A MONTHLY TIME SERIES MODEL OF MUNICIPAL WATER DEMAND1

A multivariate time series model is formulated to study monthly variations in municipal water demand. The left hand side variable in the multivariate regression model is municipal water demand (gallons per connection per day) and the right hand side contains (explanatory) variables which include price (constant dollars), average temperature, total precipitation, and percentage of daylight hours. The application of the regression model to Salt Lake City Water Department data produced a high multiple correlation coefficient and F-statistic. The regression coefficients for the right hand side variables all have the appropriate sign. In an ex post forecast, the model accurately predicts monthly variations in municipal water demand. The proposed monthly multivariate model is not only found useful for forecasting water demand, but also useful for predicting and studying the impact of nonstructural management decisions such as the effect of price changes, peak load pricing methods, and other water conservation programs.     

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.     

Factors affecting the variability of household water use in Melbourne,Australia

This study investigates the variability of household water use in Melbourne with the aim of improving the current understanding of factors affecting residential water use. This understanding is critical to predicting household water demand, particularly at an appropriate spatial and temporal resolution to support Integrated Urban Water Management based planning and to improve the understanding on how different household water demands respond to demand management strategies. The study used two sets of data each collected from 837 households under significantly different water use conditions in the years 2003 and 2011. Data from each household consist of the household characteristics and quarterly metre readings. Ordinary Least Square regression analysis followed by detailed analysis of each factor was used to identify key factors affecting household water use. The variables studied are household size, typology of dwelling, appliance efficiency, presence of children under 12 years, presence of children aged between 12 and 18 years, tenancy, dwelling age, presence of swimming pool, evaporative cooler, and dishwasher. All of them except presence of children aged between 12 and 18 years, tenancy and dwelling age were identified as variables that contribute to the variability of household water use in Melbourne. The study also found that the explanatory capacity of these variables increases with decreasing water use. This paper also discusses the significance of the explanatory variables, their impact and how they vary over the seasons and years. The variables found in this study can be used to inform improved prediction and modelling of residential water demand. The paper also explores other possible drivers to explain residential water use in light of the moderate explanatory capacity of the variables selected for this study thus, provides useful insights into future research into water demand modelling.     

Effects of watershed configuration and composition on downstream lake water quality

We evaluated the relationships between landscape characteristics and lake water quality in receiving waters by regressing four water quality responses on landscape variables that were measured for whole watersheds and three different buffer distances (30, 60, and 120 m). Classical percolation theory was used to conceptualize nutrient pathways and to explain nonlinear responses. The response variables were total nitrogen (TN), total phosphorus (TP), chlorophyll-a (Chl-a), and Secchi transparency (SD). Landscape data were obtained from satellite image-derived maps of 130 watersheds in Iowa using geographic information systems software. We developed regression models with a stepwise protocol selecting the optimal number of significant explanatory variables. Configuration variables such as contagion, the cohesion of cropland and urban land, and the aggregation index of forest were very important and more important than variables assessing landscape composition (e.g., percentage farmland). Whole watershed models predicted between 15 and 67% of the variability in TN, TP, Chl-a, and SD. Proximity-explicit data offered only slightly improved statistical power over land cover data derived from the entire watershed for variables TN, Chl-a. and SD, but not for TP.     

Scale Effects on Spatially Varying Relationships Between Urban Landscape Patterns and Water Quality

Scientific interpretation of the relationships between urban landscape patterns and water quality is important for sustainable urban planning and watershed environmental protection. This study applied the ordinary least squares regression model and the geographically weighted regression model to examine the spatially varying relationships between 12 explanatory variables (including three topographical factors, four land use parameters, and five landscape metrics) and 15 water quality indicators in watersheds of Yundang Lake, Maluan Bay, and Xinglin Bay with varying levels of urbanization in Xiamen City, China. A local and global investigation was carried out at the watershed-level, with 50 and 200 m riparian buffer scales. This study found that topographical features and landscape metrics are the dominant factors of water quality, while land uses are too weak to be considered as a strong influential factor on water quality. Such statistical results may be related with the characteristics of land use compositions in our study area. Water quality variations in the 50 m buffer were dominated by topographical variables. The impact of landscape metrics on water quality gradually strengthen with expanding buffer zones. The strongest relationships are obtained in entire watersheds, rather than in 50 and 200 m buffer zones. Spatially varying relationships and effective buffer zones were verified in this study. Spatially varying relationships between explanatory variables and water quality parameters are more diversified and complex in less urbanized areas than in highly urbanized areas. This study hypothesizes that all these varying relationships may be attributed to the heterogeneity of landscape patterns in different urban regions. Adjustment of landscape patterns in an entire watershed should be the key measure to successfully improving urban lake water quality.     

Comparison of Stream Invertebrate Response Models for Bioassessment Metrics1

Waite, Ian R., Jonathan G. Kennen, Jason T. May, Larry R. Brown, Thomas F. Cuffney, Kimberly A. Jones, and James L. Orlando, 2012. Comparison of Stream Invertebrate Response Models for Bioassessment Metrics. Journal of the American Water Resources Association (JAWRA) 48(3): 570-583. DOI: 10.1111/j.1752-1688.2011.00632.x Abstract: We aggregated invertebrate data from various sources to assemble data for modeling in two ecoregions in Oregon and one in California. Our goal was to compare the performance of models developed using multiple linear regression (MLR) techniques with models developed using three relatively new techniques: classification and regression trees (CART), random forest (RF), and boosted regression trees (BRT). We used tolerance of taxa based on richness (RICHTOL) and ratio of observed to expected taxa (O/E) as response variables and land use/land cover as explanatory variables. Responses were generally linear; therefore, there was little improvement to the MLR models when compared to models using CART and RF. In general, the four modeling techniques (MLR, CART, RF, and BRT) consistently selected the same primary explanatory variables for each region. However, results from the BRT models showed significant improvement over the MLR models for each region; increases in R² from 0.09 to 0.20. The O/E metric that was derived from models specifically calibrated for Oregon consistently had lower R² values than RICHTOL for the two regions tested. Modeled O/E R² values were between 0.06 and 0.10 lower for each of the four modeling methods applied in the Willamette Valley and were between 0.19 and 0.36 points lower for the Blue Mountains. As a result, BRT models may indeed represent a good alternative to MLR for modeling species distribution relative to environmental variables.     

LONG-RANGE STREAMFLOW FORCASTING USING NONPARAMETRIC REGRESSION1

ABSTRACT: A class of nonparametric procedures is developed for producing long-range streamflow forecasts. The forecasting procedures, which are based solely on daily streamflow data, utilize nonparametric regression to relate a forecast variable to a covariate variable. The forecast variable is a function of future streamflow and can take a wide variety of forms. The covariate variable is a function of antecedent streamflow. The forecasting procedures are quite flexible, both in terms of the duration of the forecast period and the types of forecast variables that can be considered. The procedures are used to develop long-term (1–4 months) forecasts of minimum daily flow of the Potomac River at Washington, D.C. This forecast information is an integral component of water management activities for the Washington, D.C. metropolitan area.     

Regression models for estimating concentrations of atrazine plus deethylatrazine in shallow groundwater in agricultural areas of the United States

Tobit regression models were developed to predict the summed concentration of atrazine [6-chloro--ethyl--(1-methylethyl)-1,3,5-triazine-2,4-diamine] and its degradate deethylatrazine [6-chloro--(1-methylethyl)-1,3,5,-triazine-2,4-diamine] (DEA) in shallow groundwater underlying agricultural settings across the conterminous United States. The models were developed from atrazine and DEA concentrations in samples from 1298 wells and explanatory variables that represent the source of atrazine and various aspects of the transport and fate of atrazine and DEA in the subsurface. One advantage of these newly developed models over previous national regression models is that they predict concentrations (rather than detection frequency), which can be compared with water quality benchmarks. Model results indicate that variability in the concentration of atrazine residues (atrazine plus DEA) in groundwater underlying agricultural areas is more strongly controlled by the history of atrazine use in relation to the timing of recharge (groundwater age) than by processes that control the dispersion, adsorption, or degradation of these compounds in the saturated zone. Current (1990s) atrazine use was found to be a weak explanatory variable, perhaps because it does not represent the use of atrazine at the time of recharge of the sampled groundwater and because the likelihood that these compounds will reach the water table is affected by other factors operating within the unsaturated zone, such as soil characteristics, artificial drainage, and water movement. Results show that only about 5% of agricultural areas have greater than a 10% probability of exceeding the USEPA maximum contaminant level of 3.0 μg L. These models are not developed for regulatory purposes but rather can be used to (i) identify areas of potential concern, (ii) provide conservative estimates of the concentrations of atrazine residues in deeper potential drinking water supplies, and (iii) set priorities among areas for future groundwater monitoring.     

Nutrient and Sediment Production,Watershed Characteristics,and Land Use in the Tahoe Basin,California‐Nevada1

Abstract: In efforts to control the degradation of water quality in Lake Tahoe, public agencies have monitored surface water discharge and concentrations of nitrogen, phosphorus, and suspended sediment in two separate sampling programs. The first program focuses on 20 watersheds varying in size from 162 to 14,000 ha, with continuous stream gaging and periodic sampling; the second focuses on small urbanized catchments, with automated sampling during runoff events. Using data from both programs, we addressed the questions (1) what are the fluxes and concentrations of nitrogen and phosphorus entering the lake from surface runoff; (2) how do the fluxes and concentrations vary in space and time; and (3) how are they related to land use and watershed characteristics? To answer these questions, we calculated discharge‐weighted average concentrations and annual fluxes and used multiple regression to relate those variable to a suite of GIS‐derived explanatory variables. The final selected regression models explain 47‐62% of the variance in constituent concentrations in the stormwater monitoring catchments, and 45‐72% of the variance in mean annual yields in the larger watersheds. The results emphasize the importance of impervious surface and residential density as factors in water quality degradation, and well‐developed soil as a factor in water quality maintenance.     

EVALUATION OF PRACTICES IN WATER SUPPLY FORECASTING1

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

Sensitivity and Uncertainty of Ground‐Water Discharge Estimates for Semiarid Shrublands1

Abstract: We proposed a step‐by‐step approach to quantify the sensitivity of ground‐water discharge by evapotranspiration (ET) to three categories of independent input variables. To illustrate the approach, we adopt a basic ground‐water discharge estimation model, in which the volume of ground water lost to ET was computed as the product of the ground‐water discharge rate and the associated area. The ground‐water discharge rate was assumed to equal the ET rate minus local precipitation. The objective of this study is to outline a step‐by‐step procedure to quantify the contributions from individual independent variable uncertainties to the uncertainty of total ground‐water discharge estimates; the independent variables include ET rates of individual ET units, areas associated with the ET units, and precipitation in each subbasin. The specific goal is to guide future characterization efforts by better targeting data collection for those variables most responsible for uncertainty in ground‐water discharge estimates. The influential independent variables to be included in the sensitivity analysis are first selected based on the physical characteristics and model structure. Both regression coefficients and standardized regression coefficients for the selected independent variables are calculated using the results from sampling‐based Monte Carlo simulations. Results illustrate that, while as many as 630 independent variables potentially contribute to the calculation of the total annual ground‐water discharge for the case study area, a selection of seven independent variables could be used to develop an accurate regression model, accounting for more than 96% of the total variance in ground‐water discharge. Results indicate that the variability of ET rate for moderately dense desert shrubland contributes to about 75% of the variance in the total ground‐water discharge estimates. These results point to a need to better quantify ET rates for moderately dense shrubland to reduce overall uncertainty in estimates of ground‐water discharge. While the approach proposed here uses a basic ground‐water discharge model taken from an earlier study, the procedure of quantifying uncertainty and sensitivity can be generalized to handle other types of environmental models involving large numbers of independent variables.     

Development and Evaluation of Bankfull Hydraulic Geometry Relationships for the Physiographic Regions of the United States

Bankfull hydraulic geometry relationships are used to estimate channel dimensions for streamflow simulation models, which require channel geometry data as input parameters. Often, one nationwide curve is used across the entire United States (U.S.) (e.g., in Soil and Water Assessment Tool), even though studies have shown that the use of regional curves can improve the reliability of predictions considerably. In this study, regional regression equations predicting bankfull width, depth, and cross‐sectional area as a function of drainage area are developed for the Physiographic Divisions and Provinces of the U.S. and compared to a nationwide equation. Results show that the regional curves at division level are more reliable than the nationwide curve. Reliability of the curves depends largely on the number of observations per region and how well the sample represents the population. Regional regression equations at province level yield even better results than the division‐level models, but because of small sample sizes, the development of meaningful regression models is not possible in some provinces. Results also show that drainage area is a less reliable predictor of bankfull channel dimensions than bankfull discharge. It is likely that the regional curves can be improved using multiple regression models to incorporate additional explanatory variables.     

Near-term forecasts of stream temperature using deep learning and data assimilation in support of management decisions

Deep learning (DL) models are increasingly used to make accurate hindcasts of management-relevant variables, but they are less commonly used in forecasting applications. Data assimilation (DA) can be used for forecasts to leverage real-time observations, where the difference between model predictions and observations today is used to adjust the model to make better predictions tomorrow. In this use case, we developed a process-guided DL and DA approach to make 7-day probabilistic forecasts of daily maximum water temperature in the Delaware River Basin in support of water management decisions. Our modeling system produced forecasts of daily maximum water temperature with an average root mean squared error (RMSE) from 1.1 to 1.4°C for 1-day-ahead and 1.4 to 1.9°C for 7-day-ahead forecasts across all sites. The DA algorithm marginally improved forecast performance when compared with forecasts produced using the process-guided DL model alone (0%–14% lower RMSE with the DA algorithm). Across all sites and lead times, 65%–82% of observations were within 90% forecast confidence intervals, which allowed managers to anticipate probability of exceedances of ecologically relevant thresholds and aid in decisions about releasing reservoir water downstream. The flexibility of DL models shows promise for forecasting other important environmental variables and aid in decision-making.     

A Streamflow Forecasting Framework using Multiple Climate and Hydrological Models1

Abstract: Water resources planning and management efficacy is subject to capturing inherent uncertainties stemming from climatic and hydrological inputs and models. Streamflow forecasts, critical in reservoir operation and water allocation decision making, fundamentally contain uncertainties arising from assumed initial conditions, model structure, and modeled processes. Accounting for these propagating uncertainties remains a formidable challenge. Recent enhancements in climate forecasting skill and hydrological modeling serve as an impetus for further pursuing models and model combinations capable of delivering improved streamflow forecasts. However, little consideration has been given to methodologies that include coupling both multiple climate and multiple hydrological models, increasing the pool of streamflow forecast ensemble members and accounting for cumulative sources of uncertainty. The framework presented here proposes integration and offline coupling of global climate models (GCMs), multiple regional climate models, and numerous water balance models to improve streamflow forecasting through generation of ensemble forecasts. For demonstration purposes, the framework is imposed on the Jaguaribe basin in northeastern Brazil for a hindcast of 1974‐1996 monthly streamflow. The ECHAM 4.5 and the NCEP/MRF9 GCMs and regional models, including dynamical and statistical models, are integrated with the ABCD and Soil Moisture Accounting Procedure water balance models. Precipitation hindcasts from the GCMs are downscaled via the regional models and fed into the water balance models, producing streamflow hindcasts. Multi‐model ensemble combination techniques include pooling, linear regression weighting, and a kernel density estimator to evaluate streamflow hindcasts; the latter technique exhibits superior skill compared with any single coupled model ensemble hindcast.     

PREDICTING FECAL COLIFORM BACTERIA LEVELS IN THE CHARLES RIVER,MASSACHUSETTS, USA1

In Massachusetts, the Charles River Watershed Association conducts a regular water quality monitoring and public notification program in the Charles River Basin during the recreational season to inform users of the river's health. This program has relied on laboratory analyses of river samples for fecal coliform bacteria levels, however, results are not available until at least 24 hours after sampling. To avoid the need for laboratory analyses, ordinary least squares (OLS) and logistic regression models were developed to predict fecal coliform bacteria concentrations and the probabilities of exceeding the Massachusetts secondary contact recreation standard for bacteria based on meteorological conditions and streamflow. The OLS models resulted in adjusted R²s ranging from 50 to 60 percent. An uncertainty analysis reveals that of the total variability of fecal coliform bacteria concentrations, 45 percent is explained by the OLS regression model, 15 percent is explained by both measurement and space sampling error, and 40 percent is explained by time sampling error. Higher accuracy in future bacteria forecasting models would likely result from reductions in laboratory measurement errors and improved sampling designs.     

FLOOD STAGE FORECASTING WITH SUPPORT VECTOR MACHINES1

ABSTRACT: Machine learning techniques are finding more and more applications in the field of forecasting. A novel regression technique, called Support Vector Machine (SVM), based on the statistical learning theory is explored in this study. SVM is based on the principle of Structural Risk Minimization as opposed to the principle of Empirical Risk Minimization espoused by conventional regression techniques. The flood data at Dhaka, Bangladesh, are used in this study to demonstrate the forecasting capabilities of SVM. The result is compared with that of Artificial Neural Network (ANN) based model for one‐lead day to seven‐lead day forecasting. The improvements in maximum predicted water level errors by SVM over ANN for four‐lead day to seven‐lead day are 9.6 cm, 22.6 cm, 4.9 cm and 15.7 cm, respectively. The result shows that the prediction accuracy of SVM is at least as good as and in some cases (particularly at higher lead days) actually better than that of ANN, yet it offers advantages over many of the limitations of ANN, for example in arriving at ANN's optimal network architecture and choosing useful training set. Thus, SVM appears to be a very promising prediction tool.     

Comparing Hydrogeomorphic Approaches to Lake Classification

A classification system is often used to reduce the number of different ecosystem types that governmental agencies are charged with monitoring and managing. We compare the ability of several different hydrogeomorphic (HGM)—based classifications to group lakes for water chemistry/clarity. We ask: (1) Which approach to lake classification is most successful at classifying lakes for similar water chemistry/clarity? (2) Which HGM features are most strongly related to the lake classes? and, (3) Can a single classification successfully classify lakes for all of the water chemistry/clarity variables examined? We use univariate and multivariate classification and regression tree (CART and MvCART) analysis of HGM features to classify alkalinity, water color, Secchi, total nitrogen, total phosphorus, and chlorophyll a from 151 minimally disturbed lakes in Michigan USA. We developed two MvCART models overall and two CART models for each water chemistry/clarity variable, in each case comparing: local HGM characteristics alone and local HGM characteristics combined with regionalizations and landscape position. The combined CART models had the highest strength of evidence (ω_i range 0.92–1.00) and maximized within class homogeneity (ICC range 36–66%) for all water chemistry/clarity variables except water color and chlorophyll a. Because the most successful single classification was on average 20% less successful in classifying other water chemistry/clarity variables, we found that no single classification captures variability for all lake responses tested. Therefore, we suggest that the most successful classification (1) is specific to individual response variables, and (2) incorporates information from multiple spatial scales (regionalization and local HGM variables).     

A STATISTICAL METHODOLOGY FOR PREDICTING THE POLLUTANTS IN A RIVER1

Urban and industrial areas continue to expand and consequently, to create serious water pollution problems to natural streams. The need for the development of accurate, reliable, and sensitive water quality prediction models is most desirable. The first objective of this research is to set guidelines for dividing a natural stream into more or less independent reaches based on some criteria. The second objective is to obtain the predicting equations of the water pollutants in a selected stream. The preliminary phase of this research evaluated water quality data sampled from the Pearl River which flows southwest and then turns south through the states of Mississippi and Louisiana. This evaluation served as guidelines to divide the total river basin into reaches (subsystems) appropriate to the objective of this research. Subsequent to this subsystem assignment, a stepwise multiple regression FORTRAN program was used to regress the pollutants (dependent variables) for both time and space on their water characteristics (independent variables). Based on the results obtained, the proposed statistical approach provides a practical tool for developing regression equations for the purpose of water pollutants' prediction.     

Incomes,Attitudes, and Occurrences of Invasive Species: An Application to Signal Crayfish in Sweden

This article analyzes and carries out an econometric test of the explanatory power of economic and attitude variables for occurrences of the nonnative signal crayfish in Swedish waters. Signal crayfish are a carrier of plague which threatens the native noble crayfish with extinction. Crayfish are associated with recreational and cultural traditions in Sweden, which may run against environmental preferences for preserving native species. Econometric analysis is carried out using panel data at the municipality level with economic factors and attitudes as explanatory variables, which are derived from a simple dynamic harvesting model. A log-normal model is used for the regression analysis, and the results indicate significant impacts on occurrences of waters with signal crayfish of changes in both economic and attitude variables. Variables reflecting environmental and recreational preferences have unexpected signs, where the former variable has a positive and the latter a negative impact on occurrences of waters with signal crayfish. These effects are, however, counteracted by their respective interaction effect with income.     

Field‐Scale Application of Three Types of Neural Networks to Predict Ground‐Water Levels1

Abstract: In this paper, a field‐scale applicability of three forms of artificial neural network algorithms in forecasting short‐term ground‐water levels at specific control points is presented. These algorithms are the feed‐forward back propagation (FFBP), radial basis networks (RBN), and generalized regression networks (GRN). Ground‐water level predictions from these algorithms are in turn to be used in an Optimized Regional Operations Plan that prescribes scheduled wellfield production for the coming four weeks. These models are up against each other for their accuracy of ground‐water level predictions on lead times ranging from a week to four weeks, ease of implementation, and execution times (mainly training time). In total, 208 networks of each of the three algorithms were developed for the study. It is shown that although learning algorithms have emerged as a viable solution at field scale much larger than previously studied, no single algorithm performs consistently better than others on all the criteria. On average, FFBP networks are 20 and 26%, respectively, more accurate than RBN and GRN in forecasting one week ahead water levels and this advantage drops to 5 and 9% accuracy in forecasting four weeks ahead water levels, whereas GRN posted a training time that is only 5% of the training time taken by that of FFBP networks. This may suggest that in field‐scale applications one may have to trade between the type of algorithm to be used and the degree to which a given objective is honored.