Research The Information Content of High-Frequency Environmental Monitoring Data Signals Pollution Events in the Coastal Ocean YOUNGSUL JEONG, BRETT F. SANDERS, AND STANLEY B. GRANT* Interdisciplinary Environmental Engineering Program, Henry Samueli School of Engineering, University of California, Irvine, California 92697
There are an increasing number of coastal ocean observing systems that deploy new technology for environmental sensing and stream these data in near-real-time to endusers (e.g., scientists and coastal managers) via the worldwide web. The temporal resolution, spatial coverage, and accessibility of these data open up new opportunities for better understanding and managing the coastal ocean, but they also present enormous challenges relative to data processing and data interpretation, particularly in cases where these data are to inform rapid management decision making. Here we demonstrate that changes in surf zone water quality at a popular beach in southern California are signaled by changes in the Fisher Information and Shannon Entropy of high frequency (1/4 min-1) measurements of salinity and temperature in the surf zone. These results support the hypothesis that the information content of environmental signals, such as salinity and temperature, can be used to identify changes in the water quality of the coastal ocean. More generally, the approach described heresof using information theory indices calculated from monitoring data as real-time indicators of environmental changesis quite general, and may therefore be applicable to other situations where rapid management decisions are based on high-frequency measurements of environmental parameters.
2. Materials and Methods Theoretical Background. Fisher Information and Shannon Entropy are calculated from the probability density function (pdf) that characterizes a measured signal (13, 14). Let p(x|t) denote the pdf of an environmental signal that ranges over x ∈ [a,b] at time t, where a and b represent, respectively, the lower- and upper-limits of physically meaningful values in the measured quantity. Then the Fisher Information I(t) and Shannon entropy H(t) of an environmental signal, at time t, can be represented as follows:
I(t) )
1. Introduction Effective management of environmental resources is predicated on the existence of well-conceived and appropriately implemented monitoring programs (1). Indeed, it has long been recognized that good environmental policy depends on good environmental monitoring, with examples ranging from forecasting ecosystem change (2), to managing common global resources (3), to minimizing human exposure to toxic chemicals (4), to improving urban air quality (5). In practice, environmental monitoring of toxic pollutants often takes the form of manual sampling of an environmental matrix (water, air, or soil) followed by laboratory analysis. However, it is not uncommon that the pollutant concentration varies faster than the turn-around-time of the sampling * Corresponding author phone: (949) 824 -7320; fax: (949) 8242541;
[email protected]. 10.1021/es060680r CCC: $33.50 Published on Web 09/16/2006
and analysis procedure. In such situations, the monitoring data may be of limited value for informing rapid management actions that might, for example, minimize human exposure to toxins (6, 7). Next generation environmental monitoring systemssthat utilize newly developed in situ sensor technology and transmit these data in near real time to the worldwide webs are one possible approach for decreasing the turn-aroundtime of environmental monitoring data. However, these next generation monitoring networks present a different challenge: how do managers sort through, in near-real-time, the large volumes of data generated by these systems to identify environmental events (e.g., pollution episodes) that merit a rapid response? The situation is even more challenging in the case where easily measured environmental variables (e.g., salinity and temperature in the ocean) are used as proxies for more difficult to measure pollutants (e.g., human pathogens). In these situations, pollution events may not be signaled by changes in the magnitude of the proxy variable per se, but rather by changes in the range of values over which the proxy variable naturally fluctuates, or the proxy’s information content (8, 9). This paper explores the possible application of two measures of information contentsFisher Information and Shannon Entropysfor identifying pollution events in the coastal ocean. Fisher Information and Shannon Entropy have been used to detect abnormalities in the electroencephalographic signals generated by human and turtle brains (10), and they have been proposed as possible indicators of the sustainability and dynamic steady-state of ecological systems (9, 11, 12). To our knowledge, this paper represents the first application of these indices for translating high-frequency environmental monitoring data into information suitable for near-real-time management of the coastal ocean.
2006 American Chemical Society
∫
b
a
H(t) ) -
(
)
1 dp(x|t) 2 dx p(x|t) dx
∫
b
a
(1a)
p(x|t)ln p(x|t)dx
(1b)
Both I(t) and H(t) are sensitive to the shape of the environmental signal’s pdf. In general, the wider or broader the pdf p(x|t), the more random the values of x, the smaller the value of the Fisher Information, and the larger the value of the Shannon Entropy (13, 14). Owing to the derivative term appearing in the integrand of eq 1a, Fisher Information is sensitive to changes in the local smoothness of p(x|t), whereas the Shannon Entropy is influenced more by the global properties of p(x|t) (13). To calculate I(t) and H(t) from high-frequency environmental monitoring data, the following approach was adopted. First, environmental measurements were binned into a VOL. 40, NO. 20, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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sequence of windows, where each window contains w sequential measurements. Second, histograms were generated from the w measurements in each window. Finally, a sequence of Fisher Information and Shannon Entropy values were calculated from the sequence of histograms. Let s(θk) represent a sequence of environmental measurements collected at times θk, where k ) 1,......,K . This sequence of measurements is grouped into a sequence of windows defined by the following:
W(m;w,∆) ) {s(θk), k ) 1 + m∆,......,w + m∆}
(2)
where m ) 0,1,2,......,M, and ∆ and w are selected such that w e K and (K - w)/∆ ∈ N (an even natural number) (10, 15). Physically, m identifies a particular window, w represents the number of measurements included in each window, and ∆ determines the degree of overlap between adjacent windows. Histograms p(xn|m) are prepared from measurements in the mth window, such that the histogram divisions xn(n ) 1,......,N) are spread evenly between the minimum and maximum values of s(θk)(k ) 1,......,K) with N taken as the nearest integer toward zero of xw (i.e., rounding downward). From the resulting histograms, Fisher Information and Shannon Entropy values are estimated as follows (13):
I(m) = ∆x-1
N
[p(xn+1|m) - p(xn|m)]2
n)1
p(xn|m)
∑
(3a)
N
H(m) = -∆x
∑p(x |m)ln p(x |m) n
n
(3b)
n)1
The Fisher Information and Shannon Entropy values thus calculated are assigned a time and date corresponding to the midpoint of the mth sliding window. NEOCO and Precipitation Data. The approach described above for calculating Fisher Information and Shannon Entropy was implemented on high frequency (1/4 min-1) measurements of water level, salinity, temperature, and chlorophyll fluorescence recorded by an in situ sensor located at the end of Newport Pier in Newport Beach, California (Figure 1). The sensor is part of a recently deployed network of coastal sensors, called the Network of Environmental Observations of the Coastal Ocean (NEOCO), deployed at the end of seven piers in southern California. The NEOCO sensor package contains an SBE-16 plus CTD (Sea-Bird Electronics, Inc., Bellevue, WA) and a Seapoint Chlorophyll Fluorometer (Seapoint Sensors, Inc.). These instruments are mounted on a pier piling at a depth of approximately 1 m (below mean lower low water). Fisher Information and Shannon Entropy were calculated from Newport Pier NEOCO data collected over an approximately 3 month period of time, from 29 January to 22 April, 2004. The raw water level, salinity, temperature, and chlorophyll data were low-passed filtered (with a cutoff frequency of 1/h), and then normalized with the formula js(θk) ) (s(θk) - s(θk)min )/(s(θk)max - s(θk)min ). Window sizes equal to a lunar day (w ) 24.8 h) were used for calculations involving water level; window sizes equal to a solar day (w ) 24.0 h) were used for calculations involving salinity, temperature, and chlorophyll. In all cases, the window overlap was set to ∆ ) w/2. The logic used to select these particular values of w and ∆, and the sensitivity of the resulting calculations to these specific parameter values, is described in the Supporting Information. Records of local precipitation were obtained from a rain gauge located at the John Wayne Airport in the City of Santa Ana, approximately 23 km 6216
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NE of Newport Beach and Huntington Beach (http:// www.ncdc.noaa.gov). Surf Zone Water Quality Violation Number (VN). Fisher Information and Shannon Entropy calculated from high frequency measurements of water level, salinity, temperature, and chlorophyll were compared with water quality violations in the surf zone at two beaches, Newport Beach and Huntington Beach, adjacent to the Newport Pier where the NEOCO sensor is located. Consistent with ocean bathing water quality monitoring programs throughout the world (16), bathing water quality was quantified using the surf zone concentration of three groups of fecal indicator bacteria: total coliform (TC), fecal coliform (FC), and enterococci bacteria (ENT). The concentration of these three fecal indicator bacteria groups are measured 5 days per week (excluding Friday and Sunday) by the local sanitation district at 17 shoreline sites along a 23 km stretch of the surf zone at Huntington Beach and Newport Beach, California (Figure 1). Details on the sampling and analysis procedures used, and historical trends in these data, can be found in other publications (17, 18), and at the Orange County Sanitation District website (http://www.ocsd.com). The daily number of water quality violations (referred to here as the violation number, VN) experienced at Newport Beach and Huntington Beach over the time frame 29 January to 22 April, 2004 were calculated by comparing the surf zone water quality monitoring data at Newport and Huntington Beaches with California State single-sample water quality standards as follows: TC ) 10 000, FC 400, and ENT 104 MPN/100 mL, where the concentration units are most probable number (MPN) per 100 mL of water sample. ANOVA Analysis. A series of fixed effect model analysis of variance (ANOVA) tests were conducted (MATLAB, Mathworks, Natick, MA) to evaluate the correlation between surf zone water quality, as represented by VN, and the NEOCO measurements and their Fisher Information and Shannon Entropy. In all three tests, VN was the dependent variable, but the choice of independent variables varied by ANOVA test as follows. In the first ANOVA test, the independent variables were daily average (DA) tide range (DA(L)), salinity (DA(S)), temperature (DA(T)), and chlorophyll (DA(Chl)). The parameters DA(S), DA(T), and DA(Chl) were computed from the raw NEOCO measurements (after low-pass filtering, see above) using a 24 h averaging window centered at 6:30 PDT, the time when surf zone water samples are typically collected for water quality testing by the local sanitation district. The parameter DA(L) was computed by taking the difference between the daily high-high and low-low tides measured by the NEOCO pressure sensor. In the second ANOVA test the independent variables were Fi(L), Fi(S), Fi(T), and Fi(Chl), where Fi refers to the Fisher Information index. In the third ANOVA test, the independent variables were Sh(L), Sh(S), Sh(T), and Sh(Chl), where Sh refers to the Shannon Entropy index. Daily value of the independent variables were categorized as “high” and “low” using the following threshold values: ANOVA test 1: DA(L)T ) 1.6 m, DA(S)T ) 33 ppt, DA(T)T ) 15.0 °C, DA(Chl)T ) 2.2 µg/L. ANOVA test 2: Fi(L)T ) 5, Fi(S)T ) 50, Fi(T)T ) 50, and Fi(Chl)T ) 50. ANOVA test 3: Sh(L)T ) 2.4, Sh(S)T )1.0, Sh(T)T ) 1.5, and Sh(Chl)T ) 1.0. For ANOVA tests 1 and 3, the threshold values correspond to the mean value for the entire time series. Because the Fisher Information indices varied over orders of magnitude, threshold values for ANOVA test 2 were adopted by choosing values that obviously fell between baseline and elevated values of Fisher Information.
3. Results Shannon Entropy and Fisher Information calculated from water level exhibits a fortnightly variability, with low (high) Shannon Entropy and high (low) Fisher Information co-
FIGURE 1. The top four panels are time series plots, after low-pass filtering (cutoff frequency 1/h), of the Newport Pier NEOCO measurements of water level (L), salinity (S), temperature (T), and chlorophyll (Chl). The next four panels are plots of Fisher Information (Fi, red curves) and Shannon Entropy (Sh, blue curves) calculated from the same suite of NEOCO measurements. The daily number of water quality violations (VN) in the surf zone at Newport Beach and Huntington Beach, and daily rainfall (R) are plotted in the last two panels. The locations of water quality monitoring sites are shown in the map as blue dots, and the Newport Beach NEOCO sensor is depicted as a red dot. Open, semi-open, and closed circles on the top of the plot depict the timing of full, quater, and new moons respectively. incident with neap (spring) tides (compare first and fifth panels in Figure 1). Shannon Entropy and Fisher Information calculated from salinity decrease and increase, respectively, in response to local rainfall (compare second, sixth, and 10th panels in Figure 1). Fisher Information and Shannon Entropy calculated from temperature are not obviously correlated with the fortnightly and rainfall patterns noted above, although significant variability is evident (seventh panel, Figure 1). Shannon Entropy and Fisher Information calculated from chlorophyll fluorescence increase and decrease, respectively, during periods of elevated chlorophyll fluorescence (compare the fourth and eighth panels, Figure 1). Over the 3-month time frame captured in Figure 1, there are multiple episodes of poor surf zone water quality, including a major 2-day event beginning 3 February 2004, four major events spread over several weeks starting on 16 February 2004, and numerous smaller events after 10 March 2004 (ninth panel, Figure 1). Altogether, over the study record there were 35 days when one or more water quality standards were violated (i.e., VN g 1), and 26 days when no water quality standards were violated (i.e., VN ) 0). Episodes of poor water quality from 3 February through 28 February roughly coincide with periods of low salinity and rain events (compare the second and last two panels in Figure 1). Fisher Information is quite sensitive to local changes in the smoothness of the data’s probability distribution (see ref 14 and earlier discus-
sion of eq 1). Consequently, the Fisher Information indices plotted in Figure 1 vary over multiple orders-of-magnitude in response to relatively modest changes in the measured data. The Shannon Entropy indices plotted in Figure 1, by contrast, vary less dramatically with time, reflecting the fact that this information index is less sensitive to local changes in the data’s probability distribution. A series of ANOVA studies were conducted to assess the correlation between surf zone water quality (as measured by VN) and two different sets of independent variables: (1) the daily average NEOCO measurements of salinity, temperature, chlorophyll, and daily tide range; (2) Fisher Information and Shannon Entropy calculated from the NEOCO measurements of salinity, temperature, chlorophyll, and water level. In the first study, a four-way ANOVA was performed to test the hypothesis that VN is significantly correlated with one or more of the following independent variables: daily tide range, and daily averaged salinity, temperature, and chlorophyll fluorescence (first column, Table 1). At the p < 0.01 level, VN was significantly correlated with only the daily averaged salinity (p ) 0.0002). This correlate accounted for 12.2% of the variance in VN. The second four-way ANOVA was performed to test the hypothesis that VN is significantly correlated with one or more of the Fisher Information variables (second column, Table 1). At the p < 0.01 level, VN is significantly correlated with the Fisher Information VOL. 40, NO. 20, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Four-way ANOVA Test Resultsa VNb and averaged VN and Fisher VN and Shannon raw data Information Entropy factorsc
S T Chl L S×T S × Chl S×L T × Chl T×L Chl × L S × T × Chl S×T×L S × Chl × L T × Chl × L S × T × Chl × L
p value 0.0002(12.2) 0.6367 0.2626 0.1530 -d 0.1765 0.0382 0.7368 0.9049 0.7414 0.9022 -
p value 0.0003 (10.4) 0.0044 (6.1) 0.3780 0.1667 0.1164 0.3559 0.0428 0.5532 0.4928 0.1001 0.0608 -
p value 0.0000 (24.4) 0.0089 (4.0) 0.5665 0.2693 0.0049 (4.6) 0.0085 (4.0) 0.0341 0.9882 0.5378 0.9033 0.0148 0.5840 -
a Numbers in parentheses represent percent variance in VN explained by factors. b VN, violation number of California single-sample-standard. c S, salinity; T, temperature; Chl, chlorophyll fluorescence; L, tidal range. d p value for terms marked “-” was not calculable.
calculated from salinity (p ) 0.0003) and the Fisher Information calculated from temperature (p ) 0.0044). These correlates account for, respectively, 10.4% and 6.1% of the variance in VN. The third four-way ANOVA was performed to test the hypothesis that VN is significantly correlated with one or more of the Shannon Entropy variables (third column, Table 1). At the p < 0.01 level, VN is significantly correlated with the Shannon Entropy calculated from salinity (p ) 0.0000), Shannon Entropy calculated from temperature (p ) 0.0089), the binary interactions of Shannon Entropy calculated from salinity and temperature (p ) 0.0049), and the binary interactions of Shannon Entropy calculated from salinity and chlorophyll (p ) 0.0085). These correlates account for, respectively, 24.4%, 4.0%, 4.6%, and 4.0% of the variance in VN.
4. Discussion Coastal ocean observing systems, like the NEOCO sensors described in this paper, provide an unprecedented opportunity to study high-frequency oceanographic processes that affect the health and function of coastal ecosystems (19). These observing platforms may also facilitate management of various ocean-related activities, such as shipping and beach closure policies. Indeed, a recent economic analysis by Pendleton (20) found that even a modest improvement in the spatial and temporal resolution of water quality information at popular beaches in Los Angeles County could yield a net economic benefit to the region of over $5 million annually. However, before such benefits can be realized, approaches must be developed for translating the large streams of data generated by ocean-observing systems into simple metrics that can be used by coastal managers to inform practical decisions, e.g., whether or not to post a popular marine bathing beach as unfit for swimming. In this paper we explore the idea that surf zone pollution events at two popular beaches in southern California are signaled by changes in high-frequency measurements of water level, salinity, temperature, and/or chlorophyll. Our most significant finding is that the transformation of highfrequency coastal ocean observations into Fisher Information and/or Shannon Entropy indices greatly improves the value of these data as predictors of coastal water quality. Over the time period captured in Figure 1, it appears that the daily number of bathing water quality violations (or VN) in the 6218
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surf zone at Huntington Beach and Newport Beach are significantly correlated with rainfall and depressions in daily averaged ocean salinity, but not significantly correlated with changes in tide-range, daily averaged ocean temperature, or daily averaged chlorophyll (at p < 0.01). However, when these same data are transformed into Fisher Information and Shannon Entropy, we find that VN is significantly correlated with a greater number of the resulting indices and their binary interactions, most notably salinity and temperature, and a larger percentage of the variance in VN is captured. In particular, VN is positively correlated with the Shannon Entropy of salinity and negatively correlated with the Shannon Entropy of temperature. Likewise, VN is negatively correlated with the Fisher Information of salinity and positively correlated with the Fisher Information of temperature. Put simply, water quality violations at Huntington Beach are more likely to occur when, over the course of a single day, salinity fluctuates around a larger range of values, and temperature fluctuates around a more narrow range of values. Based on an analysis of 41 years of daily measurements at Newport Beach and Huntington Beach, Boehm et al. (21) report that surf zone water quality co-varies with sea surface temperature over interannual to tidal periods. Specifically, during summertime, elevated concentrations of total coliform are associated with cooler than average sea surface temperature, while during wintertime, elevated concentrations of total coliform are associated with warmer than average sea surface temperature. These authors speculated that the negative correlation between total coliform and sea surface temperature during summers might be due to upwelling of sewage contaminated sub-thermocline waters and/or the enhanced survival of fecal indicator bacteria in colder ocean water. They also speculated that the positive correlation between total coliform and sea surface temperature during winters is caused by El Nino southern oscillations (ENSOs), which in this part of the world, are associated with positive sea surface temperature anomalies, higher-than-average rainfall, and larger volumes of contaminated stormwater runoff into the coastal ocean. Relative to the results presented in this paper, the fact that water quality violation rates are more likely to occur when salinity fluctuates over a larger range of values probably reflects the stochastic mixing of stormwater plumes (characterized by lower salinity and higher fecal indicator bacteria) into the coastal ocean (characterized by higher salinity and lower fecal indicator bacteria). That water quality violations are also more likely to occur when temperature fluctuates over a more narrow range of values is intriguing, but more difficult to explain. Presumably this temperature influence on fecal indicator bacteria is not due to the upwelling of sewage-contaminated and colder sub-thermocline water, as suggested by Boehm (see above), because the only known source of fecal indicator bacteria in sub-thermocline waters (a submarine outfall operated by the local sanitation) was eliminated when the sanitation district began disinfecting their sewage effluent 18 months prior to the start of this project. The information content of temperature appears to be lower during storm events (e.g., Shannon Entropy is depressed during a sequence of three storms in late February, compare seventh and 10th panels in Figure 1), and hence, one possible explanation is that a reduction in the daily temperature fluctuation is another indication that the surf zone is contaminated with stormwater runoff. It is also interesting to note that the rate of fecal indicator bacteria die-off is positively correlated with solar irradiance (22-26). Hence, days when the temperature fluctuates around a more narrow range of values may reflect less solar heating of the surf zone and, hence, conditions more conducive to the survival and transport of fecal indicator bacteria (27, 28).
The results presented here demonstrate that the information content of the NEOCO data, as measured by either Fisher Information or Shannon Entropy, is significantly correlated with coastal water quality at our field site. Further, comparing the Shannon Entropy and Fisher Information indices, it appears that the former are less noisy and more strongly correlated with VN. Specifically, when Shannon Entropy was used to calculate the independent variables (third column in Table 1) a greater percentage of the overall variance in VN was explained (37% for Shannon Entropy vs 16.5% for Fisher Information), and more of the variables, and their binary interactions, were deemed significant correlates. While the results presented here are clearly a first step, they support the hypothesis that the information content of high-frequency monitoring data can signal pollution events in the coastal ocean. How this information is ultimately deployed to better manage the coastal ocean remains to be seen, although several possibilities can be envisioned. In one approach, the information content of one (or more) highfrequency signals could be used to provide near real-time warnings of coastal pollution events. For example, at our field site, violations of water quality standards in the surf zone appear to be signaled by decreases in the information content of salinity and increases in the information content of temperature (see above discussion). Alternatively, Fisher Information and Shannon Entropy calculated from highfrequency salinity and temperature measurements could serve as input to statistical (29) or physical (27) now-casting models of surf zone water quality. Further, when coupled with spatial maps of coastal currents, e.g., obtained from CODAR (Coastal Ocean Dynamic Application Radar) systems (30), water quality now-casts could be tailored to specific beaches, thus improving both the turn-around-time for coastal water quality advising and their geographic precision. The approach described in this paper for interpreting coastal ocean observing data represents a new tool in the coastal manager’s “toolbox”, complementing traditional monitoring efforts and biotechnology-centered rapid warning systems, such as real time polymerase chain reaction methods for detecting fecal indicator bacteria and human viral pathogens (31-33).
Acknowledgments This research was supported by a grant from the University of California Marine Council (UC Marine Council, award no. 32114 to S.B.G.), a graduate fellowship from the University of California Marine Council to Y.J., and a grant from the Santa Ana Regional Water Quality Control Board (Supplemental Environmental Project to S.B.G., 2005). We thank two anonymous reviewers for their comments and suggestions. The NEOCO station at the Newport Pier is now managed and maintained by the Southern California Coastal Ocean Observing System (www.sccoos.org).
Supporting Information Available Parameter sensitivity analysis. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review March 21, 2006. Revised manuscript received June 28, 2006. Accepted July 27, 2006. ES060680R
