Enterococci Predictions from Partial Least Squares Regression

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Policy Analysis Enterococci Predictions from Partial Least Squares Regression Models in Conjunction with a Single-Sample Standard Improve the Efficacy of Beach Management Advisories DEYI HOU,† SHARYL J. M. RABINOVICI,‡ AND A L E X A N D R I A B . B O E H M * ,† Environmental Water Studies, Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305-4020 and Richard & Rhoda Goldman School of Public Policy, 2607 Hearst Avenue, University of California, Berkeley, Berkeley, California 94720-7320

Beach health advisories are issued if enterococci (ENT) densities exceed the 30-d geometric mean or singlesample water quality criteria. Current ENT enumeration procedures require 1 day of incubation; therefore, beach managers make policy decisions using 1-day-old data. This is tantamount to using a model that assumes ENT density on day t is equal to ENT density on day t - 1. Research has shown that ENT densities vary over time scales shorter than a day, calling into question the usefulness of the current model for decision-making. We created Dynamic Partial Least Square Regression (DPLSR) models for ENT at water quality monitoring stations within two adjacent marine recreational sites, Huntington State Beach (HSB) and Huntington City (HCB) Beach, California, using publicly available environmental data and tested whether these models overcome the drawbacks of the current model. The DPLSR models provide a better prediction of ENT than the current models based on comparisons of rootmean-square errors of prediction and the numbers of type 1 and 2 errors. We compared outcomes in terms of predicted illness, swimmers deterred from entering the water, and net benefits to swimmers for hypothetical management scenarios where beach advisories were issued based on (a) the previously collected sample’s ENT density in conjunction with the two water quality criteria, and (b) predictions from DPLSR models in conjunction with the singlesample standard. At both HSB and HCB the DPLSR scenario produced a more favorable balance between illness prevention and recreational access. The results call into question the current method of beach management and show that model-informed decision-making and elimination of the geometric mean standard will aid beach managers in achieving more favorable outcomes in terms of illness and access than are presently achieved using 1-day-old measurements, especially at beaches where water quality problems are chronic. * Corresponding author phone: (650) 724-9128; fax: (650) 7253164; e-mail: [email protected]. † Stanford University. ‡ University of California, Berkeley. 10.1021/es0515250 CCC: $33.50 Published on Web 02/15/2006

 2006 American Chemical Society

Introduction Approximately 39% of the world’s human population resides within 100 km of a coastline (1). Rapid development of coastal lands is having detrimental impacts on coastal water quality, especially in regards to microbial pollution (2-4). In 2003, there were approximately 18,000 closures and advisories due to microbial contamination along the marine coastline and the Great Lakes of the United States, representing a 51% increase from the previous year (5). While some of the increase can be attributed to more thorough monitoring and more stringent policies, this explanation provides little reassurance to a public concerned about the safety of the waters in which they swim. Formal epidemiology studies illustrate that microbial contamination from sewage and runoff poses a health risk to swimmers (e.g., 6-9). Specific health outcomes include gastrointestinal illness (GI) and severe respiratory disease (10). Although the exact etiologies of the diseases are unknown, concentrations of fecal indicator bacteria (FIB) have proven to be good proxies for estimating health outcomes at marine beaches (11). The U.S. Beaches Environmental Assessment and Coastal Health Act requires that all coastal states and tribes have regulations to protect beachgoers at recreational beaches along the U.S. coastline (12). In California (CA), beaches are posted with advisories when water quality standards are violated according to guidelines established by CA Assembly Bill 411. The criteria consist of single-sample standards and 30-day geometric mean standards for three FIB: total coliform (TC), fecal coliform (FC), and enterococci (ENT). These organisms were chosen for the criteria on the basis of epidemiology studies that show a correlation between health outcomes and exposure to indicator densities during swimming (10, 11). The standards are provided in the Supporting Information (SI). Current FIB measurement technologies require approximately 1 d of incubation before results can be obtained. Thus, beach management decisions on day t are made using measurements from day t - 1. Implicit in this management strategy is the assumption that bacteria densities on day t are equal to measurements on day t - 1, or FIB(t) ) FIB(t - 1). Recent work illustrates that many pollution events at marine beaches are shorter than 1 day in duration and only minimally correlated with FIB densities the following day (13, 14). Thus, the 1-day lag seriously impairs the efficacy of management decisions (15, 16). The specific objectives of the present study are (a) to determine if using predictive models of ENT densities to inform policy decisions can overcome limitations of the current model that assumes ENT(t) ) ENT(t - 1), and (b) to present a framework for measuring the success of beach management models that includes evaluating not only predictive capabilities, but also actual outcomes for swimmers in terms of illnesses and recreational access. We choose ENT as the models’ dependent variable because it is the best FIB for assessing risk in marine waters (11, 18). Predictive models are currently used at Lake Michigan beaches to aid managers in making informed policy decisions (17), but presently models have not been applied to management of marine bathing beaches. Models are created for water quality monitoring stations located within two contiguous marine beaches in CA using environmental variables as factors in partial least squares regression (PLSR). The model predictions are subsequently used to make informed hypothetical policy VOL. 40, NO. 6, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Map of the field site. HCB extends from station 27N to the dotted line between 15N and 9N. HSB extends from the dotted line to 0N, just north of the Santa Ana River. decisions regarding the posting of advisories at each station. The effect of these advisories on swimmer health and access is then determined.

Materials and Methods Study Site Description. Huntington State and City Beaches (33°38′ N, 117°59′ W) are located in CA (Figure 1). There are many potential ENT sources to the beaches: urban runoff from the Talbert Marsh and Santa Ana River, effluent discharged through a wastewater outfall 7.5 km offshore, and contaminated groundwater discharge (19-21). The Santa Ana River and the Talbert Marsh outlets discharge freshwater primarily during the wet season (approximately November through March). During the dry season, the river and the marsh are essentially tidally influenced saltwater wetlands with little if any freshwater discharge. We created ENT models for the seven water quality monitoring sites within Huntington State Beach (HSB) and Huntington City Beach (HCB). Monitoring sites 0, 3N, 6N, and 9N are within HSB, and stations 15N, 21N, and 27N are within HCB. Although HSB and HCB are directly adjacent to one another, historical water quality analysis reveals that water quality at HSB, particularly near stations 6N and 9N, is significantly more impaired than water quality at HCB (14). Models were created with publicly available data obtained from local and national data repositories. Data. ENT data from October 1999 through December 2000 were obtained from the beach monitoring agency (22). Samples were collected from monitoring stations shown in Figure 1 at ankle depth in the morning and enumerated using the 24-hour EPA Method 1600 (23). The lower and upper detection limits of the assay were 2 and 400 colony forming units (CFU)/100 mL, respectively. If a sample’s ENT density was reported as 400 CFU/100 mL, then it was assumed that the measured density was equal to the detection limit, a practice we have used previously (e.g., 14). Samples were collected between 3 and 5 times per week depending on season leaving a total of 177 days of measurements during 2000 available for our study. We obtained environmental data for the field site from publicly available data depositories. These include volumetric flow of stormwater discharge, rainfall, sea surface temperature, upwelling index, wind velocity, wave height and direction, visitor number, atmospheric pressure, solar insolation, sampling time, and tide level and range. We included lagged time series of rainfall and storm runoff as well, because CA beach managers advise beachgoers that beach water quality is impaired by stormwater runoff for 3 days after a storm event. These factors were chosen for inclusion in our study because previous work showed that they can affect FIB densities at beaches (14, 24-26). Our SI contains information on the data and their sources. ENT, rainfall, storm discharge, and visitor numbers were log-transformed prior to use because they are better ap1738

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proximated by log-normal rather than normal distributions based on Lilliefors tests and quantile-quantile plots (Matlab, Mathworks, Natick, MA). All variables were standardized to have zero mean and unit variance. Partial Least Squares Regression Models. PLSR is a robust multivariate regression method that has been widely used in scientific and engineering fields for developing predictive models and exploring relationships among variables (e.g., 27, 28). PLSR produces independent factor scores as linear combinations of independent variables (principle components), and a regression is preformed between the scores and the response (29). It is useful for creating predictive models when there are many collinear factors. We chose to use PLSR over ordinary least squares regression (OLSR) to model ENT for the following reasons. (1) Some of our factors are well-correlated, and in contrast to OLSR, this does not violate the assumptions of PLSR (27, 30) (see SI for examples of collinear factors). (2) For OLSR, it is recommended that the modeler include 10-20 times as many observations as he has variables (31, 32). We used as little as 10 observations to make ENT predictions with over 10 variables in our predictive models, thus PLSR was deemed more appropriate than OLSR. (3) PLSR is recommended over OLSR for models using time series as factors (33, 34). Because our factors are time series, we deemed PLSR more appropriate than OLSR. An example performance comparison of PLSR and OLSR models is given in the SI. PLSR algorithms return variable coefficients and measures of variable importance on projection (VIPs) for each predictor. In contrast to OLSR, the VIP is used to determine the relative importance of each predictor, rather than the coefficient. The VIP can range from 0 to over 1; if a predictor has a VIP between 0.8 and 1.0, it is considered to be influential in the PLSR model; if it is greater than 1.0 it is considered to be very influential (29). The sign of the coefficient for a predictor informs the modeler whether the dependent variable is positively or negatively correlated to the predictor. Before creating models, we divided the 177 days when water samples were collected during 2000 into two categories: wet and dry. Wet days were defined as any day with rainfall over 1.27 mm, or within 7 d of a storm event (defined as a sequence of two or more consecutive days with rainfall totaling more than 2.54 mm and storm runoff larger than 0.0283 m3 s-1). Wet and dry days were modeled independently because we expect different factors to modulate ENT delivered to the beach via storm runoff from the watershed outlets than ENT delivered to the beach by low-momentum dry weather flows or other nonpoint sources (such as bird feces) (14). Models to Determine Important Factors. We first created PLSR models for each monitoring station within HSB and HCB using every environmental factor for wet and dry days separately between January 1 and December 31, 2000 (SimcaP, Umetrics, Sweden). ENT density of the previously collected sample was also added as a factor. Note that storm runoff and rainfall related variables were not used in the dry day models. For simplicity, interaction terms between factors were ignored and linearity between factors and response was assumed. The purpose of these models was to determine which factors were important predictors of ENT on wet and dry days, respectively, and should thus be retained for use in development of predictive models. An independent variable was retained if VIPs were larger than 0.8 in models for 3 or more of the 7 stations. As long as ENT sources to the beach do not change over the years, these variables should be important predictors for ENT in other years as well. Predictive Models. Next we created predictive Dynamic PLSR models (hereafter referred to as DPLSR) for each station using only the retained independent variables with the purpose of generating ENT predictions for each “target day”

when an actual water sample was collected during 2000. The term dynamic reflects our use of 10 d of observations in the same category (dry or wet days) preceding the “target day” to train the DPLSR model (35), thus allowing our models to capture variability over time in the way factors affect ENT densities. The 10 days typically spanned 3 weeks in the winter and 2 weeks in the summer due to seasonal differences in sampling frequencies. The dynamic model was then used to predict ENT on the target day by inputting environmental data measured on the target day into the model. Overall, 1,239 DPLSR models were created to predict ENT densities on 177 days at 7 monitoring stations. DPLSR model outputs in excess of the ENT single-sample standard in CA (104 CFU/100 mL) were examined to determine if predictions were influenced by an outlier in the training data set. If the predicted high value of ENT was a result of the influence of an independent variable with a VIP larger than 1.5, the prediction was accepted. Otherwise, if 15 and 20 d DPLSR models (trained as the 10 d model, but with more data) also predicted elevated ENT, then the prediction from the 10 d model was accepted. If there were disagreements between the 10, 15, and 20 d models outputs, then the results from the 15 d model were used. The model outputs were further capped by 400 CFU/100 mL and 2 CFU/100 mL to mimic actual upper and lower detection limits, respectively. A chart illustrating the discrimination process for obtaining ENT predications is shown in Figure S1 of the SI. Model Evaluation. The accuracy of the DPLSR and current models’ ENT predictions was examined by calculating the root-mean-square error of prediction (RMSEP) and the numbers of type 1 and type 2 errors. RMSEP was calculated as follows:

RMSEP )

x∑ 1

n

n i)1

(Epred.i - Eobs.i)2

(1)

where n is the number of data points, and Epred.i and Eobs.i are the log-transformed predicted and observed ENT for sample i, respectively. Type 1 and 2 errors are of particular significance in the beach management setting because false negative and false positive water quality warnings are a consequence of the 1-d lag implicit in the current model (15). Thus, they are a key measure of the potential effectiveness of a given model in actual policy formation or decisionmaking. The type 1 and 2 errors were calculated assuming the null hypothesis is that the beach adjacent to a station is and should be open considering the single-sample ENT standard as a trigger for posting. To assess how using DPLSR models in management decision-making might impact swimmer health and recreational access relative to the current model, we followed the benefits transfer policy analysis procedure outlined by Rabinovici et al. (16) adjusted so that inputs reflect a marine setting. The limitations of using benefits transfer are discussed in detail by Rabinovici et al. (16). Subsequently, the Rabinovici et al. method was used to weigh the tradeoffs between reducing illnesses and preserving recreational access at HSB and HCB under two hypothetical management scenarios in which beach advisories were issued based on current and DPLSR ENT model predictions (hereafter referred to as current and DPLSR scenarios, respectively). For comparison purposes, we also included results from a scenario where there was no beach management (that is, the beach is never under advisory). For the current scenario, decisions to issue an advisory at a stretch of beach were triggered by violation of the 30-d geometric mean (35 CFU/100 mL) and singlesample (104 CFU/100 mL) standards, as this is common practice. For the DPLSR scenario, we used only single-sample standard violations to trigger issuance of an advisory. We

deemed this appropriate because the DPLSR models produce single-day point predictions, which are only suitable for decision-making relative to the single-day, single-sample standard. When an advisory was triggered at a particular station, we assumed the stretch of beach closest in proximity to that station and within the beach boundary was posted as unfit for swimming until information was obtained that the beach was no longer out of compliance with applicable water quality standards (similar to real management strategy in place at the beaches). The incidence of swimming-related illnesses (R) among swimmers at HSB and HCB on a given day was estimated using the dose-response relation between ENT density and risk of GI reported by Wade et al. (11):

R)

∑R ) ∑S [be k

k

k

0.3log (ENTk) + 0.099

- b]

(2)

k

where k is a counter for each region of shoreline within HSB and HCB: 0N, 3N, 6N, or 9N; and 15N, 21N, or 27N, respectively. For the purpose of this study, we considered the region k to be the length of shoreline within the beach boundary closest in proximity to station k. ENTk is the ENT density in the surf zone of each region with units CFU/100 mL, and is considered constant and equal to the ENT density measured at station k. It is well-established that ENT density can vary spatially along a beach. However, the precise manner it which it varies is not well understood. Thus, assuming it is constant within a specific region is reasonable as a starting point for our analysis, and has been assumed by other researchers (36). Sk is the number of swimmers in region k and was derived assuming that the number of visitors to HSB and HCB was evenly distributed along the shoreline, and that 38% of them are swimmers (37). Swimmers are defined as the group of beach goers who would choose to swim during nonadvisory conditions. We assumed that when there was an advisory in place at the beach a fraction of the swimmers (i) would still choose to enter the water such that Sk ) 0.38iNk where Nk is the total number of visitors to region k. When i ) 1 and all swimmers ignore the advisory, then Sk simplifies to its value when there is no advisory Sk ) 0.38Nk. There is presently no published information about the value of i. In the present study we assumed i ) 0.1, and discuss how this choice affects the results in the SI. b is the background rate of illness and was set to 0.03 (10). It is important to point out that there are other epidemiology studies that provide different dose-response relationships for assessing risk. In particular, Kay et al.’s (38) case-control study estimates lower and higher risks at lower and higher ENT, respectively, than does Wade et al. (11). We deemed the Wade et al. relationship appropriate for our study because it is a meta-analysis and combines data from many epidemiology studies. The number of people deterred from entering the water at the beaches each day when there was an advisory (A) was calculated as follows:

A)

∑0.38(1 - i)N

(3)

k

k

where the variables i, Nk, and k have been defined previously. If no advisory was issued, then A ) 0. As with R, A was calculated for HCB and HSB on days when a sample was collected from the surf zone by beach managers. The benefits transfer approach outlined by Rabinovici et al. (16) was applied to weigh outcomes under the two modeldriven decision scenarios, and also the no management scenario. The net benefit to swimmers (those beach visitors who would choose to swim under nonadvisory conditions) includes contributions from (1) those swimmers who enter VOL. 40, NO. 6, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Root Mean Square Errors of Prediction (RMSEPa, defined in Eq 1) for Dynamic Partial Least Squares Regression (DPLSR) and Current Models at Each Station for the Year 2000

TABLE 1. Summary of Swimmers and ENT Concentrations (CFU/100 ML) at Our Study Site for the Year 2000a

station

no. of samples collected

total no. of swimmers

average swimmers (d-1)

geometric mean ENT

HSB HCB

708 531

415,577 1,143,788

2348 ( 464 6462 ( 908

16.8+1.9/-1.7 8.0+0.9/-0.4

a Results for HSB and HCB include swimmers and ENT within the entire beach (stations 0, 3N, 6N, and 9N are within HSB, and stations 15N, 21N, and 27N are within HCB). Ninety-five percent confidence intervals are given for averages and geometric means. Total swimmers represents the total number of individuals who would choose to swim under nonadvisory conditions over the 177 days in 2000 included in our study.

the water and experience a loss from acquiring GI but benefit from recreational swimming and (2) those who are deterred from entering the water and experience a benefit from avoiding illness but a loss associated with lost recreation. These contributions can be summed each day when ENT density data exist across stations to calculate the day’s net benefits (NB) for HSB and HCB:

NB )

{

∑[S V

- RkVhealth] if there is no advisory

∑[R V

- SkVrec] if there is an advisory

k rec

k

k health

(4)

k

where Sk and Rk have been defined earlier, and Vhealth and Vrec are the value of avoiding illness and of swimming recreation. The value of Vhealth used is $280, which represents the willingness-to-pay (WTP) value to avoid a mild case of gastrointestinal symptoms (16, 39). The value of Vrec used is $14.95, which is the value per person per swimming activity day estimated for the Pacific coast U.S. Bureau of Census Region (40). These values are similar to values cited by Rabinovici et al. (16).

Results and Discussion Water Quality and Visitor Numbers During 2000. HSB typically had higher ENT densities than HCB as evidenced by the higher geometric mean at HSB (16.8 CFU/100 mL) compared to that at HCB (8.0 CFU/100 mL) (see Table 1 for confidence intervals) supporting the assertion that water quality was worse at HSB than at HCB during 2000. HCB was more intensely visited compared to HSB (Table 1). This is due in part to the larger size of HCB (5.4 km) compared to that of HSB (3.6 km), and also the presence of more amenities at HCB (Huntington Pier, vendors, and volleyball courts). Important Predictors for DPLSR Models. PLSR models constructed from wet and dry days separately at each monitoring station were used to determine the important predictors to be retained in the DPLSR predictive models. The R2 values for these models are given in Table S4. Table S5 summarizes the average and range of VIP for each variable and the number of stations where the VIP was greater than 0.8 for wet and dry days. It also shows whether the coefficients for the predictors are positive or negative at stations where the VIP is greater than 0.8. Important Predictors for Wet Days. On wet days the following variables were determined to be important predictors of ENT and thus were retained for the predictive models: rainfall, SAR discharge, upwelling index, tide range, wind speed, N/S wind velocity, HCB and HSB visitor number, sample time, wave direction and height, littoral drift direction, ENT density of the previous sample collected, SAR discharge of the previous day, rainfall of the previous day, and rainfall of 2 and 3 days prior to the modeled day. Of these variables, 1740

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model

0

3N

6N

9N

15N

21N

27N

DPLSR current

0.54 0.64

0.64 0.77

0.63 0.78

0.63 0.75

0.61 0.68

0.56 0.69

0.57 0.68

a

RMSEP are measured in log-space.

SAR discharge, rainfall of the previous day, N/S wind velocity, and ENT of the previous sample were important at all 7 stations with average VIP greater than 1, thus these are very influential variables for prediction of ENT on wet days. The signs of coefficients for each of the important variables suggest that at the majority of stations high values associated with SAR discharge of the modeled day and previous day, rainfall of the modeled and previous day, upwelling index, tide range, wind speed, N/S wind velocity, HCB attendance, wave height, and ENT density of the previous day, and presence of SW or W waves led to higher ENT densities. In contrast, lower values of HSB attendance and rainfall occurring 2 and 3 days prior to the modeled day, absence of SSW and WSW waves, and downcoast littoral drift led to higher ENT densities. There is heterogeneity in the sign of coefficients between stations for some of the influential predictors: in particular HCB attendance, SW, W, and WSW waves, and rainfall of the previous day (Table S5). This heterogeneity suggests that ENT at different stations within HSB and HCB are affected by predictors in diverse ways. In DPLSR predictive models, the coefficients for the variables are not held fixed to the values or signs reported in Table S5, but allowed to vary to account for changes in ENT response to environmental predictors. Important Predictors for ENT on Dry Days. On dry days, the following variables were deemed important based on the VIP criteria of 0.8: upwelling index, tide range and level, water temperature, atmospheric pressure, N/S wind velocity, HSB and HCB visitor number, W, WSW, and SSW waves, solar insolation of the previous day, sample time, and ENT of the previous sample. Of these, the visitor numbers and the ENT of the previously collected sample were important at all sites with average VIP greater than 1. The coefficients of the important dry day variables listed above indicate that high values associated with the upwelling index, tide range, N/S wind velocity, HCB attendance, tide level, solar insolation of the previous day, and ENT of the previous day corresponded to high ENT densities on the target day at the majority of stations. On the other hand, low values associated with sea temperature, atmospheric pressure, HSB attendance, sample time, and the absence of waves from the SSW and W gave rise to higher ENT densities at the majority of stations. At half the stations where WSW waves were important, their absence corresponded to high ENT densities, and at the other half, their presence corresponded to high ENT densities. As with the results for wet days, there is heterogeneity among coefficient signs at various stations, and signs and magnitudes of coefficients are not fixed for the predictive models. Model Evaluation: Predictive Capabilities. Figure S2 compares the predictions of the current and DPLSR models of ENT with the actual measured ENT at each station within HSB (panels A and B) and HCB (panels C and D). Predicted and measured ENT are closer to the 1:1 line in panels B and D than in panels A and C. A representative residual plot is shown in Figure S3. The improved predictive power of DPLSR models is more clearly borne out upon examination of the RMSEPs for the models at each station (Table 2), which are all smaller for DPLSR models compared to the current models.

TABLE 3. Type 1 and Type 2 Errors for HSB and HCB beach

model

Type 1

Type 2

correct postingsa

total points

HSB

DPLSR current DPLSR current

22 63 4 20

55 62 13 19

40 33 8 2

708 708 531 531

HCB

a Correct postings refers to the number of predictions that correctly indicated that the beach was in exceedance of the single-sample standard.

This confirms that the DPLSR models do a better job predicting ENT than the model currently used by beach managers. The DPLSR models are not perfect as there remains a discrepancy between observed and predicted values. Using the DPLSR models’ predictions to issue beach advisories caused by exceedance of the single-sample standard produced fewer type 1 and 2 errors compared to using predictions from the current models (Table 3). Type 1 errors were reduced by 65% and 80%, and type 2 errors by 11% and 32%, at HSB and HCB, respectively. The DPLSR models were thus more effective than the current models at predicting both when the beach should be open and when it should be closed. The reductions in type 1 errors are greater than those of type 2 errors suggesting DPLSR models are especially better at predicting when beaches should be open rather than closed. Model Evaluation: Decision-Making Outcomes. Using DPLSR model predictions in conjunction with the singlesample standard would have reduced the total station-days of advisories by over 50% at both HSB and HCB. Over the 177 days in 2000 examined in this study, a total of 190 and 62 station-days of advisories would have been issued at HSB under the current and DPLSR scenarios, respectively. At HCB, there would have been 28 and 12 station-days of advisories if they had been issued based on the current and DPLSR scenarios, respectively. Although the current model is very good at predicting the number of station-days of advisories that should have been issued under the single-sample and 30-d geometric mean standards (186 (HSB) and 26 (HCB) station-days), it is very poor at predicting the timing of these advisories because of the 1-d lag associated with obtaining sample results (Table 3 shows errors resulting for singlesample standard). The DPLSR scenario predicts a reduced number of advisories at both beaches. The reduction is a result of (a) not including the 30-d geometric mean standard (reducing advisories by 95 (HSB) and 7 (HCB) station-days)

and (b) type 2 errors (reducing advisories by 55 (HSB) and 13 (HCB) station days, Table 3). We next examine the impacts on swimmer health and beach access of the improved timing and reduced total number of advisories achieved by the DPLSR scenario in comparison to the current scenario. Health Outcomes. If no advisories had been issued at HSB during 2000, 7,956 GI illnesses would have occurred over the 177 days when estimates were possible (average 45 d-1, confidence intervals given in Table 4). Management based on the DPLSR scenario would have reduced this figure to 6,883 (average 39 d-1), while use of the current scenario would have reduced it even further to 5,087 (average 29 d-1). Box and whisker plots showing the range of daily illness estimates are shown in Figure S4. This finding implies DPLSR and current management scenarios would have prevented 1,073 (13%) and 2,869 (36%) of the 7,956 illnesses at HSB that would have occurred if there were no beach management, respectively. The fewest number of illnesses is predicted to occur under the current scenario, suggesting it is more effective at reducing illness than the DPLSR scenario; however, the per day averages for management based on the two models are not significantly different (Table 4, p > 0.05). Thus, the DPLSR scenario can achieve essentially the same daily illness rate as the current scenario by issuing 62 station-days of advisories rather than 190. This is possible because the DPLSR scenario is more effective than the current model at triggering advisories when ENT concentrations, and thus health risks, are high. At HCB, the predicted illnesses are overall higher in comparison to HSB because there were more visitors (Table 4, Figure S4). The illnesses predicted to occur under the two management scenarios (DPLSR total 15,490, DPLSR average 88 d-1; current total 15,229, current average 86 d-1) are similar to each other and to the number predicted to occur if there were no decision-making framework in place (total 15,731, average 89 d-1). The total illness counts suggest that using the current scenario for management is more effective than the DPLSR scenario in reducing illness; however, the per day averages for the two management scenarios are not significantly different from each other or from the no policy outcome (Table 4, p > 0.05). The DPLSR scenario essentially achieves the same illness rate as the current scenario with 12 rather than 28 station-days of advisories. It is interesting to note that the number of illnesses prevented by implementing beach management at HCB (241 and 502 for DPLSR and current scenarios, respectively) is small compared to that at HSB, and represents a small fraction (2-3%) of the illnesses expected to occur at the beach under no management.

TABLE 4. Comparison Among Total and Daily Average Illnesses, Deterred Swimmers, and Net Benefits over the 177 out of 366 days in 2000 When ENT Measurements Were Made for HSB and HCB under Two Hypothetical Decision-Making Scenarios (Current and DPLSR) and a Scenario Where No Decisions Are Made (no posting)a beach HSB

decision-making scenario current DPLSR no posting

HCB

current DPLSR no posting

a

illnesses total (average ( CI, d-1)

deterred swimmers total (average ( CI, d-1)

net benefit total (average ( CI, d-1)

5,087 (29 ( 6) 6,883 (39 ( 8) 7,956 (45 ( 9)

121,872 (689 ( 192) 31,699 (179 ( 75) 0

$1,948,117 ($11,006 ( 2,985) $3,638,023 ($20,553 ( 4,508) $3,985,150 ($22,515 ( 4,585)

15,229 (86 (14) 15,490 (88 ( 14) 15,731 (89 ( 14)

30,705 (173 ( 107) 10,161 (57 ( 54) 0

$12,058,172 ($68,125 ( 10,440) $12,525,992 ($70,768 ( 10,328) $12,694,994 ($71,723 ( 10,282)

CI is the 95% confidence interval associated with the daily average.

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Reducing incidence of illness is a primary objective of beach management. Our total illness estimates show that use of the current scenario results in the fewest illnesses. However, at both beaches, the per day average illnesses resulting from issuance of advisories based on the DPLSR and current model predictions are not significantly different at 95% confidence. If preventing illnesses were the only goal, then a continuous beach closure preventing all human exposure to seawater would be the most effective management strategy. Benefit transfer is one approach for evaluating the balance between illness prevention and beach access, another important goal of beach management that we discuss next. Recreation Outcomes. At HSB under the current scenario, there would have been a total of 121,872 deterred swimmers over the 177 examined days during 2000 (average 689 d-1, confidence intervals in Table 4, Figure S4 shows box and whisker plots). Under the DPLSR scenario there would have been a total of 31,699 (average 179 d-1) deterred swimmers. The per day averages under the two scenarios are significantly different (p < 0.05). The reduction in deterred swimmers is a direct consequence of the fewer number of advisories issued under the DPLSR scenario. This finding suggests that policy decision-making based on DPLSR model predictions in conjunction with the single-sample standard could increase beach access by allowing 90,173 more swim visits than the current scenario while maintaining illness rates at a level similar to those achieved under the current scenario. This represents 22% of the total number of swim visits to HSB predicted to occur if their had been no advisories (Table 1). At HCB, there were fewer days posted with advisories and therefore fewer swimmers deterred than at HSB under both management scenarios. There would have been a total of 30,705 (average 173 d-1) deterred swimmers if management decisions were made on the basis of the current scenario. The DPLSR scenario would have reduced the number of deterred swimmers to a total of 10,161 (average 57 d-1). Although the totals and daily averages favor the DPLSR scenario, the daily averages are not significantly different (p > 0.05), a direct consequence of there being very few advisories issued under both scenarios at HCB and thus many days when there were no deterred swimmerssthereby increasing the standard deviation of the daily average. Based on the total numbers, issuing advisories based on the DPLSR model predictions in conjunction with the single-sample standard increases beach access at HCB by allowing 20,544 more swim visits over the current model-based predictions while maintaining illness rates at a level similar to those currently achieved. The number of people gaining access is less than the number at HSB, and represents just 2% of all swim visits to HCB that would have occurred if the beach had never been under advisory (Table 1). Net Benefits Analysis. The total net benefits to swimmers under each decision-making scenario are summarized in Table 4 in terms of the total values across the 177 days examined in 2000 and per day averages. Histograms showing the distributions of daily net benefits for each beach are shown in Figure S4. Also shown are net benefits when there is no beach management (no policy). At HSB, the aggregate net benefit to swimmers of beach advisory decision-making under the current scenario is $1,948,117 (average $11,006 d-1). When decisions for this stretch of beach are made under DPLSR scenario, the net benefits are almost twice as high (total $3,638,023, average $20,553 d-1). The per day averages are significantly different (p < 0.05). This finding illustrates that the increase in access that occurs under the DPLSR model scenario relative to the current model scenario more than offsets any increased illness rates. DPLSR model decision-making in conjunction 1742

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with the single-sample standard at HSB would clearly provide a large benefit to swimmers. At HCB, the net benefits to swimmers of beach advisory decision-making under the current scenario is $12,058,172 (average $68,125 d-1). The net benefits are about 4% higher when decision-making is based on the DPLSR scenario (total $12,525,992, average $70,768 d-1). The per day averages under the two scenarios are not significantly different (p > 0.05). Although the box and whisker plots in Figure S4 confirm that daily net benefits under the two scenarios are similar, they also show that the DPLSR scenario eliminates most of the days with large negative net benefits under the current scenario. These low net benefit days represent times when the beach was under advisory in the current scenario when there were low ENT densities. HCB had overall good water quality and few advisories relative to days of open beach. The change in access and illness between the two management scenarios was small relative to the illnesses and access outcomes under the no policy scenario, thus their net benefits were very similar. A noteworthy outcome of this analysis is that “doing nothing” (the no-policy scenario) is more net beneficial than either of the two management scenarios at both HSB and HCB (Table 4). At HCB, all three scenarios have similar net benefits based on the daily averages, but the overall no policy outcome is $169,002 and $636,822 higher than the DPLSR and current scenario outcomes, respectively. The differences at HSB are more striking, even though the only statistically significant difference in daily average net benefits is between the no policy and current scenario; the overall no policy outcome is $347,127 and $2,037,033 higher than the DPLSR and current scenario outcomes, respectively. The simplicity of our conceptual approach to valuation surely contributed to this result, in that we did not weight the economic valuations of health and recreation based on risk aversion and ignored the remote but nonzero possibility of a very serious FIB-related illness outbreak that could tip the net benefit assessment in favor of advisories. While we recognize that eliminating beach monitoring and advisories entirely might be politically and scientifically undesirable, these results do add to an increasing sense of concern about the effectiveness of common beach advisory procedures. On the basis of the aggregate outcomes, the DPLSR scenario provides similar illness rates and fewer deterred swimmers than the current scenario at both HSB and HCB, and thus the DPLSR scenario is more favorable to swimmers at both beaches. At HSB, when average daily outcomes are compared, the DPLSR is significantly more beneficial to swimmers. This is a direct consequence of this scenario’s ability to achieve essentially the same illness rates while allowing 90,173 more swimmers beach access (representing 22% of swimmers at HSB). The improved timing of beach advisories enabled by DPLSR predictions and elimination of the 30-d geometric mean standard, which triggers advisories when health risks are not high, contributes to the success of DPLSR scenario at HSB. At HCB, the average daily outcomes were not significantly different under the two scenarios. This is because there are few advisories issued at this beach relative to days of open beach, and the changes in the number of illnesses and access between the two scenarios are both slight. DPLSR allows 20,544 more swimmers access than the current scenario, but this represents just 2% of the swimmers at HCB. The results indicate that using models that predict ENT densities in marine waters based on environmental factors in beach management decision-making can lead to economically valuable improvements in recreational access with minimal impact on swimmer safety, especially at beaches such as HSB where compliance with water quality criteria is a persistent problem.

Acknowledgments We acknowledge the helpful comments of Daniel Keymer, Greg Shellenbarger, and 3 anonymous reviewers. Linwood Pendleton provided the attendance data. Funding from NOAA Oceans and Human Health Grant NA04OAR4600195 and the UPS Foundation are gratefully acknowledged.

Supporting Information Available Information on data used in the PLS models, the performance of OLSR in comparison to DPLSR, and how the variable i influences the results; Tables S1, S2, S3, S4, and S5; and Figures S1, S2, S3, and S4. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review August 2, 2005. Revised manuscript received January 11, 2006. Accepted January 18, 2006. ES0515250

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