Geostatistical prediction of microbial water quality throughout a stream

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Environmental Modeling

Geostatistical prediction of microbial water quality throughout a stream network using meteorology, land cover, and spatiotemporal autocorrelation David Andrew Holcomb, Kyle P Messier, Marc L Serre, Jakob G Rowny, and Jill R Stewart Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b01178 • Publication Date (Web): 11 Jun 2018 Downloaded from http://pubs.acs.org on June 11, 2018

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Environmental Science & Technology

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Geostatistical prediction of microbial water quality

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throughout a stream network using meteorology,

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land cover, and spatiotemporal autocorrelation

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David A. Holcomb,† Kyle P. Messier,‡ Marc L. Serre,† Jakob Rowny,† Jill R. Stewart*,†

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†Department of Environmental Sciences and Engineering, Gillings School of Global Public

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Health, University of North Carolina, Chapel Hill, North Carolina 27599-7431, United States

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‡Department of Civil, Architectural, and Environmental Engineering, University of Texas,

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Austin, Texas 78712, United States

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ACS Paragon Plus Environment

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TOC Graphic

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ABSTRACT. Predictive modeling is promising as an inexpensive tool to assess water quality.

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We developed geostatistical predictive models of microbial water quality that empirically

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modelled spatiotemporal autocorrelation in measured fecal coliform (FC) bacteria concentrations

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to improve prediction. We compared five geostatistical models featuring different

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autocorrelation structures, fit to 676 observations from 19 locations in North Carolina’s Jordan

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Lake watershed using meteorological and land cover predictor variables. Though stream distance

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metrics (with and without flow-weighting) failed to improve prediction over the Euclidean

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distance metric, incorporating temporal autocorrelation substantially improved prediction over

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the space-only models. We predicted FC throughout the stream network daily for one year,

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designating locations “impaired”, “unimpaired”, or “unassessed” if the probability of exceeding

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the state standard was >90%, 10% but 0.1 but < 0.9 were considered unassessed. Additionally,

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any points with > 0.5 probability of exceeding the standard were considered more likely than not

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to be impaired.

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Results and Discussion

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Geostatistical model comparison. We fit an OLS model, assuming uncorrelated error, and four

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geostatistical models, distinguished by four different covariance models for the error function, to

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FC concentration data. Table 1 compares the performance of the five models, which were

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assessed foremost by minimizing AIC, followed by RMSE and corrected prediction R2. The

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OLS model and the three spatial models performed similarly, with the OLS model faring slightly

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worse by all three metrics and the Euclidean space-only model performing slightly better by

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AIC. The three spatial models all estimated the same proportion of spatial autocorrelation (3% of

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the total variance) regardless of covariance model structure. Incorporating temporal

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autocorrelation greatly improved performance, substantially reducing AIC and RMSE and

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allowing the space/time model to explain over 70% of the variance in FC concentration. The

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mean function explained the greatest variance portion (59%) in all four geostatistical models; the

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OLS model also explained 59% of the total variance. The correlated error component of the

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space/time model accounted for 34% of the total variance, far exceeding the 3% correlated error

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in the spatial models. RSME and R2 values for space/time model predictions at individual

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sampling sites ranged from 0.61 – 1.48 ln(cfu)/100 mL and 0.42 – 0.88, respectively (Table S4).


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Table 1. Comparison of model performance and proportion of variance explained by geostatistical

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model components.

Performance metrics

Model

Proportion of variance explained Error function

Covariance structure AIC

RMSE*

𝐑𝟐 *

Mean function

[ln(cfu)]

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Correlated error proportion

Unexplained variance (nugget) proportion

OLS

Nugget

2214

1.21

0.59

0.59

-

0.41

Space-only

Euclidean + nugget

2187

1.19

0.61

0.59

0.03

0.38

Stream distance

Stream distance + Euclidean + nugget

2191

1.19

0.61

0.59

0.03

0.38

Flowweighted

Flowweighted stream distance + Euclidean + nugget

2191

1.19

0.61

0.59

0.03

0.38

Space/time

Euclidean + nugget

2090

1.02

0.71

0.59

0.34

0.07

*Calculated from LOOCV prediction residuals

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Effects of stream distance and spatiotemporal autocorrelation: error function models.

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Compared with the OLS model assuming uncorrelated error, we observed a strong improvement

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in model performance by considering temporal autocorrelation but little improvement when

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modeling the error function using only spatial autocorrelation (Table 2). Incorporating a stream

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distance metric had no effect on model performance, as Euclidean distance-based autocorrelation


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dominated the spatially-correlated error. The longest spatial range was associated with the flow-

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weighted stream distance component, but the small partial sill suggests limited impact of stream

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processes in driving FC concentrations—further reflected in the negligible partial sill and

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reduced spatial range of the stream distance model without flow-weighting.

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Scale may be an important factor in the relative importance of land and stream-based

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processes driving microbial contamination; over-land processes appear to dominate in-stream

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processes in our small watershed, with sampling locations at most 20 km apart. A recent study

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conducted on a similarly small watershed likewise realized only minor performance gains by

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modeling correlated error using a flow-weighted stream distance metric, despite observing

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substantial spatial autocorrelation.59 By contrast, other studies conducted on whole river basins

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found the stream distance metric (with various flow-weighting schemes) improved FIB

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estimation, suggesting that in-stream effects may grow dominant at larger scales.30,39

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Considering larger spatial scales generally increases the number of flow-connected sampling

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locations analyzed, which may lead to performance gains from flow-weighted and stream

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distance metrics.60 Several studies predicting other physiochemical characteristics in streams

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obtained mixed results regarding the relative performance of Euclidean versus (flow-weighted)

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stream distance metrics.35,57,61–63 The appropriate distance metric for modeling a particular water

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quality characteristic is dependent on several interacting factors, including the underlying

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processes driving the characteristic, the spatial scale of the analysis, and the distribution of

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sampling locations on the network.64


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Table 2. Error function parameter estimates. Unexplained variance (nugget)

Stream distance covariance

Euclidean covariance

Model Partial sill [ln(cfu)2]

Partial sill [ln(cfu)2]

Spatial range [km]

Temporal range [days]

Partial sill [ln(cfu)2]

Spatial range [km]

OLS

1.48

-

-

-

-

-

Space-only

1.36

0.112

8.8

-

-

-

Stream distance

1.36

0.112

8.9

-

3.4 × 10−4

10.4

Flowweighted

1.36

0.098

9.3

-

0.012

22.7

Space/time

0.24

1.23

12.8

2.1

-

-

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Including time substantially decreased the amount of uncorrelated error, though temporal

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autocorrelation fully decayed in two days. In contrast to the spatial models, the space/time model

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only estimates spatial autocorrelation for observations made within this short temporal range,

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revealing much stronger spatial patterns. The short temporal range, increased spatial range, and

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large partial sill suggest that localized microbial water quality is dependent on broader

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environmental conditions that are subject to substantial temporal variability. This is in keeping

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with previous research at freshwater beaches, in which the day of sampling explained the largest

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portion of FIB concentration variance between multiple beaches.19 As such, the space/time

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model may be useful for predicting water quality at unmonitored locations when microbial

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concentrations are known elsewhere, but is limited for prediction at unmonitored times.

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Effects of land cover and meteorology: mean function models. We used the standardized

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predictor variables to specify a full mean function for the flow-weighted model (Table S3). The


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model with the lowest AIC following backwards elimination retained the following predictors:

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percent forested upstream watershed area, percent agricultural upstream watershed area, hourly

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average surface temperature, precipitation in the preceding two days, precipitation in the

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preceding seven days (excluding the previous two days), and the interaction between the two

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precipitation terms. The other four models were fit to the same set of predictors. The parameter

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estimates differed slightly between the five models due to the influence of covariance structure

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(Table S2), but the mean function for all five models accounted for the same proportion of the

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total variance in the data (Table 1).

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The direction of effect estimates (Figure 2) largely coincided with our expectations.

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Increasing forest cover was protective against microbial pollution,11,14,65,66 while antecedent

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rainfall and warmer temperatures were associated with increased microbial

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concentrations.11,13,16,23,25,67 Precipitation in the preceding two days was associated with the

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largest increase in FC concentration. Agricultural land use also exhibited a strong positive

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relationship with FC, though it was the least precise parameter estimate and previous studies

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report conflicting effects of agriculture on FIB.11,66,68 This uncertainty could relate to the

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geographic distribution of agricultural land on the periphery of the study area: although many

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sites had agricultural lands upstream, the watersheds generally transitioned to other land uses

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nearer the sites.

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Despite previous studies suggesting urbanization increases microbial pollution, we did

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not observe a significant association between increasing impervious surfaces and FC

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concentration.11,14,66,69 Though urbanized land was common, most watersheds had low

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impervious surface percentages, reflecting low-intensity development with potentially diffuse

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impacts on FC loading. We also failed to detect a significant effect of solar radiation, which is


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known to inactivate microbes in the environment.65,67,70–72 This may be due in part to the spatial

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coarseness of the solar radiation measurement, for which a single value measured at the NOAA

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Durham station was used for all samples collected at a given time. Site-specific topography and

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canopy cover could have substantially altered the amount of solar radiation reaching the water.

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To address these limitations, future applications may consider model-based estimation of solar

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radiation, which has been used effectively in mechanistic FIB models.28,73–75

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The models presented here provide nuanced estimates of the overall effects of

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precipitation by considering the interaction between the two precipitation timeframes. More

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recent precipitation has a stronger effect on microbial concentration than precipitation further

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removed in time, but the negative interaction estimate suggests that past precipitation mitigates

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the impact of more recent precipitation (SI). In systems where FC sources accumulate on land

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before precipitation flushes contamination into water bodies, it follows that past precipitation

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reduces the stock of contamination available for subsequent rain to wash into the stream.

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Precipitation intensity may also act as an important driver of contamination in some systems,

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although it did not appreciably affect the predictive performance of the models presented in this

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paper (data not shown).

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Although likely similar to many other mixed-use watersheds, the associations between

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FC and the predictors considered in this study should be generalized with caution. The study area

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comprised a small watershed with limited LULC composition, the effects of which were derived

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essentially from 19 observations for each LULC class (corresponding to the 19 sampling sites).

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As with the covariance components, scale likely also affects the magnitude of predictor effects.

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The pronounced sensitivity to precipitation might be tempered in larger systems featuring

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spatially heterogenous meteorological conditions and a wider range of LULC characteristics.


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Furthermore, we might expect associations with meteorology to differ in systems dominated by

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sources with distinctive loading dynamics, such as agricultural watersheds receiving intermittent

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manure applications.

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Figure 2. Mean function GLS parameter estimates (points) and 95% confidence intervals (bars)

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for the space/time model. Estimates are for standardized (mean-centered, standard deviation-

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scaled) input variables, and represent the expected change in ln(FC) concentration for a 1 standard

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deviation increase in the input variable with all other variables held constant. Note that the three

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rain terms are related through the interaction and cannot be interpreted in isolation (SI). The

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intercept corresponds to the expected ln(FC) concentration when all other predictors equal their

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respective means.

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Space/time prediction of microbial water quality. The space/time geostatistical model was

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chosen to predict FC concentrations at unmonitored locations and times. We predicted universal

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kriging means and standard errors at each prediction location at 11 a.m. for each of the 365 days

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between April 1, 2010 and March 31, 2011 and calculated the probability each prediction

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exceeded the NC standard of 200 cfu/100 mL, from which a corresponding impairment status

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was assigned. Figure 3 illustrates the spatial and temporal trends in prediction mean, standard


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error, and impairment status. Prediction error was lower on days FC were measured (Figure 3B),

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but the short temporal range largely prevented observational data from affecting predictions on

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consecutive days (Figure 3E). Predictions outside the temporal range were made entirely on the

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basis of the mean function, which can be observed in the flattening of localized prediction means

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between days with and without sample data (Figures 3A and 3D).

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Mean FC concentrations exceeding the standard were predicted on every day of the

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study; on 36 days (10% of study period), more than 90% of stream miles had predicted FC

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means above the standard. Assigning impairment status only to predictions with a high

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probability (< 90%) of being above or below the state standard, some portion of the watershed

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was considered impaired on 209 days (57%), while unimpaired stream miles were predicted on

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190 days (52%). We observed no strong spatial patterns of impairment; rather, impairment

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tended to be event driven, wherein large portions of the watershed briefly became impaired

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before a relatively rapid return to a generally unassessed state (Figure 3G). While unimpairment

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likewise displayed no strong spatial pattern, the temporal trends for unimpaired stream miles

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appeared more seasonally driven, with notable background levels of unimpaired stream miles

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during the winter months. Conversely, relatively few stream miles were considered unimpaired

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during months in which impairment events are more common, even when no impairment event

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was ongoing; in such cases, the majority of the watershed was considered unassessed.


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Figure 3. Predicted spatial and temporal trends in microbial water quality. The top two rows

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(panels A-F) map the prediction means (panels A and D), standard errors (panels B and E), and

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impairment status (panels C and F) for the whole study area on two consecutive days. The bottom

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row (panel G) is the percentage of stream miles assigned each impairment status by day for the

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entire one-year study period, using the same scale as the impairment status maps; the dashed line

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represents the percentage of stream miles more likely impaired than not. Water samples were

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collected for the first day, which is reflected in the lower standard errors (panel B) compared with


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the following day (panel E), for which no sample data are available. Areas assigned an impaired

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status on the first day (panel C) largely correspond to the areas of reduced standard error arising

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from the observational data (panel B).

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Role of predictive models and observational data in assessing watershed impairment. Our

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space/time model predicted that the Jordan Lake near-upstream watershed frequently suffered

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from unsafe levels of microbial contamination. However, despite 33% of all prediction means

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exceeding the state standard, only 5% of all predictions could be confidently considered

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impaired, and only 6% were confidently assessed as unimpaired. The other 89% of predictions

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were unassessed, meaning we could not determine whether FC concentrations fell above or

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below the NC standard after accounting for prediction uncertainty. Access to water sample data

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on the day of prediction was strongly associated with an increased ability to assign impairment

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status. Under a simple linear regression, any FC observations on a given day was associated with

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a 20% reduction (p < 0.001) in unassessed stream miles.

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Because impairment appears largely event-driven, increases in related meteorological

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variables, particularly precipitation, produced elevated mean FC predictions. However, the high

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temporal variability and low temporal autocorrelation range of FC concentrations limited the

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ability of models alone to predict impairment status with high-confidence. Access to recent

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monitoring data, however, reduced prediction uncertainty sufficiently to confidently assign

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impairment status to larger portions of the stream network. While a recent study in a similar

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watershed observed clear spatial patterns in FIB, they did not translate into the substantial

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reductions in prediction error necessary to confidently assess impairment status. 59 That their

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samples were collected monthly, without intentional storm sampling or considering temporal

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autocorrelation, suggests spatial relationships may impact background FIB concentrations, only


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to be drowned out by events driving brief, widespread impairment. This dynamic suggests

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frequent, sample-based monitoring remains necessary to confidently assess the safety and legal

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status of a water body. Implementing spatiotemporal predictive models may reduce the number

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of concurrent sampling locations required to adequately assess water quality throughout a stream

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network, providing the means to increase sampling frequency without increasing monitoring

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expenses.

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In developing geostatistical models that consider the spatiotemporal patterns and

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environmental drivers of microbial water quality impairment, we identified clearly dominant

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factors in each structural model component that together largely explain observed FC

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concentrations and enable their prediction. Precipitation dominated in the model component that

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predicts FC directly, while temporal patterns dominated spatial patterns in the component that

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contributes indirectly to prediction by considering autocorrelation in the outcome. Rather than

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orienting monitoring activities around specific locations of heightened concern, the dominance of

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precipitation and temporal effects suggests a monitoring strategy that targets sampling according

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to temporal criteria, employing frequent sampling to better capture diverse meteorological

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conditions driving impairment events. Because we constructed the model using remotely sensed

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and continuously reported predictors and we jointly estimated the different model component

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parameters using likelihood-based methods, others may apply the model to geographically sparse

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monitoring data to assess microbial water quality impairment throughout stream networks

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without the need for additional specialized measurements or knowledge. Environmental

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managers, regulators, and researchers can implement our model to inform management

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decisions, target remediation efforts, and issue timely warnings for the protection of public

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health.


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AUTHOR INFORMATION

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Corresponding Author

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*Email: [email protected]; phone: (919) 966-7553

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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This work was supported in part by the Water Resources Research Institute of the University of

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North Carolina, project number 70252. We are grateful to Prahlad Jat for assisting with the

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stream network analysis and display.

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Supporting Information Available. Profiling for maximum likelihood estimation; universal

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kriging prediction error approximation; additive function values for flow-weighting; exploratory

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analysis of input variables; visual interpretation of error function; mean function parameter

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estimates; derivation of precipitation interaction effects; prediction at individual sampling sites;

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animated maps of daily watershed predictions. This information is available free of charge via

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the Internet at http://pubs.acs.org.

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