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.     

Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande1

Abudu, S., J.P. King, Z. Sheng, 2011. Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande. Journal of the American Water Resources Association (JAWRA) 48(1): 10‐23. DOI: 10.1111/j.1752‐1688.2011.00587.x Abstract: This paper presents the application of autoregressive integrated moving average (ARIMA), transfer function‐noise (TFN), and artificial neural networks (ANNs) modeling approaches in forecasting monthly total dissolved solids (TDS) of water in the Rio Grande at El Paso, Texas. Predictability analysis was performed between the precipitation, temperature, streamflow rates at the site, releases from upstream reservoirs, and monthly TDS using cross‐correlation statistical tests. The chi‐square test results indicated that the average monthly temperature and precipitation did not show significant predictability on monthly TDS series. The performances of one‐ to three‐month‐ahead model forecasts for the testing period of 1984‐1994 showed that the TFN model that incorporated the streamflow rates at the site and Caballo Reservoir release improved monthly TDS forecasts slightly better than the ARIMA models. Except for one‐month‐ahead forecasts, the ANN models using the streamflow rates at the site as inputs resulted in no significant improvements over the TFN models at two‐month‐ahead and three‐month‐ahead forecasts. For three‐month‐ahead forecasts, the simple ARIMA showed similar performance compared to all other models. The results of this study suggested that simple deseasonalized ARIMA models could be used in one‐ to three‐month‐ahead TDS forecasting at the study site with a simple, explicit model structure and similar model performance as the TFN and ANN models for better water management in the Basin.     

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.     

PROCESS-ORIENTED ESTIMATION OF SUSPENDED SEDIMENT CONCENTRATION1

ABSTRACT: Least squares regression and ARIMA models were developed from suspended sediment data for the Ausable River, Southern Ontario, Canada. A poor correlation between discharge and suspended sediment concentration results from the dynamics of the physical system, including seasonality, antecedent conditions, and hysteresis. Regression model results were significantly improved by the division of the data set into seasons and the addition of simple. but physically meaningful variables. Misleading improvements obtained from the regression of sediment load and discharge are discussed. ARIMA models provided accurate forecasts of sediment concentration on a real-time basis, but the rigorous data requirements limit their use in modeling suspended sediment concentrations in Canadian rivers.     

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.     

An assessment of time series methods in metal price forecasting

The international price for metals is pivotal in the profitability equation for mining companies. If producer prices rise, assuming production levels and costs remain the same, profits are expected to increase. Accordingly, producers welcome any means by which price instability and unpredictability can be reduced. The paper analyses the ability of two user-friendly time series forecasting techniques to predict future lead and zinc prices. The conclusion is that price forecasting is difficult. It should, however, be acknowledged that whilst neither of the two models are definitive, they are useful for the mining company vis-à-vis its planning process. In particular, the results from the analysis in this paper suggest that ARIMA modelling provides marginally better forecast results than lagged forward price modelling. The methodologies employed in this paper have a broad based application to base metal forecasting by mining companies in general, that is, the applications are transferable.     

Chlorophyll a Simulation in a Lake Ecosystem Using a Model with Wavelet Analysis and Artificial Neural Network

Accurate and reliable forecasting is important for the sustainable management of ecosystems. Chlorophyll a (Chl a) simulation and forecasting can provide early warning information and enable managers to make appropriate decisions for protecting lake ecosystems. In this study, we proposed a method for Chl a simulation in a lake that coupled the wavelet analysis and the artificial neural networks (WA–ANN). The proposed method had the advantage of data preprocessing, which reduced noise and managed nonstationary data. Fourteen variables were included in the developed and validated model, relating to hydrologic, ecological and meteorologic time series data from January 2000 to December 2009 at the Lake Baiyangdian study area, North China. The performance of the proposed WA–ANN model for monthly Chl a simulation in the lake ecosystem was compared with a multiple stepwise linear regression (MSLR) model, an autoregressive integrated moving average (ARIMA) model and a regular ANN model. The results showed that the WA-ANN model was suitable for Chl a simulation providing a more accurate performance than the MSLR, ARIMA, and ANN models. We recommend that the proposed method be widely applied to further facilitate the development and implementation of lake ecosystem management.     

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.     

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.     

DESK TOP METHODOLOGY FOR MODELING BIOCHEMICAL OXYGEN DEMAND IN STREAMS1

: The modeling of dissolved oxygen in streams is a widely used technique, upon which a great deal of money has been spent. This paper concludes that the standard methods of DO modeling by computer are unnecessarily complex, and that for some purposes, they can be replaced without loss of accuracy by desk top BOD models. Taking as an example, a set of data used in DO modeling, it is shown (a) that the data are grossly inconsistent, (b) that simultaneous gathering of data introduces errors in streams of long travel time, (c) that much more data as to pollutant concentrations should have been obtained, and (d) that 24-hour DO data could have been dispensed with.     

LORENDAS: A COMPUTER BASED SYSTEM FOR THE MODELING OF LONG-RANGE ENERGY DEVELOPMENT AND SUPPLIES*

This paper reviews a time-dynamic linearprogramming modeling system designed for quantitative analysis of worldwide energy resource development and processing activities over a 25 - 30 year time horizon. The model includes explicit representation of exploration and production operations for energy minerals, as well as of the downstream supply, conversion and distribution of different energy forms, accounting for interfuel substitution. The uses of this model, which include forecasts of resource development, assessment of new technologies and analysis of energy policies, are discussed. The paper outlines a series of smaller, national or regional energy planning models which can be derived from the worldwide LORENDAS modeling structure and tailored to the needs of individual developing countries.     

Transition Pathways to Sustainable Agricultural Water Management: A Review of Integrated Modeling Approaches

Agricultural water management (AWM) is an interdisciplinary concern, cutting across traditional domains such as agronomy, climatology, geology, economics, and sociology. Each of these disciplines has developed numerous process‐based and empirical models for AWM. However, models that simulate all major hydrologic, water quality, and crop growth processes in agricultural systems are still lacking. As computers become more powerful, more researchers are choosing to integrate existing models to account for these major processes rather than building new cross‐disciplinary models. Model integration carries the hope that, as in a real system, the sum of the model will be greater than the parts. However, models based upon simplified and unrealistic assumptions of physical or empirical processes can generate misleading results which are not useful for informing policy. In this article, we use literature and case studies from the High Plains Aquifer and Southeastern United States regions to elucidate the challenges and opportunities associated with integrated modeling for AWM and recommend conditions in which to use integrated models. Additionally, we examine the potential contributions of integrated modeling to AWM — the actual practice of conserving water while maximizing productivity. Editor's note : This paper is part of the featured series on Optimizing Ogallala Aquifer Water Use to Sustain Food Systems. See the February 2019 issue for the introduction and background to the series.     

Determination of Frequency for Remeasuring Ground and Vegetation Cover Factor Needed for Soil Erosion Modeling

Determining a remeasurement frequency of variables over time is required in monitoring environmental systems. This article demonstrates methods based on regression modeling and spatio-temporal variability to determine the time interval to remeasure the ground and vegetation cover factor on permanent plots for monitoring a soil erosion system. The spatio-temporal variability methods include use of historical data to predict semivariograms, modeling average temporal variability, and temporal interpolation by two-step kriging. The results show that for the cover factor, the relative errors of the prediction increase with an increased length of time interval between remeasurements when using the regression and semivariogram models. Given precision or accuracy requirements, appropriate time intervals can be determined. However, the remeasurement frequency also varies depending on the prediction interval time. As an alternative method, the range parameter of a semivariogram model can be used to quantify average temporal variability that approximates the maximum time interval between remeasurements. This method is simpler than regression and semivariogram modeling, but it requires a long-term dataset based on permanent plots. In addition, the temporal interpolation by two-step kriging is also used to determine the time interval. This method is applicable when remeasurements in time are not sufficient. If spatial and temporal remeasurements are sufficient, it can be expanded and applied to design spatial and temporal sampling simultaneously.     

Time series modelling of global mean temperature for managerial decision-making

Climate change has important implications for business and economic activity. Effective management of climate change impacts will depend on the availability of accurate and cost-effective forecasts. This paper uses univariate time series techniques to model the properties of a global mean temperature dataset in order to develop a parsimonious forecasting model for managerial decision-making over the short-term horizon. Although the model is estimated on global temperature data, the methodology could also be applied to temperature data at more localised levels. The statistical techniques include seasonal and non-seasonal unit root testing with and without structural breaks, as well as ARIMA and GARCH modelling. A forecasting evaluation shows that the chosen model performs well against rival models. The estimation results confirm the findings of a number of previous studies, namely that global mean temperatures increased significantly throughout the 20th century. The use of GARCH modelling also shows the presence of volatility clustering in the temperature data, and a positive association between volatility and global mean temperature.     

A Complex Systems Model Approach to Quantified Mineral Resource Appraisal

For federal and state land management agencies, mineral resource appraisal has evolved from value-based to outcome-based procedures wherein the consequences of resource development are compared with those of other management options. Complex systems modeling is proposed as a general framework in which to build models that can evaluate outcomes. Three frequently used methods of mineral resource appraisal (subjective probabilistic estimates, weights of evidence modeling, and fuzzy logic modeling) are discussed to obtain insight into methods of incorporating complexity into mineral resource appraisal models. Fuzzy logic and weights of evidence are most easily utilized in complex systems models. A fundamental product of new appraisals is the production of reusable, accessible databases and methodologies so that appraisals can easily be repeated with new or refined data. The data are representations of complex systems and must be so regarded if all of their information content is to be utilized.The proposed generalized model framework is applicable to mineral assessment and other geoscience problems. We begin with a (fuzzy) cognitive map using (+1,0,–1) values for the links and evaluate the map for various scenarios to obtain a ranking of the importance of various links. Fieldwork and modeling studies identify important links and help identify unanticipated links. Next, the links are given membership functions in accordance with the data. Finally, processes are associated with the links; ideally, the controlling physical and chemical events and equations are found for each link. After calibration and testing, this complex systems model is used for predictions under various scenarios. Published on line     

FORECASTING QUARTER-MONTHLY RIVERFLOW1

Recent developments with respect to transfer function-noise models are reviewed and used to model and forecast quarter-monthly (i.e., near-weekly) natural inflows to the Lac St-Jean reservoir in the Province of Quebec, Canada. The covariate series are rainfall and snowmelt, the latter being a novel derivation from daily rainfall, snowfall and temperature series. It is clearly demonstrated using the residual variance and the Akaike information criterion that modeling is improved as one starts with a deseasonalized ARMA model of the inflow series and successively adds transfer functions for the rainfall and snowmelt series. It is further demonstrated that the transfer function-noise model is better than a periodic autoregressive model of the inflow series. A split-sample experiment is used to compare one-step-ahead forecasts from this transfer function-noise model with forecasts from other stochastic models as well as with forecasts from a so-called conceptual hydrological model (i.e., a model which attempts to mathematically simulate the physical processes involved in the hydrological cycle). It is concluded that the transfer function-noise model is the preferred model for forecasting the quarter-monthly Lac St-Jean inflow series.     

ASM2G在污水处理中的研究与应用

针对用静态模型常规设计在设计效果与模拟分析上的不足,作者在研究动态机理模型ASM2d的基础上开发了污水处理仿真程序ASM2G,以分析污水生物处理,并进行模拟分析与辅助设计.本文首先介绍了此自编程序的机理模型ASM2d;其次说明了ASM2G的模拟过程;最后,通过对实际污水处理厂的模拟比较,说明了ASM2G在模拟分析上的优势,同时也反映了ASM2d能够较好地反映污水处理的运行状况,是一个较成熟的动态机理模型.文章试图为找到一种经济有效的设计方法提供一定的参考.     

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.     

Integrating Satellite Imagery with Simulation Modeling to Improve Burn Severity Mapping

Both satellite imagery and spatial fire effects models are valuable tools for generating burn severity maps that are useful to fire scientists and resource managers. The purpose of this study was to test a new mapping approach that integrates imagery and modeling to create more accurate burn severity maps. We developed and assessed a statistical model that combines the Relative differenced Normalized Burn Ratio, a satellite image-based change detection procedure commonly used to map burn severity, with output from the Fire Hazard and Risk Model, a simulation model that estimates fire effects at a landscape scale. Using 285 Composite Burn Index (CBI) plots in Washington and Montana as ground reference, we found that an integrated model explained more variability in CBI (R ² = 0.47) and had lower mean squared error (MSE = 0.28) than image (R ² = 0.42 and MSE = 0.30) or simulation-based models (R ² = 0.07 and MSE = 0.49) alone. Overall map accuracy was also highest for maps created with the Integrated Model (63 %). We suspect that Simulation Model performance would greatly improve with higher quality and more accurate spatial input data. Results of this study indicate the potential benefit of combining satellite image-based methods with a fire effects simulation model to create improved burn severity maps.     

Ecological effects monitoring in environmental impact assessment: What can it accomplish?

The premise that, strictly speaking, impact monitoring is impossible, is presented and discussed It is shown that a wide range of published objectives for environmental effects monitoring can be seen as special cases of the basic goal of reducing uncertainty in predictions. Monitoring in environmental-impact situations can only be used as a check on one of the two time series required to define impact. Four approaches to generating the other time series required in the difference calculation of impact are discussed, with the conclusion that the best approach relies on process-based simulation models. Impact analysts are encouraged to consider carefully what can and cannot actually be accomplished with environmental monitoring to assist impact detection.