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Environmental Modeling

Real-Time Nowcasting of Microbiological Water Quality at Recreational Beaches: A Wavelet and Artificial Neural Network Based Hybrid Modeling Approach Juan Zhang, Han Qiu, Xiaoyu Li, Jie Niu, Meredith Becker Nevers, Xiaonong Hu, and Mantha S Phanikumar Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b01022 • Publication Date (Web): 29 Jun 2018 Downloaded from http://pubs.acs.org on July 5, 2018

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Environmental Science & Technology

Real-Time Nowcasting of Microbiological Water Quality at Recreational Beaches: A Wavelet and Artificial Neural Network Based Hybrid Modeling Approach Juan Zhang1, Han Qiu2, Xiaoyu Li3, Jie Niu1*, Meredith Nevers4, Xiaonong Hu1, and Mantha S. Phanikumar2* 1

Institute of Groundwater and Earth Sciences, Jinan University, Guangzhou 510632, China. Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI 3 Department of Mathematics and Statistics, Auburn University, Auburn, AL 4 USGS Great Lakes Science Center, Lake Michigan Ecological Research Station, Chesterton, IN 46304 *Corresponding Authors e-mails: [email protected], [email protected], Phone: (517) 432-0851 2

Abstract The number of beach closings due to bacterial contamination continues to be on the rise in recent

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years, putting beachgoers at risk of exposure to contaminated water. Current approaches predict

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levels of indicator bacteria using regression models containing a number of explanatory

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variables. Data-based modeling approaches can supplement routine monitoring data and provide

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highly accurate short-term forecasts of beach water quality. In this paper, we apply the nonlinear

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autoregressive network with exogenous inputs (NARX) method with explanatory variables to

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predict Escherichia coli (E. coli) concentrations at four Lake Michigan beach sites. We also

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apply the nonlinear input-output network (NIO) and nonlinear autoregressive neural network

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(NAR) methods in addition to a hybrid wavelet-NAR (WA-NAR) model and demonstrate their

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application. All models were tested using 3 months of observed data. Results revealed that the

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NARX models provided the best performance and that the WA-NAR model, which requires no

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explanatory variables, outperformed the NIO and NAR models; therefore, the WA-NAR model

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is suitable for application to data scarce regions. The models proposed in this paper were

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evaluated using multiple performance metrics including sensitivity and specificity measures and

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produced results comparable or superior to previous mechanistic and statistical models

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developed for the same beach sites.

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models (R2 ~ 0.8 for the beach sites and ~0.9 for the river site) indicate that the new class of

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models shows promise for beach management.

The relatively high R2 values between data and the NARX

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1. Introduction

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Levels of fecal indicator bacteria (FIB) are monitored at coastal and inland recreational beaches

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to protect the public from exposure to contaminated water.1 According to the NRDC,2 10% of all

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monitoring samples in 2013 exceeded EPA's benchmark value and the Great Lakes region,

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which included 902 coastal beaches from 8 US states in 2013, had the highest exceedances rate

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(13%) of all beaches in that region, indicating that swimmers continue to face health risks from

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microbiological pollution at beaches. Beach water quality is highly dynamic and can change

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quickly in a matter of minutes, depending on a number of environmental factors; therefore, to be

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useful and protective of public health, notifications should be issued in a timely manner.

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Traditional culture-based methods, however, require a 18 to 24 hour laboratory assay, during

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which time beach-goers could potentially be exposed to contaminated water. Alternative

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methods for beach management, including rapid methods such as quantitative polymerize chain

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reaction (qPCR) and predictive modeling, continue to receive significant attention in recent

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years.3-5 Even with rapid methods, real-time or even same-day water quality results may not

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always be available.1 While faster techniques that provide results in 6 hours or less have been

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developed and tested,6-10 using qPCR requires significant up-front investment and expertise for

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analysis. The US EPA has encouraged the use of qPCR for enterococci and the 2012

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Recreational Water Quality Criteria provide a Beach Action Value (BAV) for qPCR-based

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testing of 1,000 CCE (calibrator cell equivalents)/100 mL.

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Due to the lag time between the time of sampling and the time when results are available, models

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are useful tools to supplement monitoring data.1 A variety of models have been used in the past

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to forecast FIB levels at beaches, and they generally belong to two broad categories: mechanistic

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or process-based models,4,11-17 which are based on conservation principles, and statistical

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regression models and other data-based approaches.3,4,18-19 Mechanistic models of beach water

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quality require detailed information on sources, including flow and FIB levels from tributaries.

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While mechanistic models are excellent tools for gaining insights into key processes4, they

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require considerable resources and training for model setup, running and post-processing. If the

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objective is to protect public health by making timely and accurate predictions at beach sites,

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data-based approaches may be attractive since the technology can be transferred from one site to

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another with relative ease.

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While multiple regression (MR) models of beach water quality have received considerable

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attention in the past due to their simple and robust nature and ease of implementation, other

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data-based methods such as Artificial Neural Networks (ANN)20 have the potential to improve

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the accuracy of forecasts.21-24 These methods, however, have not found widespread application in

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beach management. ANNs were successfully used in the past to forecast many of the factors that

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directly or indirectly impact FIB levels at beaches including rainfall patterns,25-28 stream

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flows,29-31 suspended sediment concentrations,32-34 lake water levels,35-37 wave breaking and

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changes in beach profiles.38-40 The success of these earlier studies provides ample motivation for

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applying ANN methods to beach management. Zhang et al.41 applied an ANN model to forecast

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levels of enterococci at the Holly Beach in Louisiana. They used 15 environmental variables

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such as salinity, water temperature and wind speed as inputs to their model. For datasets



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collected during years 2007-2009, the performance of their ANN model was superior (linear

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correlation coefficient, LCC = 0.857) to that of multiple-regression (MR) models implemented in

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the US EPA Virtual Beach model42 – e.g., LCC=0.337 for a non-linear Virtual Beach model for

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the same dataset. The use of explanatory environmental variables as inputs to beach water

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quality models is a well-known approach in the development of multiple-regression models. In

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another study,43 ten environmental variables were used as inputs to forecast the FIB

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concentrations of an urban waterway in the Chicago River utilizing the ANN method. ANN

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models have advantages over traditional MR models when the underlying function

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approximating the data is highly complex and nonlinear. In fact, ANN models are known to

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work even when the underlying function cannot be expressed in terms of any known

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mathematical functions. Therefore, the ANN model, as in the approach of Zhang et al.,41 can be

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viewed as a progression of the MR approach.

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In addition to these previous studies, it is also possible to use ANNs in a fundamentally different

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data-based approach -- to generate short-term forecasts that rely on data alone without any

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explanatory variables.44 The idea is that if a suitable method of time series analysis exists, then

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the information needed to make short-term forecasts is all contained within the data, and no other

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explanatory variable is required to provide additional information. Although ANN methods

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described above have proven extremely useful for making short- and long-term forecasts in

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many areas of science and engineering, microbiological water quality data are characterized by

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nonstationarity (i.e., statistical properties such as the mean and variance do not remain constant

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over time). ANN methods have well-known limitations in dealing with non-stationary datasets,45

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while wavelet transforms can be robust tools for handling nonstationary datasets. Wavelet


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methods have been used in the last two decades for analysis of both time series and spatial data.46

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An important feature of wavelet analysis is the ability to decompose the original data into high

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and low frequency contributions (i.e., fine and coarse features in the data) for further analysis.

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Wavelets have been used, for example, for analysis of nearshore hydrodynamics47 including

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longshore currents along a sandy coast48 and to address questions related to solute transport in

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rivers49 and heterogeneous porous media.50 Therefore, by combining the strengths of wavelet

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transforms (the ability to deal with nonstationary data) with those of ANN methods (the ability to

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deal with nonlinearity), a powerful class of hybrid methods can be constructed for reliable,

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short-term forecasts.

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Wavelet-ANN (WANN) methods have been the focus of several recent papers, and the methods

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produce reliable forecasts of daily river discharge and suspended sediment concentration, rainfall

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runoff, snow melt-driven floods, and droughts.51-56 The objective of this paper is to explore the

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possibility of applying ANN and combined wavelet-neural network models for nowcasting FIB

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levels at recreational beaches in order to support advisory and beach closure decisions. Daily

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monitoring data are routinely available for many beach sites in the United States; however, as

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noted earlier, beach management based on water quality sampling alone is inadequate due to a

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24-hour delay in running the assays, during which time conditions at the beach can change

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quickly. Therefore specific questions that will be addressed in the paper include the following:

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(1) if daily monitoring data are used in a ANN or WANN modeling framework, is it possible to

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forecast tomorrow’s FIB levels using yesterday’s monitoring data? (2) is it possible to generate

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forecasts with a high degree of confidence as quantified by standard metrics such as the

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coefficient of determination (R2) and the root mean square errors (RMSE)? (3) how do ANN and



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WANN methods perform relative to statistical (MR) and fully three-dimensional mechanistic

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models developed for the same datasets? The first question is related to data requirements and

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feasibility of the WANN approach since the method requires sufficiently long time series data to

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meet the requirement of wavelet decomposition. Since only daily monitoring data are available, a

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data augmentation method has to be used before applying the WANN model and this leads to

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consideration of whether the original data follow a certain distribution, which is considered a

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data feasibility question. The second question is important because previous modeling activities

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have generally achieved R2 values less than 0.7,57-58 with the exception of Safaie et al.4 For this

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reason, we set a higher standard for our proposed models to achieve an R2 value of 0.7 or better.

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Generally, an R2 value greater than 0.7 is considered a strong relationship, according to Moore et

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al.;59 therefore, for the third question if the WANN approach can yield forecasts with R2 values

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comparable to or higher than 0.7 without the use of explanatory variables, then it represents a

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significant advance over the current model-based approaches for beach management. The

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datasets used in this research have been selected to facilitate direct comparisons with MR and

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mechanistic models developed earlier4. To the best of our knowledge, there is no published work

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that examines the application of the WANN approach for forecasting FIB levels at recreational

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beaches and one of our aims in this paper is to fill this gap.

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2. Methods

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Three types of ANN models, the Nonlinear Input-Output (NIO)60 Nonlinear Autoregressive

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neural network (NAR)61 and the Nonlinear Autoregressive Network with eXogenous inputs

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(NARX)62 network, are applied in this work.20 The details of these three models are described in

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the supporting information (SI), sections S1-S3. In all models, the dependent variable of interest


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from the point of prediction is the log10 transformed E. coli data (referred to as LGEC herein).

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Briefly, the NIO model (Model 1) predicts E. coli levels at the three beach sites (OD1, OD2,

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OD3) using past values of E. coli data at the river mouth (BD) since discharge from the river

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mouth is known to impact bacteria levels at the three beaches4. The NAR model (Model 2), on

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the other hand, predicts E. coli levels at any site using only the past values of E. coli at the same

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site. In both models (NIO and NAR) other than the E. coli data, no explanatory variables are

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used unlike the NARX model that uses explanatory variables such as turbidity and wave height

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in addition to the past values of E. coli at the site where predictions are being made. The input

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parameters used in the NARX models in our work (Models 3 and 4) included (in addition to the

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E. coli data): (1) 24-hour rainfall, (2) 4-hour water temperature (WTEMP4HR), (3) natural log of

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turbidity at the beach sites (LNTURB), (4) daily log10(discharge) from the river mouth

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(LGDISCH24HR), (5) an interaction term that is the product of daily discharge and turbidity at

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the river mouth (LOAD24) and (6) onshore wind speed, which is the speed of wind blowing

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from the lake towards the land (WNDSPD_ONSHORE) and (7) natural log of the 4-hour

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significant wave height (LNWHSIG4HR). Model 3 used parameters 1, 2, 3, 4, and 5 in the above

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list while Model 4 used 1, 2, 3, 6, and 7. The wavelet decomposition technique (described in

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section S4 in the Supporting Information) is combined with the NAR model to further improve

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the accuracy of the NAR model prediction. In ANN models, the available data are usually

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divided into three subsets - training, validation and testing periods (more information is available

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in the Supporting Information). Since the model used for beach management will be first trained

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and validated, we report the testing R2 and RMSE values for all models. Moreover, the model

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sensitivity and specificity metrics58 are also used to assess model performance. Sensitivity

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(specificity) refers to the probability of exceedance (non-exceedance) of the EPA standard (i.e.,



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the BAV) that can be predicted by the models. These metrics provide additional information on

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the usefulness of the models for beach management.

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The focus of the present paper is on nowcasting bacterial levels at four sites in Southern Lake

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Michigan. Unlike some previous applications in which the wavelet decomposition was

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performed on the whole time series data including the testing period, a practice that is misleading

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as it leads to highly inflated values of R2, in the present work, the network has no information on

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the wavelet coefficients for future data while making a forecast since wavelet decomposition for

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the forecast period has not yet been done.

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2.1 The WA-NAR hybrid model:

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A WA-NAR hybrid model is obtained by combining the two methods, the NAR and the discrete

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wavelet transform (DWT). The wavelet decomposition coefficients of the FIB data are passed

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into the NAR model to make a short-term forecast. We can examine the correlation between

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different wavelet components and the original time series data. For the WA-NAR model inputs,

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the original LGEC time series of each site are decomposed into various detail components (W's)

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at different resolution levels and one approximation component (C) at the last coarse resolution

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level using the á Trous algorithm.63 A key detail involves the number of wavelet levels required

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to approximate the original data. Although there is no existing theory to tell how many resolution

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levels are needed for any given time series, it is generally believed that L = int [log10 ( N )] levels

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are needed,64 where L denotes the number of wavelet levels and N is the number of data points

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in the time series.

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Monitoring programs in the Great Lakes region start with the beginning of the beach season and

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continue through summer (approximately late May-late August). Assuming the availability of

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daily data for a 3-month period not counting weekends, we get N ≈ 80 and L = 1 . This means

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that data obtained from a daily monitoring program are not sufficiently dense for a

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straightforward application of the wavelet theory; however, monitoring data can be augmented /

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up-sampled in several ways to facilitate the application of the WANN method. The approaches

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essentially make an assumption about how data varies between sampling times (successive

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days). One approach is to augment the monitoring data using model hindcasts based on a

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well-tested mechanistic model that uses small time steps. This represents a process-based method

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of interpolating data on successive days, allowing the generation of high-resolution time series

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data (e.g., hourly or every minute) needed for the WA-NAR approach. Other alternative

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approaches include regular interpolation method, the simplest being linear interpolation, and

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Markov Chain Monte Carlo65-66 (MCMC) sampling with Kalman filtering67 to remove the noise.

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The choice of the method should depend on the factors that contribute to elevated bacterial levels

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at the sites. At the beach sites considered in the present work, loading from nearby tributaries

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was the primary factor18 contributing to the pollution. The presence or absence of a peak at a

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beach on any given day depends on the direction of the river plume within the lake

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environment16,68 (i.e., plume traveling toward the beach or away from it). River plume directions

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generally shift over the course of several days, although within-day shifts are possible;4,16,68-69

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therefore, daily sampling provides a reasonable temporal resolution on most days from the point

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of capturing the peaks. We note, however, that time scales shorter than the diurnal scale cannot

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be resolved using daily monitoring data and statistical sampling, and mechanistic model

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hindcasts have the ability to resolve additional details (e.g., peaks) at the sub-diurnal time scales.



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After comparing the time series data obtained by the Markov Chain Monte Carlo (MCMC)

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approach at half-daily resolution with mechanistic modeling results4, we decided to use

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half-hourly data based on MCMC method combined with Kalman filtering for the application of

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the WA-NAR model. The half-hourly “observed” data prior to the current time of prediction

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were generated by using the semi-diurnal time series data. More details are provided in the

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Supporting Information section S5. The WA-NAR method was implemented using the wavelet

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and neural network toolboxes in MATLAB version 9.1, R2016b (The Mathworks Inc., Natick,

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MA). We also implemented the above method to decompose the variables that have strong

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correlation with LGEC. All the wavelet decomposition coefficients of input variables are used as

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inputs into the NAR model for nowcasting. For the newly generated half-hourly data, the first

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70% of E. coli concentration data (1361 hours) were used for training; 15% of data (291 hours)

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were used for validation and the remaining 15% were used for testing purpose.

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2.2 Site description

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To demonstrate the application of the WA-NAR method to nowcast elevated FIB levels at

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beaches, we use E. coli data collected during the summer of year 2008 at four sites in southern

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Lake Michigan. Out of the four sites, one site (BD) represents the river mouth while the

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remaining three sites (OD3, OD2, OD1 in increasing distance from BD, see map in Figure 1) are

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beach sites. The three beach sites are primarily impacted by contamination from the river mouth

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at BD, therefore E. coli and turbidity values at the BD site are important inputs that control the

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dynamics of E. coli at the three beach sites4. Additional details of the sites and the data can be

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found in Safaie et al.4

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Burns Ditch (BD) is the river mouth of the Little Calumet River in northwest Indiana. The three

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sampling locations OD1, OD2, and OD3 are located to the west of the outfall in the town of

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Ogden Dunes. E. coli concentrations in Burns Ditch are historically high, and likely influence

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shoreline E. coli concentrations, depending on the flow direction of the river plume.18 During

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2008, water samples were collected at each location and analyzed for E. coli within 4-6 hours in

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the laboratory using a defined substrate technology (IDEXX Inc., Westbrook, ME). For

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modeling purposes, E. coli data were log10-transformed since the value could vary by orders of

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magnitudes. Water samples were also analyzed in the laboratory for turbidity (NTU; 2100N

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Turbidimeter, Hach Company, Loveland, CO).

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3. Results

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The R2 and RMSE values for the testing period data sets of all models are listed in Table 1 while

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the results of R2 and RMSE during all three periods (training, validation and testing) are shown

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in Table S6 (in the Supporting Information). We now report the testing period R2 and RMSE

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values as pairs in the following sections.

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3.1 The NIO model

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Figures 2(a) and S2 show the results of the Model 1, the NIO model. The value of (R2, RMSE) is

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(0.53, 0.33) during the testing period at OD1 site, which is the farthest beach site to the waterway

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(Figure 1). The (R2, RMSE) values for the testing period are (0.43, 0.53) and (0.46, 0.32) at the

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OD2 and OD3 sites respectively (Table 1).

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3.2 The NAR model

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The past values of the original LGEC data were used as inputs to predict the LGEC values at all

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four sites. The performance metrics for Model 2, the NAR model are shown in Figures 2(c) and

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S3. The value of (R2, RMSE) is (0.8, 0.11) during testing period at BD site (Figure S3(a)). Figure



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2(c) shows model performance during the three periods of training, validation and testing at the

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OD1 site with the (R2, RMSE) value of (0.38, 0.24) during the testing period. The values are

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(0.34, 0.41) and (0.59, 0.45) at OD2 and OD3 sites (Figure S3) respectively.

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3.3 The NARX model

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In order to determine the inputs of the NARX model from the ten environmental factors

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measured at the sites (see Supporting Information for details and explanation of variable names),

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cross-correlation between the ten environmental factors and LGEC for different time lags were

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examined in addition to the auto-correlation of LGEC. The results are listed in Tables S1-S4 for

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the four sites. Two sets of NARX models were developed based on different combinations of

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explanatory variables for nowcasting LGEC datasets at the four sites. The NARX models are

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trained and tested based on different combinations of time series at all four sites such that

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environmental variables with similar values of correlation coefficients and with a strong

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correlation with E. coli concentrations fall into similar groups. Four-hour water temperature

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(WTEMP4HR) and daily rainfall are also considered as the input variables for the NARX models,

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which were found to be important input variables as they affect the FIB concentrations and

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contribute to elevate contaminant levels in the receiving water.70 Rainfall data comes from the

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National Park service weather station that is located in Porter, IN. We used aggregated rainfall

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data from the previous 24 hours as an explanatory variable. Figures 2(e) and S4 show the Model

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3 (NARX model) results based on LGDISCH24HR (log10 of 24-hour discharge from the river),

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BD_LNTURB (natural log of turbidity at the river mouth BD), LNTURB (natural log of

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turbidity at the beach site), water temperature (WTEMP4HR), rainfall and LGEC as inputs,

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which are the parameters with high correlation coefficients with the dependent variable LGEC at

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four sites. The R2 and RMSE during testing period are listed in Table 1, and the (R2, RMSE)


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values during all periods are shown in Table S6. Figure S4(a) shows the Model 3 result at the BD

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site. The value of (R2, RMSE) for the testing period is (0.86, 0.16). Figure 2(e) shows the

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performance of Model 3 at the OD1 site with an (R2, RMSE) value of (0.8, 0.15) during the

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testing period. The corresponding (R2, RMSE) values are (0.82, 0.31) and (0.80, 0.23) at sites

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OD2 and OD3 respectively.

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In another version of the NARX model (Model 4, Table 1), the input variables LNTURB,

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LNWHSIG4HR, WNDSPD_ONSHORE, WTEMP4HR, rainfall and LGEC are used and tested

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at all four sites. The results of Model 4 are shown in Figure S5 and the results of R2 and RMSE

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during testing period are shown in Table 1, and the corresponding R2 and RMSE for all three

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periods are listed in Table S6.

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3.4 The WA-NAR hybrid model

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E. coli data spanning a period of 86 days (from early June to the end of August 2008) are

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available for developing the models. Details of data augmentation / up-sampling are included in

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the Supporting Information and the results based on three wavelet levels are reported in Table S5.

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Since the number of wavelet coefficients used in the model increases with the wavelet levels, we

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have attempted to use an optimum number of wavelet levels that minimize forecast errors and

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avoid over-fitting.

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As can be expected, the most important components are those that have a high correlation with

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the original data. The correlation coefficients between the last level of the previous sub-time

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series and the original time series (e.g., r (t − 1, t ) and r (t − 2, t ) etc.) are shown in Table S5 for

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the detail (W) and approximation (C) components for the E. coli data at all four sites. Based on

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the strength of these correlation coefficients, the important sub-time series components ( Wi,n , Cn ,

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i = 2,3,4 , n = 1,2,... n hours lagging time) were used as the inputs to the WA-NAR model. 13 ACS Paragon Plus Environment


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The wavelet decomposition coefficients of the past values of the half-hourly LGEC data were

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used as input to forecast LGEC. The scatterplot and time series for comparing the observed and

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simulated LGEC datasets at BD site using Model 5, the WA-NAR model are showed in Figure 3

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and Figure S7. The (R2, RMSE) value for testing period at the BD site is (0.86, 0.05) (Table 1).

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The corresponding values at the OD1, OD2 and OD3 sites are (0.62, 0.07), (0.57, 0.1) and (0.62,

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0.11) respectively. The higher R2 and the lower RMSE values were obtained for the BD site

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relative to the sites at OD1, OD2 and OD3.

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As explained in the methods section and the Supporting Information, after training the network

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by the WA-NAR model, the network was used to predict the future LGEC at the four sampling

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sites. The input values are the random time series that were generated by MCMC slice sampling

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with the original observations retained at the original sampling times. The feedback loop only

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performs a one-step-ahead prediction when the NAR network is “open”. While the loop of the

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NAR network is closed when the training of model is completed, it performs multi-step-ahead

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predictions. The predictions were done at 0.25-, 0.5- and 1-day (i.e., 12, 24, and 48 half-hourly

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data points respectively) time scales, and the R2 and RMSE values were calculated for all three

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cases (Table 2). The (R2, RMSE) values for 0.25-day ahead prediction are (0.83, 0.04), (0.51,

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0.06), (0.7, 0.08) and (0.53, 0.08) at the four sites, respectively. Similarly, the prediction results

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of (R2, RMSE) at 0.5- and 1-day ahead predictions are listed in Table 2.

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The sensitivity and specificity metrics for all models are showed in Table S6 and Figure S8. It

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can be seen that when there are no exceedances the models have zero sensitivity. For all the

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models evaluated, sensitivities are greater than 0.3, and specificities are greater than 0.9.


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4. Discussion

338

We found that the WA-NAR model was substantially more accurate than the NAR model at all

339

four sites as shown by the higher R2 values and lower RMSE values. The discrete wavelet

340

transform allowed most of the noisy data to be removed and facilitated the extraction of

341

quasi-periodic and periodic signals in the original time series. The wavelet coefficients obtained

342

by decomposing the original data contain all of the important information at different temporal

343

scales and can be used to make short-term predictions. The wavelet transform improved the

344

performance of the NAR nowcasting model by providing useful information at various

345

decomposition levels. Hence the WA-NAR model is a potentially useful new method for

346

nowcasting indicator bacteria originating from river plumes and at river beach/park sites. The

347

NARX models also show the accurate simultaneous prediction with environmental variables as

348

inputs. Comparing the results of ANN models between BD site and OD sites, the former (BD site

349

model) is superior to the latter one (OD sites models). This result is mainly determined by the

350

special geographical location of the sampling sites. The lake / beach sites (OD sites) are strongly

351

affected by waves, wind, bacterial loading from shoreline sand and bird inputs, re-suspension of

352

bottom sediment and many other processes making it relatively more difficult to make accurate

353

predictions at the beach sites. Our results indicate that FIB levels at river sites can be predicted

354

more accurately compared to beach sites. The river mouth (BD site) has significant impact on the

355

dynamics of E. coli at beaches Therefore LGEC data at the BD site brings information that can

356

positively influence predictions at the beach sites. The comparisons shown in this work are

357

encouraging and provide motivation to further examine this class of methods for beach

358

management, especially when combined with automated continuous monitoring and prediction

359

of beach water quality.14



Page 16 of 34

360 361

With the half-hourly LGEC data that is a random time series generated using the MCMC slice

362

sampling and replaced with original observations as input, the WA-NAR model was used to

363

nowcast the E. coli concentrations at different time scales (0.25-, 0.5- and 1-day). The results

364

(Table 2) indicate that the predicted results are acceptable for beach management, responding to

365

the first question we sought to address in the introduction. The standard metrics (R2 and RMSE)

366

were used to quantify the performance of each model, and some models have R2 values greater

367

than 0.7 indicating a high degree of confidence with the forecast, responding to the second

368

question. Moreover, predictive models with sensitivity greater than 0.3, and specificity greater

369

than 0.9 can also be considered as good (Table 1). The ANN models developed in this work are

370

better than the MLR models reported in Park et al.,34 for example. The R2 and RMSE values

371

compared with those from MLR and mechanistic models, especially R2 values higher than 0.7 in

372

our NARX models and R2 values around 0.7 for the WA-NAR model without the use of

373

explanatory variables, prove that the ANN and wavelet-ANN based approaches considered in

374

this work are promising. The WA-NAR models are particularly appealing for application to data

375

scarce regions without access to any data on explanatory variables (the third question we sought

376

to address in the introduction).

377 378

Despite the differences in the parameters of the two NARX models evaluated in this work

379

(Models 3 and 4), the two models produced comparable performance. Model 4 used the

380

significant wave height and onshore wind speed - two important parameters known to influence

381

E. coli in coastal waters. Onshore winds push river plumes towards the shore inducing an

382

alongshore current that can carry shore-hugging plumes several kilometers along the shoreline


Page 17 of 34


383

from the river mouth. Wave activity has the potential to resuspend E. coli from bottom sediment.

384

It is encouraging to note that both NARX models (Models 3, 4) produced high R2 values (0.86

385

and 0.94) at the river site BD. It can be expected that further network optimization and data

386

exploration (including the use of data transformations and identification of significant interaction

387

terms) will lead to additional improvements in the performance of these models pushing the R2

388

limit further up to values around 0.9.

389 390

The NARX models (e.g., Model 4) described in this paper produced some of the highest values

391

of R2 in the literature and are comparable to or better than the statistical and mechanistic

392

modeling results reported earlier4. The MCMC method was used to generate half-hourly interval

393

LGEC data so that tomorrow’s values can be predicted using yesterday’s monitoring data. Such

394

an approach to up-sample data is also needed at the beginning of the beach season when the

395

amount of available data is limited. Using the wavelet decomposition data and training and

396

validation results from the previous year’s beach season is another promising approach but this is

397

beyond the scope of the present paper. The ANN or WANN models described in this paper can

398

also be applied to recreational waters with different conditions (e.g., marine beaches with tides

399

and influence of salinity or beaches where shoreline sand, bird inputs and the presence of

400

breakwaters modify circulation and FIB fate and transport) and to predict harmful algal blooms71

401

in lakes which are influenced by several of the same explanatory variables used in this work.

402

While a majority of the published mechanistic nearshore models use observed data collected in

403

the past to generate model hindcasts, it is possible to link well-tested watershed models72-75 that

404

describe surface and subsurface transport processes76-77 with beach water quality models to

405

generate continuous forecasts in real-time. However, very few sites use linked watershed - beach



Page 18 of 34

406

water quality models for making real-time nowcasts of beach water quality, perhaps due to the

407

enormous effort involved in independently testing and linking the two types of models. By

408

including rainfall and other relevant explanatory variables in a NARX or WA-NAR model, the

409

models can represent watershed-scale fate and transport processes that control the fluxes of FIB

410

delivered to downstream receiving water bodies such as lakes. Another class of models that have

411

considerable promise for beach management combine the use of wavelet decomposition with the

412

best NARX class of models that use explanatory variables such as turbidity as input. This class

413

of WA-NARX models are a natural extension of the WA-NAR models evaluated in this work.

414 415

Acknowledgments

416

This work was partially supported by National Natural Science Foundation of China (41530316).

417

We acknowledge the use of the IAN symbol libraries in creating the Abstract Art

418

(http://ian.umces.edu/symbols).

419 420

Supporting Information

421

The methods of ANN models, wavelet decomposition, MCMC sampling and Kalman filtering

422

are presented in Supporting Information sections S1-S5. Figures S1-S8 show the architecture of

423

NAR neural network, as well as plots of wavelet decomposition and, the models’ performance,

424

the random number generation of the logarithm of E. coli using the MCMC method and the

425

predicted versus observed LGEC using the ANN models at OD sites. The tables of the

426

auto-correlation coefficients of LGEC and the cross-correlation coefficients between LGEC and

427

other input parameters at the four sites are presented in Tables S1-S4. Auto-correlation


Page 19 of 34


428

coefficients for different wavelet components are included in Table S5. The values of R2 and

429

RMSE for the training, validation and test periods are listed in Table S6.

430 431

References

432

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632 633 634


Tables Table 1 The model results for LGEC during the testing period. Models Model 1

Model 2

Input Parameters NIO

NAR

Model 3 NARX Model 4

Model 5

WA-NAR

LGEC at BD site LGEC at BD site LGEC at OD1 site LGEC at OD2 site LGEC at OD3 site LGEC LGDISCH24HR BD_LNTURB LNTURB WTEMP4HR Rainfall LGEC LNTURB LNWHSIG4HR WNDSPD_ONSHORE WTEMP4HR Rainfall Wavelet-decomposed coefficients of LGEC

Sites OD1 OD2 OD3 BD OD1 OD2

R2 0.53 0.43 0.46 0.8 0.38 0.34

RMSE 0.33 0.53 0.32 0.11 0.24 0.41

OD3

0.59

0.45

BD

0.86

0.16

OD1

0.8

0.15

OD2

0.82

0.31

OD3

0.8

0.23

BD

0.94

0.07

OD1

0.77

0.26

OD2

0.83

0.23

OD3

0.82

0.29

BD

0.86

0.05

OD1

0.62

0.07

OD2

0.57

0.1

OD3

0.62

0.11

635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 29 ACS Paragon Plus Environment


650 651

Table 2. The model performance metrics of R2 and RMSE for different prediction time scales Sites BD

OD1

OD2

OD3 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678

Page 30 of 34

Prediction time (d) 0.25 0.5 1 0.25 0.5 1 0.25 0.5 1 0.25 0.5 1

R2 0.83 0.8 0.91 0.51 0.34 0.77 0.7 0.62 0.56 0.53 0.54 0.6

RMSE 0.04 0.04 0.07 0.06 0.06 0.07 0.08 0.08 0.15 0.08 0.08 0.13

Figures Figure 1. Map of southern Lake Michigan showing the beach sites and the tributaries. Figure 2. (a and b) Performance of the NIO model with LGEC data at BD site as input: (a) Linear regression plot of the simulation results at OD1. (b) Time series of data and simulations at OD1. (c and d) Performance of the NAR model with original LGEC data at the beach site as input: (c) Linear regression plot of the simulation results at OD1. (d) Time series of data and simulations at OD1. (e and f) Performance of the NARX model (Model 3) with LGEC, LGDISCH24HR, LNTURB, WTEMP4HR and rainfall as inputs: (e) Linear regression plot of the simulation results at OD1. (f) Time series of data and simulations at OD1. In the scatterplots (panels on the left), blue, red and green symbols denote data used during the training, validation and test periods respectively while lines of the same color represent the best-fit lines. The black dashed line in the left panels represents the perfect fit (1:1) line. The time series of original data (black circles) and simulation results (blue, red and green lines) are shown in the panels on the right. Figure 3. Performance of the WA-NAR model at BD site based on wavelet decomposition of LGEC as inputs. (a) Linear regression plot of the simulation results. (b) Time series of data and simulations. In the left panel, the x- and y-axes represent the observed and simulated LGEC values.


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Real-Time Nowcasting of Microbiological Water ... - ACS Publications

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