Environ. Sci. Technol. 2003, 37, 5511-5517
Model of Microbial Transport and Inactivation in the Surf Zone and Application to Field Measurements of Total Coliform in Northern Orange County, California ALEXANDRIA B. BOEHM* Department of Civil and Environmental Engineering, Environmental Engineering and Science Program, Stanford University, Stanford, California 94305-4020
The classic model of pollutant transport in the surf zone of a long, sandy beach developed by Inman et al. (J. Geophys. Res. 1971, 76, 3493) is altered to account for first-order pollutant inactivation in an effort to understand how rip cell dilution and bacterial inactivation control the length of shoreline adversely impacted by microbial pollution from a point source. A dimensionless number Γ dictates whether physical processes (dilution of microbes in the surf zone by rip cell mixing) or biological processes (microbial inactivation) control the distribution of pollution along the shoreline. Estimates of Γ for beaches in Northern Orange County, California, indicate that dilution is the primary factor controlling total coliform levels surrounding two drains that release nuisance runoff directly onto the beach. It is also shown that, even when alongshore currents are fast, pollutant levels will drop e-fold at distances under 4000 m from the point source due to dilution alone. Because dilution is ultimately controlled by wave climate and shoreline morphology, the results suggest the strategic position of drains and other point sources in high dilution wave environments will reduce potential adverse effects on beach water quality. In addition, the results stress the importance of understanding hydrodynamics when conducting microbial source tracking at wave-dominated marine beaches.
Model Development For the purposes of this study, the surf zone is defined as the region of the coastal zone from where waves begin to break to the shoreline (Figure 1). Detailed field work (1) has revealed that when conservative material is introduced to the surf zone, it undergoes rapid mixing across the width and depth of the surf zone by wave-driven turbulence, transport parallel to the shore by wave-driven longshore currents, and dilution by rip cell exchange of ocean water between the surf zone and offshore. The depth-averaged longshore transport velocity (ql) can be estimated from the angle the waves make with the shoreline (R), the slope of the beach (S), and the height of the breakers (hb) (in meters) using the LonguetHiggens equation (23, 24):
ql ) 20.7Sxghb sin R cos R
Introduction Fecal indicator bacteria (FIB), including total coliform (TC), fecal coliform (FC), and enterococci (ENT), have been adopted throughout the world as an index of water quality (2-4). This is motivated by the following observations. First, these organisms are present at high concentrations in several important sources of coastal pollution including untreated and partially treated sewage, urban runoff, and agricultural runoff (3). Second, there is a documented human health risk associated with recreating in and consuming shellfish from coastal waters contaminated with FIB from sewage fields (5-8) and urban runoff (9). Third, the detection of FIB in marine waters is straightforward and relatively inexpensive, making practical the implementation of comprehensive coastal water-quality monitoring programs. FIB pollution of marine waters is a growing problem in the United States. In 2000, there were over 13,000 recreational * Telephone: (650)724-9128; fax: (650)725-3164; e-mail: aboehm@ stanford.edu. 10.1021/es034321x CCC: $25.00 Published on Web 11/05/2003
beach closures due to FIB, over twice the number in 1999 (10). Given the economic costs associated with beach closures and postings (11) and the potential health threats elevated FIB levels impose (9, 12), an understanding of how physical and biological factors modulate FIB concentrations after their release into the environment is needed. In an effort to further this understanding, the present study was under-taken to examine how physical and biological processes influence microbial pollution in the surf zone of a wave-dominated marine beach. Researchers have previously investigated the transport of conservative suspended pollutants (1) and light petroleum spills (13) in the surf zone. Because it is well-established that FIB in temperate waters typically undergo inactivation at a rate that can be modeled as first order with respect to FIB concentrations (e.g., refs 14-22), it is not clear that the physical models of pollutant transport apply to the problem of FIB pollution. In the study described below, a model originally developed by Inman et al. (1) to predict conservative pollutant transport in the surf zone is altered to account for the nonconservative behavior of FIB. The goal of constructing this model is not to develop a deterministic method for predicting FIB levels along a shoreline. Rather, the model allows estimation of the characteristic length scale over which dilution alone reduces FIB levels and a dimensionless number that dictates whether inactivation, dilution, or both processes determine the length of shoreline adversely impacted by FIB from a point source. The model is subsequently applied to a TC at a field site in Northern Orange County, California.
2003 American Chemical Society
(1)
where g represents the gravitational acceleration constant and ql is in m s-1. The cross-shelf velocities qw and qr describe the depth-average velocities of water entering the surf zone over the top of breaking waves and exiting the surf zone in rip currents in the x direction. At the present, there are no theoretical expressions for these velocities. Inman and co-workers (1, 25) produced a body of work in the 1970s describing the transport of a conservative suspended pollutant in the surf zone. Using a “tanks-inseries” model, they showed that the concentration of pollutant a distance y alongshore from a steady point source at y ) 0 is
C ) Co(Rl)y/Y
(2)
where Co is concentration of the pollutant at the source; Y is the rip cell spacing; and Rl, which varies from 0 to 1, characterizes the dilution that occurs over a single rip cell due to the offshore exchange with ocean water (Rl ) 0 VOL. 37, NO. 24, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. (A) Top view of surf zone with variables used in model. (B) Side view showing triangular cross section with slope S ) tan β. See text for descriptions of variables. corresponds to complete dilution and Rl ) 1 corresponds to no dilution). This solution is for the case were water outside the surf zone contains no contaminant. Equation 2 predicts the exponential decay of pollutant along the shoreline. This is in general agreement with field observations of dye released from a continuous point source to the surf zone (1, 26), and nutrient concentrations in the surf zone originating from watershed outlets (J. Largier, personal communication, 2002). Thus despite the complex hydrodynamics in and near the surf zone, the simple box model employed by Inman et al. (1) appears to account well for the physics of surf zone transport. Previous work in Huntington Beach, CA (27-29), revealed that FIB appeared to decline exponentially in the direction of littoral drift from documented point sources. While the decay might be explained by physical dilution of surf zone water with clean ocean water, it might also be explained by the first-order decay of FIB moving at a constant velocity ql with no dilution. To understand if one of these two processes is dominant in attenuating FIB in the surf zone, the Inman et al. (1) model described above was altered to account for the nonconservative behavior of FIB. It is assumed that the most important nonconservative behavior is first-order decay of FIB due to inactivation, which has been studied extensively under various conditions (14-22). (The term inactivation in this study refers to the decline in microbes with time as measured by a standard culturing technique.) While other potential removal mechanisms such as adsorption to sediment (30), deposition on the shoreline, and sedimentation (31) may be important removal mechanisms for FIB in natural waters, they have not been included in the present study because there are few scientifically documented field observations and measurements illustrating their importance. Further study on FIB sorption to particles in marine waters is warranted in order to fully understand the importance of these processes in controlling microbial fate at urban beaches. A mass balance over an elemental length of fluid in the surf zone (Figure 1) yields the following differential equation:
(
)
2qr ∂C ∂C ) -ql +k C ∂t ∂y xb
(3)
where C(y, t) is the concentration of FIB, xb is the width of the surf zone measured from the shoreline to the edge of the breaker zone, k is the first-order inactivation constant, ql is as defined previously, and t and y are time and distance along the shore. In formulating eq 3, the following assumptions have been made: (i) the surf zone is well-mixed in the x and z directions; (ii) the cross-sectional area of the surf 5512
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zone is triangular in shape with a constant slope; (iii) both onshore flux of clean water and offshore flux of polluted water occur intermittently at the offshore boundary of the surf zone; (iv) there are no regional gradients in the flow field (i.e., qw ) qr); (v) there is no accumulation of the pollutant outside the surf zone (i.e., no pollutant enters via qw); (vi) qr and ql are constant with respect to y; and (vii) turbulent diffusion is not significant as compared to advection in the y direction. Most of these assumptions are discussed in detail by Inman et al. (1). Assumption iii is tantamount to assuming that ejection of water accumulated in the surf zone due to breaking waves is not isolated to rip currents but occurs along the entire surf zone. Assumption iii should not effect the results presented here so long as y is greater than rip cell spacing. In light of these simplifying assumptions, eq 3 should be regarded as a first-order approximation of a highly complex system that is not completely understood. Nevertheless, as mentioned earlier, such a conceptualization of surf zone transport has proven successful at capturing the fundamental behavior of conservative pollutants (1). For the steady-state case where the pollutant point source is continuous, the solution of eq 3 suggests that the concentration of a contaminant away from its source decays as an exponential with distance from the source:
ln(C/Co) ) -
y leff
(4a)
with
1 1/ldil + 1/ldie
(4b)
qlxb and ldie ) ql/k 2qr
(4c)
leff ) ldil )
ldil and ldie physically represent the longshore distances over which FIB levels decrease to 1/e their initially values due to cross shore-mediated exchange of surf zone and offshore ocean water and to FIB inactivation, respectively. On the basis of eq 4, the length of shoreline impacted by FIB pollution depends on coastal morphology, wave climate, and persistence of FIB in the environment. Theoretically, eq 4 can be used to predict the length of coastline that will be impacted by a point source, provided that approximations can be made for ldil and ldie. Unfortunately, ldil is difficult to estimate because of the uncertainty involved in predicting qr. The ratio of ql/qr can be conceptualized as a measure of dilution. When waves break perpendicular to the coast line, ql/qr ≈ 0, and there is complete dilution. Dilution decreases (ql/qr increases) as R decreases and waves attack the shoreline at a more oblique angle. Rather than use eq 4 as a predictive tool, the length scales ldie and leff, which are relatively easy to quantify, are used to calculate ldil, which describes the length scale over which rip currents reduce pollutant levels. In addition, the model is used to gain insight into whether biological processes (inactivation) or physical processes (dilution) control the attenuation of FIB upcoast or downcoast of a FIB source to the surf zone. Their relative importance is reflected in the magnitude of the dimensionless parameter:
Γ)
leff 1/ldie ) ldie 1/ldil + 1/ldie
(5)
which ranges from 0 to 1. When inactivation dominates, Γ ) 1, and leff ) ldie. When dilution alone controls pollutant levels away from a source, Γ ) 0. Under these limits, the FIB
A 200 m long man-made jetty that protects the entrance to Newport Harbor is located 2000 m south of drain S (green bar in Figure 2). At the onset of this work, it was not clear what, if any, impact the jetty might have on TC transport. On one hand, the jetty may be sufficiently far from the drain that its presence has little impact on the fate of TC. Alternatively, the jetty may promote cross-shelf exchange and dilution (32) of TC-laden water, significantly impacting the fate of TC.
Materials and Methods
FIGURE 2. Map of the field site showing water quality monitoring stations (b), piers (red rectangles), and the Newport Harbor jetty (green rectangle). Monitoring stations located closest to drains are shown with white and black hatched symbol. Map background from USGS Seamless data. Inset in the lower left corner shows location of field site (black box) within the Southern California Bight. concentration in the surf zone should decay exponentially with distance away from a point source with an effective decay length scale given by
leff )
{
ldie if Γ f 1 ldil if Γ f 0
(6)
Model Application Field Site. To illustrate an application of the model, TC levels surrounding two drains are examined during dry weather (June, July, and August; abbreviated JJA) along the waveenergy-dominated coast of Northern Orange County, California (Figure 2). Rainfall occurs primarily between November through March in Orange County, and stormwater and sanitary sewer systems are separate, thus discharge from the drains during JJA is primary nuisance runoff (29). TC is chosen for the analysis because it is the only FIB measurement available for the drains. Although TC has not caused a significant number of beach closures in Northern Orange County within the last several years, it has recently instigated closures at other beaches in the United States including many in Santa Cruz, CA (Steve Peters, County of Santa Cruz Environmental Health, personnel communication, 2003). The drains were present along the shoreline between 1973 and 1979, near monitoring stations 21N (drain N) and 21S (drain S), on beaches oriented 126/306 ° and 108/288 ° from true north, respectively. The historical drains were chosen over modern FIB sources because (i) their existence is welldocumented through photographs and historical records (29); (ii) they are located significantly far from other TC sources (i.e., the Santa Ana River) so that TC surrounding the drains likely emanated from the drains alone; (iii) their discharge is not directly influenced by the ebb and rise of the tide (as are the discharges of seasonal rivers and marshes) (27); and (iv) the momentum of dry weather drain discharge is small in magnitude relative to the momentum of the longshore current and thus can be approximated as momentumless, as required by the model. While the historic drains are perfect for illustrating the utility of the model, the acquisition of historic environmental data on alongshore currents, as required for the model, proved difficult. This issue and the method used to address it will be discussed in more detail in the Materials and Methods section.
TC Monitoring. Between 1973 and 1979, the Orange County Sanitation District collected water samples from the surf zone at up to 17 sites in Huntington and Newport Beaches at least three times per week. The data from a subset of these stations (10 circles in Figure 2) centered around drains N and S are used in this study. Sites are named according to their distance in thousands of feet north or south of the SAR outlet (i.e., stations 15N and 15S are 15 000 ft north and south of the SAR, respectively). In the early morning, monitoring began at the most upcoast (northern) station, proceeded south, and was completed in a few hours. At each station, approximately 100 mL of water was collected in sterile bottles from ankle depth on an incoming wave, immediately stored on ice, and transported to the laboratory within 6 h where it was analyzed for TC following Standard Method 9221B. Measurements of Beach Slope. Crude estimates of beach slope (S) were obtained for beaches near the drains during JJA by measuring the distance from piers located close to each drain (red lines extending seaward in Figure 2) to the sea bed using a weighted, graduated rope. At least five measurements were made at each pier. A linear least-squares regression was preformed on the data to extract slopes. It was assumed that the slope of the pier was negligible as compared to the measured slope of the beach. The presence of the piers undoubtedly influenced the measurements, and beach slopes are known to be dynamic. Nevertheless, the relative slopes between the different beaches are expected to represent reasonable estimates. Marine Observations. The Huntington Beach lifeguards record surf direction and size three times per day (at approximately 7:00, 13:00, and 17:00 h). Wave direction is reported relative to magnetic north to the nearest 10°; breaker height is reported as a range of minimum to maximum. Records from 1990 through 2001 were used to estimate seasonal wave climates for the dry weather season (JJA) and also to calculate littoral currents using eq 1. Because wave data are not available from 1973 to 1979, it is necessary to assume that the wave climates observed during JJA of these years represent the typical wave climates for JJA from 1973 to 1979. Although supra-decadal oscillations in atmospheric and oceanic conditions that might affect the wave climate are not captured by the 11-year time-series of wave conditions, this is probably a reasonable assumption, especially given the year-to-year similarities in wave conditions (to be discussed in Results and Discussion section). It is also assumed that the wave conditions reported at Huntington Beach apply equally well to beaches at drains S and N, a sensible assumption given the close proximity of the beaches (all within 12 km). In addition, observations at Newport and Huntington Beach by local coastal science experts and lifeguards over many years corroborate this assumption (David Pryor, Associate California State Park Resource Ecologist, personal communication, September 2003). Estimation of ldie. The length scale along the beach over which FIB from the drains are attenuated due to inactivation alone (ldie) was estimated as follows. The littoral currents ql (speed and direction) were calculated with eq 1 for beaches at drains N and S every day during JJA between 1990 and 2001 using marine observations of breaker height (average VOL. 37, NO. 24, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Average Wave Climates during the Summer Months of JJA As Estimated from Marine Observations Recorded from 1990 through 2001 by the Huntington Beach Lifeguardsa
direction
% of total observations
average height (m)
angle of attack at 21N
angle of attack at 21S
W WSW SW SSW S
4(3 11 ( 7 45 ( 8 21 ( 5 19 ( 10
0.52 ( 0.08 0.57 ( 0.08 0.59 ( 0.09 0.68 ( 0.10 0.77 ( 0.10
23° D 45.5° D 68° D 89.5° U 67° U
8° D 30.5° D 53° D 75.5° D 82° U
a Errors describe inter-annual variations in wave climates and were obtained by calculating percents and average heights for each year and then computing the standard deviations. The angle of attack of waves from a specified direction upon the shoreline at beaches near 21N and 21S and the resulting direction of littoral drift are given (U, upcoast; D, downcoast). Angles were calculated using the strike of the coastline as 108 and 126° from true north for beaches at drains N and S, respectively.
of maximum and minimum wave heights) and direction, measured S, and R (calculated by comparing the strike of the coastline at each drain and the direction of the waves; Table 1). The resulting ql were separated based on their direction (upcoast or downcoast) and placed into logarithmically spaced bins to construct histograms. Although ql were calculated for JJA for 1990-2001, it was assumed they represent typical JJA ql; therefore, the histograms apply equally well to JJA from 1973 to 1979. k values for TC, FC, and ENT can be found in the literature for various environmental conditions (e.g., refs 14-22) including variations in sunlight, salinity, and temperature. TC inactivation rates (k) were obtained by digitizing a histogram of measured rates from Chamberlain and Mitchell (33), who monitored TC during 87 in-situ experiments near a marine outfall. Although their study was conducted in the 1970s, modern evaluation of TC inactivation rates at the field site (29) and FC (a subset of TC) inactivation rates under various environmental conditions at differing locations fall within the range of the histogram (18, 34). While perhaps not a perfect representation of the complex distribution of TC inactivation rates relevant to the surf zone, the histogram serves as a reasonable starting point for the model. ldie were calculated by randomly sampling ql and k distributions 10 000 times and taking the quotient. These were subsequently divided into logarithmically spaced intervals and displayed as histograms representing typical ldie for each drain in the upcoast and downcoast directions. Estimation of leff. leff were calculated from the TC monitoring data as follows. When the concentration of TC at 21N (for drain N) or 21S (for drain S) was greater than or equal to a threshold of 100 most probable number (MPN)/ 100 mL (n ) 103 and 147 for 21N and 21S, respectively), a linear least-squares curve fit was performed using the logarithm of TC concentrations at 21N or 21S and the two stations upcoast and downcoast of the stations (see Figure 2) to obtain a slope (which is equivalent to l-1 eff ). The threshold of 100 MPN/100 mL was chosen since it is an order of magnitude greater than typical summertime values in the study area (29). Data collected on days when there was not a negative gradient in pollution levels moving away from the source were excluded from the analyses (n ) 10 and 13 upcoast and downcoast of drain N, respectively; and n ) 13 and 11 upcoast and downcoast of drain S). These days arose when TC levels were low and close to detection limits or when TC levels were quite close at all stations used in the regression as would occur during a sewage spill along the shoreline. Histograms of leff were constructed as previously described. 5514
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-1 -1 -1 ) and ldil((l-1 Calculations of Γ and ldil. Γ(leffldie eff - ldie) ) at both drains were estimated during periods of upcoast and downcoast littoral currents by randomly sampling the appropriate distributions of ldie and leff 10 000 times. Histograms were constructed as previously described.
Results and Discussion Inactivation Length Scale ldie. The prevailing wave climate (both direction and height) in JJA is summarized in Table 1 along with the angle at which the waves impinge upon the shorelines at drains N and S and the direction of resulting littoral drift (based on the Longuet-Higgens equation). Averages and standard deviations of wave height and frequency of occurrence were calculated by comparing values for each of the 11 yr. On the basis of the standard deviations, there is not a large year-to-year variation in wave climate. Waves emanate from the south and southwest approximately 64% of the time, with the largest waves, on average, arriving from the south. JJA waves can generate upcoast and downcoast littoral drift at both drains. Hence, pollution from the drains will be advected in upcoast or downcoast directions, depending on the direction of the impinging waves. Measurements of beach slope indicate that the beach at drain S is steeper than that at drain N (S ) tan β ) 0.05 and 0.03, respectively). This result is consistent with the observation of a wider surf zone at beaches near drain N as compared to drain S and frequent occurrence of spilling breakers at drain N and plunging breakers at drain S. A histogram of TC inactivation rates adopted from Chamberlain and Mitchell (33) is given in Figure 3A. The values were obtained from 87 in-situ experiments near an oceanic outfall after accounting for dilution and dispersion. The values are log-normally distributed with two peaks at 1.4 × 10-5-1.8 × 10-5 s-1 (16% of total observations) and at 8.9 × 10-6-1.1 × 10-5 s-1 (16% of total). Black vertical lines show inactivation rates obtained from mesocosm experiments conducted with unseeded TC-laden water from Huntington Beach (29); the high and low rates were estimated for water exposed to natural sunlight and no light, respectively. The fact that these values bracket those reported by Chamberlain and Mitchell (33) indicates that their values are not inappropriate for the field site. The histogram spans a range of values reported in the literature for FC (a subset of TC) (18, 34) further corroborating the use of these values. Although surely not a perfect representation of the range of inactivation rates experienced by these organisms in the surfzone, the values serve as a reasonable starting point for the analyses. Figure 3B shows histograms of ql for beaches at both drains (labeled N and S). Solid and dotted lines represent ql directed in the upcoast and downcoast directions, respectively. The number of marine observations utilized to obtain each histogram is given in the figure. At drain N, ql directed upcoast and downcoast are distributed log-normally about 0.5-0.6 m s-1. The upcoast directed ql have a secondary peak centered about 0.013-0.016 m s-1, representing about 50% of the upcoast directed estimates. These small ql are a result of the nearly perpendicular attack of waves from the southsouthwest (Table 1). At drain S, upcoast littoral currents are log-normally distributed about 0.4-0.5 m s-1 with 100% of the estimates between 0.2 and 0.6 m s-1. The downcoast currents are spread over a wider range of values from 0.1 to 2 m s-1. The highest frequency of currents occurs in the 0.6-1.6 m s-1 range (87%). According to these estimates, the fastest littoral currents occur near drain S and are directed downcoast, indicating that FIB may be transported further in this direction at drain S as compared with the upcoast direction, and both directions at drain N. Dye experiments conducted at Huntington Beach during southerly waves
FIGURE 3. Histograms of k (A), ql (B), and ldie (C). For ql and ldie, distributions are given for beaches near drains N and S during upcoast (filled squares, solid line) and downcoast (open circles, dotted line) alongshore flow. The frequency with which values are observed for each bin is denoted by a marker placed at the highest end of each bin. revealed littoral speeds of about 0.5 m s-1 (27), indicating that the predictions made here are not outside the range of an actual observation. Estimates of ldie (obtained by randomly sampling appropriate ql and k distributions) for conditions causing upcoast (solid) and downcoast (dotted) littoral flow are shown in Figure 3C. At both drains, ldie varies from 103 to 106 m in both upcoast and downcoast directions with the exception of estimates for drain N during upcoast littoral drift conditions that fall between 250 and 1000 m (51% of total). These small ldie occur during periods of small wave height or waves from the south-southwest (small ql) and high inactivation rates (perhaps during periods of high solar intensity; 29, 33). It is important to note under the majority of conditions ldie are greater than 10 000 m. Examining the magnitude of leff relative to ldie will reveal if TC is attenuated primarily by dilution or inactivation. Decay Length Scale leff. Histograms of leff are given in Figure 4 for drains N (top panel) and S (bottom panel) for the upcoast and downcoast directions (dashed and solid lines, respectively). The number of leff values used in creating each histogram is given in the figure. The average r 2 of the curve fits used to calculate leff is 0.7. At drain N, leff upcoast and downcoast of the drain are similar; approximately 60% are between 3000 and 4500 m, and 6% and 15% of leff upcoast and downcoast, respectively, are greater than 10 000 m. At drain S, leff are, on average, smaller than at drain N. Upcoast of drain S, leff is typically between 2500 and 4500 m, while downcoast, even smaller leff are found (30% of leff < 2000 m). As mentioned in the Field Site section, the Newport Harbor jetty is located approximately 2000 m downcoast of drain S. The fact that 70% of leff > 2000 m indicates that the jetty influences the fate of TC from drain S when littoral currents are directed downcoast. This finding calls into question the application of the model to TC directed downcoast of drain S as the jetty and the altered rates of dilution it may cause have not specifically been taken into account. One of the original assumptions regarding the model formulation was that y should be greater than the distance between rip currents (Y) for eq 3 to apply. According to lifeguards familiar with both Huntington and Newport Beaches, rip currents are highly dynamic and are sensitive to tide level and even the presence of bathers (Lieutenant Michael Baumgartner, Huntington Beach Lifeguards, per-
FIGURE 4. Histograms of leff calculated for TC upcoast (filled squares, solid line) and downcoast (open circles, dotted line) of drains N (top panel) and S (bottom panel). The frequency with which values are observed for each bin is denoted by a marker placed at the highest end of each bin. sonal communication, 2002). Depending on wave conditions, however, they report the distance between rip currents is between 100 and 800 m. Short and Brander (35) examined rip cell spacing at sites around the world and observed that the largest rip current spacing was on the order of 500 m at west facing beaches. Both the lifeguard approximations for Y and Short and Brander’s findings support the assumption that leff > Y; thus, eq 3 is an acceptable solution to the model. Dilution Length Scale ldil. ldil upcoast and downcoast of each drain calculated from eq 5 are shown in Figure 5A. At drain N, they range from 0 to 4000 m and from 1000 to 4000 m in the upcoast and downcoast directions, respectively. The small length scales in the upcoast direction ( ldie, a situation not predicted to occur within the framework of the model. Possible explanations for this include that k values used to estimate inactivation rates are overestimated leading to underestimates of ldie, leff are overestimated by the curve fitting routine, or there are additional sources of TC upcoast of drain N along the shoreline. The latter can occur if assumption v of the model is violated, and there is an accumulation of pollutant outside the surfzone, which is subsequently re-introduced into the surf zone away 5516
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from the point source. Such a situation can indeed be encountered when there is rapid cross-shelf exchange as is possible during south-southwest waves (1). Given the range of Γ values at drain N, dilution is primarily responsible for the attenuation of TC in both directions. Inactivation must play an important role during south-southwest swell or when k values are relatively high, resulting in Γ close to 1. Γ estimated for drain S range from 0.01 to 1. The concentration of TC upcoast of the drain is primarily controlled by dilution based on the fact that 58% Γ E 0.15. However, inactivation must play an important role in TC attenuation some of the time since nearly 40% of Γ are between 0.15 and 1. Downcoast from drain S, 98% Γ E 0.2 pointing to dilution control of TC. However, as with estimates of ldil, this result cannot be interpreted without considering the effect of the harbor jetty. Assuming the jetty causes increased dilution of surf zone polluted water relative to rip currents, then the conclusion that TC levels are dilution controlled is likely to be correct. To be certain, however, a detailed model of circulation near the jetty is needed under various wave conditions to understand its role in dilution. Implications. In general, the characteristic decay length scale for TC is nearly an order of magnitude less than the inactivation length scale. This illustrates the important role dilution plays in the attenuation of TC upcoast and downcoast of the drains. Relative to the model outlined above, leff ≈ ldil. Calculations of ldil reveal that dilution alone reduces TC from the point sources e-fold within at most 8 rip cells, or 4000 m, in the direction of littoral currents. Because the decay length scale from drain S in the downcoast direction is often greater than or equal to the distance between the drain and the harbor jetty, the jetty undoubtedly influences the alongshore transport of TC. Results presented above also illustrate that inactivation can play an important role in the decay of TC away from the drains if littoral currents are slow and/or inactivation rates are fast. These conditions occur when wave angle of attack is close to 90° (i.e., waves are from approximately the south-
southwest), wave heights are small, or sunlight intensity is great (29). ldil is independent of the pollutant under study. It depends on coastal morphology, including beach slope, orientation, and wave climate. Therefore, the conclusion that ldil < 4000 m or 8 rip cells is extendible to other FIB at Huntington and Newport Beaches. In the worst case scenario, where there is slow inactivation of FIB and fast littoral currents, FIB and their associated health risks should be significantly reduced within at most 4000 m from their source. Given the importance of dilution in the spatial attenuation of FIB pollution in the surf zone, drains and man-made water shed outlets that release FIB should be placed along regions of the shorelines where ldil is small. Such a region would likely have a steep slope within the surf zone (small xb) and be subjected by large waves whose angle of attack produces small ql. The dependence of ldie and Γ on inactivation rate makes them organism-specific. The results presented above for TC would likely apply to FC since inactivation rates are similar to those of TC used in this study (34). ENT is more sensitive to sunlight than TC and FC (22, 29). In dark conditions, evidence points to their inactivation rates being on the order of 10-5 s-1 (36, 37), which is within the range of inactivation rates used in this study for TC. If ENT are indeed more sensitive to environmental stress than coliforms, then their inactivation length scales should be shorter, and for a given leff, Γ is likely to be larger and closer to 1 than the same values for TC or FC. Thus, it is possible that inactivation plays a slightly more important role in the alongshore attenuation of ENT away from a point source than it does for coliform bacteria.
Acknowledgments This work was made possible by former employees of the Orange County Sanitation District, Fountain Valley, CA, who are responsible for the monitoring data collected from 1973 to 1979. A.B.B. was supported by a University of California faculty fellowship, Stanford University, the Henry Luce Foundation, and the Powell Foundation. S. Grant and S. Weisberg provided input on previous versions of the manuscript. Comments and information from the following individuals are appreciated: C. McGee, J. Warrick, R. Reeves, M. Mazur, L. Honeybourne, D. Pryor, G. Shellenbarger, the Newport and Huntington Beach lifeguards, and three anonymous reviewers.
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Received for review April 9, 2003. Revised manuscript received September 11, 2003. Accepted September 22, 2003. ES034321X
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