Published online 23 June 2008
Published in J Environ Qual 37:1559-1566 (2008)
DOI: 10.2134/jeq2007.0310
© 2008 American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
TECHNICAL REPORTS
Surface Water Quality
Temporal Variation and Persistence of Bacteria in Streams
Shesh R. Koiralaa,c,d,
Randall W. Gentrya,c,d,*,
Edmund Perfectb,
John S. Schwartza and
Gary S. Saylerc
a Civil and Environmental Engineering, the Univ. of Tennessee, Knoxville, TN 37996
b Dep. of Earth and Planetary Sciences, the Univ. of Tennessee, Knoxville, TN 37996
c Center for Environmental Biotechnology, the Univ. of Tennessee, Knoxville, TN 37996
d Inst. for a Secure and Sustainable Environment, the Univ. of Tennessee, Knoxville, TN 37996
* Corresponding author (rgentry{at}utk.edu).
Received for publication June 14, 2007.
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ABSTRACT
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Better understanding of bacterial fate and transport in watersheds is necessary for improved regulatory management of impaired streams. Novel statistical time series analyses of coliform data can be a useful tool for evaluating the dynamics of temporal variation and persistence of bacteria within a watershed. For this study, daily total coliform data for the Little River in East Tennessee from 1 Oct. 2000 to 31 Dec. 2005 were evaluated using novel time series techniques. The objective of this study was to analyze the total coliform concentration data to: (i) evaluate the temporal variation of the total coliform, and (ii) determine whether the total coliform concentration data demonstrated any long-term or short-term persistence. For robust analysis and comparison, both time domain and frequency domain approaches were used for the analysis. In the time domain, an autoregressive moving average approach was used; whereas in the frequency domain, spectral analysis was applied. As expected, the analyses showed that total coliform concentrations were higher in summer months and lower in winter months. However, the more interesting results showed that the total coliform concentration exhibited short-term as well as long-term persistence ranging from about 4 wk to approximately 1 yr, respectively. Comparison of the total coliform data to hydrologic data indicated both runoff and baseflow are responsible for the persistence.
Abbreviations: ACF, autocorrelation function • ANOVA, analysis of variance • ARMA, autoregressive moving average • CFU, colony forming units • NOAA, National Oceanic and Atmospheric Administration • NWIS, National Water Information System • PACF, partial autocorrelation function • USEPA, U.S. Environmental Protection Agency • USGS, U.S. Geological Survey
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INTRODUCTION
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RESEARCH is needed to better understand the temporal and spatial variance of bacteria in watershed systems, sometimes differing by orders of magnitude, with respect to the environmental and especially hydrologic factors that influence this variance. Various factors may influence bacterial survival in hydro-environmental systems such as sunlight, temperature, soil moisture conditions, salinity, soil condition, settling, association with particles, etc. (Burton et al., 1987; Jamieson et al., 2003). Bacteria may reach a stream through drainage, storm runoff, or ground water. Their die-off and resuspension in stream water impact the concentrations observed (Jamieson et al., 2005). Recent research has focused on the spatial characterization of fecal bacteria indicators with hydrologic data (Gentry et al., 2006, 2007), but techniques that can better characterize the temporal delivery mechanisms, and elucidate conceptual models are necessary for further understanding of observation scaling and monitoring.
The primary hypothesis tested in this study was that total coliform data exhibit persistence in long-term monitoring records that can be quantified and correlated with hydrologic conceptual models. The hypothesis was tested through systematic analysis of 5 yr of daily total coliform data from a station on the Little River, in eastern Tennessee. Total coliform data was selected due to the fact that it is commonly collected by water treatment plant operators at a higher frequency than other bacterial species. Our objectives were to: (i) evaluate temporal variation in total coliform concentration, and (ii) determine whether the total coliform concentrations exhibited any long- or short-term persistence.
Although the assessment of fecal contamination within natural water systems is typically conducted with Escherichia coli (E. coli) or enterococci, the total coliform data may be more useful for observing the persistence of bacteria in natural systems rather than source tracking. Traditional indicator organisms are generally total coliform, fecal coliform, and fecal streptococci. Total coliform and E. coli have been used as indicators of potential fecal contamination for almost 100 yr (Feng et al., 2002). The primary assumption is that if bacteria commonly associated with mammalian intestinal tracts are present in a water system then this water may contain pathogenic bacteria or viruses. From an epidemiological point of view, the presence of total coliforms and E. coli in recreational waters is correlated with a higher incidence of gastrointestinal disease, so the requirement of low levels of these constituents reduces disease risk (Dufour, 1984).
Some researchers have sought to develop better modeling methodologies for forecasting E. coli concentrations or loads (Olyphant et al., 2003; Reeves et al., 2004). A review of the traditional methodologies for modeling microbial pollution at the watershed scale has been presented by Jamieson et al. (2004). Recent research has sought to more robustly relate the influence of watershed-scale processes, such as flow, sediment transport, and precipitation, to fecal indicators in streams (Mallin et al., 2001; Byappanahalli et al., 2003; Tyrrel and Quinton, 2003; George et al., 2004; Reeves et al., 2004; Gentry et al., 2006, 2007).
It is believed that watershed hydrologic processes are responsible for the temporal variation of pollutant concentrations and the flux in streams and rivers (Kirchner et al., 2000; Shang and Kamae, 2005). A watershed retains pollutants and releases them after some time indicating that there is a likely persistence of pollutants in the watershed. Persistence implies that an effect exists between an observation, the concentration of a pollutant in the stream, and future observations. As an example, the previous conditions of a pollutant in the watershed influence the present pollutant concentration. Persistence can either be weak or strong, short- or long-term (Beran, 1994; Malamud and Turcotte, 1999). Short-term persistence implies that the effect of an observation becomes negligible after a short period of time. Long-term persistence implies that the effect of an observation on future observations remains significant after a long period of time. Thus, short-term and long-term persistence specifies whether there is an effect for only short lags, or also for much longer lags. The terms weak and strong refer to how strongly the concentration values that are separated by a given number of points (the lag) are correlated with one another. The short-term and long-term persistence are evaluated based on the periodicities. Kirchner et al. (2000) quantified the persistence of chloride in the Hafren catchment at Plynlimon, Wales by observing the long-term time series of chloride data. Recently, Shang and Kamae (2005) quantified the persistence in the data representing suspended sediments of the Yellow River at Tongguan, Shanxi, China. In another study, nitrate demonstrated persistence in a stream system (Zhang and Schilling, 2005). However, the role of bacterial data persistence in natural stream systems is limited in the literature.
Sample Data and Study Area
The total coliform data used for this study was collected daily by the City of Maryville, from the Little River above the intake to the city's water treatment plant. The sampling site was located about 250 m downstream of the United States Geological Survey Gage 03498500 at Little River Upstream of Maryville, TN (Fig. 1
). The watershed land use ranges from forestland in the Great Smokey Mountain National Park at the headwaters to mixed-use (developing urban and agricultural) toward the tailwater section of the basin. The site location was beneficial since previous bacterial studies, within a smaller scale subbasin to the Little River, have been performed in the recent past (Gentry et al., 2006, 2007). The total coliform analysis was performed by the City of Maryville's water quality laboratory using the membrane filtration technique (USEPA, 2002). The sample data include the total coliform in colony forming units per 100 mL (cfu/100 mL) from 1 Oct. 2000 through 31 Dec. 2005.
Discharge data from the near vicinity of the total coliform sample collection was collected by and is available dating back to July 1951 from United States Geological Survey (Gage 03498500) and was downloaded via the National Water Information System web (NWIS) interface (USGS, 2006). From the gage station, the basin drainage area is 697 km2. Similarly, rainfall data near the total coliform sampling site is also available from the National Climatic Data Center of the National Oceanic and Atmospheric Administration (NOAA) dating back to May 1890 from McGhee Tyson station, Knoxville TN (NOAA, 2006). In our analysis both discharge and rainfall data were used from October 2000 through December 2005 for concurrent analysis of the total coliform data.
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Methodology
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The overall analysis requires an inspection of the temporal trends and correlation with subsequent analyses in the time domain and the frequency domain. Temporal variation was determined using the analysis of variance (ANOVA) method, whereas persistence was determined by developing an autoregressive moving average (ARMA) model and spectral analysis. Before implementing any time series analysis, the data must be evaluated for any dominating trend signals; for example, strong positive or negative linear trends that may dominate any other signals present in the data and must be removed. Scatter, autocorrelation function (ACF), and partial autocorrelation function (PACF) were employed to determine the linear trend, if any, and the seasonality of the data. If present, the linear trend was removed by a simple linear regression technique. Seasonality can easily be identified in the time series data as predictable cyclic fluctuations within the annual period domain; thus, it was not necessary to remove the seasonal signal before further analysis since it had no effect on the overall analysis. The time and frequency domain analyses were performed using the detrended data to quantify the persistence of total coliform in the watershed and will be explained in further detail in the following sections.
Time Domain Analysis
Time domain analysis begins with calculating the autocorrelation function (ACF).
The autocorrelation function, rk, is given by (Tamhane and Dunlop, 2000),
 | [1] |
where rk is the autocorrelation coefficient at lag k, xi is the series at i = 1, 2, 3, ..., N observations, 
is the mean of N observations. The positive values of rk indicate memory in the series. The kth order partial autocorrelation of X is the partial correlation between xt and xt+k, where the influence of xt+1, xt+2,....., xt+k-1 have been removed. The PACF is calculated from the following formulae (DeLurgio, 1998):
 | [2] |
 | [3] |
where 
's are the autoregressive parameters defined by the kth order partial autocorrelation and jth order recursive process. Equations [2] and [3] were used in the identification of the autoregressive order in the ARMA model. The ARMA model is given by (DeLurgio, 1998),
 | [4] |
where 
's are the moving average parameters, the x's are the original series, and the a's are the series of residuals, p and q are the order of autoregressive and moving average, respectively.
ARMA models have been used in previous studies to characterize the correlations within a time series (Malamud and Turcotte, 1999). An ARMA model captures the deterministic components (dominant linear trends) of a time series and leaves behind the stochastic component (residuals). The stochastic component of a time series is defined as persistence if temporally adjacent values are positively correlated (Beran, 1994). The persistence may be short-term or long-term depending on the time range over which they are correlated. Hence, the residuals from the ARMA model were used to determine the underlying short-term persistence using the autocorrelation of the data set.
Frequency Domain Analysis
Many natural phenomena have variability that is frequency dependant and that dependence may yield information about the underlying physical mechanisms (Percival and Walden, 1993). Spectral analysis may reveal certain features of a time series that are not obvious from other analytical perspectives (Percival and Walden, 1993). Spectral analysis uses a finite Fourier transformation to decompose the data series into a sum of sine and cosine waves of different amplitudes and wavelengths with estimation of the Fourier coefficients. Subsequently, the smoothed periodograms (plots of Fourier coefficients versus periods) are used to estimate the spectral densities. These spectral densities measure the variance of data in the frequency domain.
The Fourier transform decomposition of the series xt is given by (SAS Institute, 2003),
 | [5] |
where t is the time subscript, t = 1, 2, 3,..., N. xt are the data, N is the number of observations in the time series, m is the number of frequencies in the Fourier decomposition: m = N/2 if N is even; m = (N – 1)/2 if N is odd, a0 is the mean term: a0=2, ak are the cosine coefficients, bk are the sine coefficients, and wk are the Fourier frequencies: wk=
. The plots of the Fourier coefficients ak and bkagainst frequency or periods are periodograms. The amplitude periodogram Jk is defined by (SAS Institute, 2003),
 | [6] |
It should be noted that the periodogram is an inconsistent estimator of the spectrum (SAS Institute, 2003). The sampling error associated with estimates of sum of squares is very large, which may result in an overly wide confidence interval set up around the intensity estimates at each frequency (Warner, 1998). This problem can be solved if spectral densities are used rather than periodograms. Spectral densities (Fkx) are smoothed approximations of the discrete periodograms given by (SAS Institute, 2003),
 | [7] |
where Wj is the Kernel or weight function which is the vector of 2p+1 smoothing weights, normalized to sum to 
, which runs from W–p to Wp. In this study, a Tukey-Hanning window was used to smooth the periodogram.
Spectral density estimates need to be characterized by statistical significance so that the meaningful peak may be identified. Thus, significance testing was performed using the procedure outlined by Koopmans (1974) and Warner (1998). The upper and lower bounds of a confidence interval around each spectral estimate were computed using the chi-square distribution. The mean of the spectral density was calculated and checked against the lower bound of the 95% confidence interval. If the value of the lower bound exceeded the mean spectral density, the peak associated with this value was considered significant.
Another important aspect of the analysis required a determination of the degree of correlation between random time series at given periods, which is termed a coherency analysis. This coherency analysis (Shumway and Stoffer, 2006) approach was used to investigate the relationship between hydrologic variables (discharge and rainfall) and total coliform. Squared coherencies were computed as a function of period and used to determine if values were significantly different from zero. High values of squared coherency indicate that data are more correlated at corresponding periods or frequencies.
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Results and Discussion
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The total coliform concentrations ranged from 30 to 5120 cfu/100 ml on 4 Jan. 2001 and 22 Feb. 2001, respectively. As is typical for many natural systems, the monthly average concentration of total coliform in the Little River watershed generally increased from January to July and decreased after July (Fig. 2a
). On average, January had the lowest concentration, whereas July had the highest concentration. As was expected, a seasonal comparison showed that winter had the lowest average total coliform, whereas summer had the highest of all seasons (Fig. 2b), which is likely related to the temperature and lower flow. Similar analysis of the hydrologic variables indicated that March had the highest and October the lowest discharge. Also from the analysis, September had the highest and August had the lowest precipitation (Fig. 3
). A time series plot of the total coliform, shown in Fig. 4
, indicates a significant downward trend (p value < 0.0001) from week 40 forward. This may be due to the implementation of best management practices in the watershed over the past several years (TVA, unpublished data, 2003). As expected, the repeating oscillating pattern of the ACF and the PACF plot of the weekly average total coliform data indicate seasonality in the series (Fig. 5
). To minimize the outlier effect for further analysis, the weekly average total coliform data were used to quantitatively determine the seasonality.
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Fig. 2. Average total coliforms with box plots for (a) monthly: January = 1, February = 2, etc. and (b) seasonal.
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Fig. 3. (a) Monthly average discharge based on daily average with box plots: January = 1, February = 2, etc. (b) Monthly average rainfall based on daily total with box plots: January = 1, February = 2, etc.
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Fig. 5. (a) Autocorrelation function of total coliform; and (b) partial autocorrelation function of total coliform.
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The best ARMA model evaluation for total coliform concentration [ARMA (1, 1)] was able to explain about 24% of the variability in the estimate. The ACF plot of the residuals indicates that the periodicities are significant at lags of 4 and 14 wk (Fig. 6
). The spectral analysis of total coliform showed periodicities and persistence (short-term as well as long-term). Multiple significant peaks were identified ranging from 15 to 137 peaks and are shown in Fig. 7
and summarized in Table 1
. The highest spectral density peaks were identified at periodic cycles of 15 and 55 wk. Further analyses indicated that the peaks were not white noise, but were highly significant (p value < 0.0003) for a Fisher's 
of 12.61.
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Fig. 6. Autocorrelation of residuals from autoregressive moving average model of total coliform with 95% confidence bound. Lag, associated with large-sized symbols, indicates significance at the 95% confidence limit.
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Fig. 7. Spectral density with average and lower 95% confidence limit for total coliform. Periodic cycle associated with large sized symbols, indicates significance at the 95% confidence limit.
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So that the total coliform data could be compared to hydrologic data, spectral densities were also calculated for precipitation and stream discharge. The resulting analysis identified no significant peaks for precipitation (indicating white noise) and the highest spectral density peak for discharge was at 55 wk (see Table 1). The spectral densities, means, and lower confidence intervals are shown in Fig. 8
. The results are similar to that of Kirchner et al. (2000), who found white noise for precipitation and the presence of persistence for discharge. The spectral peak for discharge at the 55 wk periodic cycle is similar to the 55 wk periodic cycle peak for total coliform. This suggests that there is an association between total coliform concentration and the period of high annual discharge, sometimes referred to as the annual flood. It has been reported that coliforms can survive in soil and bed sediments for an extended period of time, sometimes several months (Sherer et al., 1992; USEPA, 2001). It is possible that during the annual high flow event, the coliforms are resuspended and this results in an increased concentration. These results may also indicate common phenomena for discharge and total coliform at the 55 wk frequency.
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Fig. 8. Spectral density with average and lower 95% confidence limit for (a) discharge, and (b) rainfall. Periodic cycle associated with large-sized symbols, indicates significance at the 95% confidence limit.
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To further discern the behavior of hydrologic variables and total coliform, coherency analysis was used for evaluating the data, and the results are shown in Fig. 9
. Values of the squared coherency for total coliform and discharge were significant at periods of 3, 7, 10, and 46 wk (see Table 2
). Between total coliform and precipitation, the squared coherency was significant at about 5 wk. Squared coherency between precipitation and discharge was generally significant at short-range frequencies (< 22 wk) and long-range frequencies (> 90 wk). These observations suggest that discharge is responsible for long-term persistence and precipitation is responsible for short-term persistence. The likely conceptual model for the Little River watershed is that short-term persistence of total coliform is due to storm-induced overland flow, whereas long-term persistence is due to possible subsurface inputs during baseflow. These findings may corroborate the findings of Gentry et al. (2007) who had only discrete time data over a year time frame, whereas this time series extends over multiple years. The effects of precipitation and overland flow on total coliform concentrations for short-term persistence are very important at scales smaller than 1 d, which have not been analyzed in this study due to the sampling frequency of total coliform, and is a limitation of the study. It appears likely that the total coliform may be retained or persist in the ground water reservoir and then discharge to streams resulting in long-term persistence, similar in nature to the mechanisms presented by Dussart-Baptista et al. (2003). Hence, it should be noted that while some coliform concentration reductions may be possible in the short term, past inputs of total coliform will likely continue to influence the concentration of total coliform in the stream for the long term. Further research in different hydrologic and catchment settings and using different water quality parameters is required to further elucidate hydrologic influences on stream bacteria, such as total coliform. Also, since total coliform includes several genera of bacteria, the different peaks in the spectral analysis may be related to different genera. It can be speculated that, depending on various environmental and transport factors, the bacteria are showing persistence at different time scales. However, these hypotheses would require further experimental testing for validation.
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Fig. 9. Coherency analysis for total coliform and hydrologic variables: (a) total coliform versus discharge, (b) total coliform versus rainfall, and (c) discharge versus rainfall. Solid horizontal lines delimit statistical significance at the 0.05 probability level.
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Conclusions
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Time and frequency domain analyses of total coliform concentration time series data have been performed to investigate the temporal variation and persistence of total coliform in a stream. It was found that total coliform concentrations were higher in summer months and lower in winter months, as expected. Time domain analyses were performed using an autoregressive moving average model, whereas the frequency domain analyses were performed using spectral analysis. The time domain analyses indicate short-term persistence in the time series (4 to 15 wk) whereas frequency domain analysis showed short-term (15 wk) as well as long-term (55 wk) persistence. It appears that precipitation is the likely cause for short-term persistence, where long-term persistence is controlled by discharge (baseflow). Although the analysis indicates both short-term as well as long-term persistence, the study results could not distinguish which is more significant based on the present data set. By understanding which hydrological processes, as identified in this study, influence total coliform concentrations, improved watershed management strategies may be developed.
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ACKNOWLEDGMENTS
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We would like to thank Dr. Patrick Mulholland for his important suggestions during the preparation of this manuscript. We also like to thank Doyle Prince, City of Maryville, TN for providing the coliform data for analysis. Funding for this research was also provided by the Center for Environmental Biotechnology and the Inst. for a Secure and Sustainable Environment at the Univ. of Tennessee.
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NOTES
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All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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TOP
ABSTRACT
INTRODUCTION
