phases yielding faster adsorption rates.     

二次指数平滑法的成都市餐厨垃圾产量预测

餐厨垃圾的产生量直接影响其处理规模,指数平滑法是对于缺乏基础数据的模型预测的一种有效方法。本文以2001～2009年成都市餐厨垃圾产量数据为基础,运用二次指数平滑预测法对成都市餐厨垃圾产量进行预测,预测结果显示2010年成都市餐厨垃圾产量将达到514.96 t/d。     

Coupling PCSWMM and WASP to Evaluate Green Stormwater Infrastructure Impacts to Storm Sediment Loads in an Urban Watershed

We coupled rainfall–runoff and instream water quality models to evaluate total suspended solids (TSS) in Wissahickon Creek, a mid‐sized urban stream near Philadelphia, Pennsylvania. Using stormwater runoff and instream field data, we calibrated the model at a subdaily scale and focused on storm responses. We demonstrate that treating event mean concentrations as a calibration parameter rather than a fixed input can substantially improve model performance. Urban stormwater TSS concentrations vary widely in time and space and are difficult to represent simply. Suspended and deposited sediment pose independent stressors to stream biota and model results suggest that both currently impair stream health in Wissahickon Creek. Retrofitting existing detention basins to prioritize infiltration reduced instream TSS loads by 20%, suggesting that infiltration mitigates sediment more effectively than detention. Infiltrating stormwater from 30% of the watershed reduced instream TSS loads by 47% and cut the frequency of TSS exceeding 100 mg/L by half. Settled loads and the frequency of high TSS values were reduced by a smaller fraction than suspended loads and duration at high TSS values. A widely distributed network of infiltration‐focused projects is an effective stormwater management strategy to mitigate sediment stress. Coupling rainfall–runoff and water quality models is an important way to integrate watershed‐wide impacts and evaluate how management directly affects urban stream health.     

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.