System-wide Monitoring Program

Synthesis of the Water Quality Data from 1995 to 2000
Chapter 5: Tidal and Diel Periodicity in NERR-SWMP Water Quality Data.

Introduction
Water chemistry measures in NERR estuaries are highly periodic in nature. Preliminary analyses (Wenner et al. 2001) using classical harmonic regression techniques found that, for the vast majority of NERR sites, between 70% and 90% of the short-term variability in dissolved oxygen was explainable using only tidal (24.84 h) and diel (24.00 h) model components with corrections for trend. The percent of variance attributed to these two cycles was typically 80-95% for water temperature and salinity and greater than 90% for water depth. Effects of other natural or anthropogenic influences and disturbances will ride atop this “roller coaster” of diel and tidal periodicity. To carefully detect, measure and understand atypical influences and disturbances, we must first fully understand the typical variability, the periodic fluctuations in data. This portion of the synthesis of NERR water quality data quantifies this periodicity, in particular the relative importance of diel vs. tidal influences, in water quality measurements.

Methods
DThe available data at each of the 55 sites were time series of 8 water quality measurements made by a YSI meter every half-hour for the study’s 3-6 year duration. Meters were to be redeployed approximately fortnightly, although QA/QC “deployments” across all sites ranged in length from less than a day to several months. A cursory inspection of the data revealed that deployment of a meter often resulted in an abrupt change in the mean level of any observed water quality measure. More seriously, there are clear indications that the observed amplitudes of periodic fluctuations at times also changed dramatically with new deployments. Together with the realization that the duration of daylight, and hence in all probability the shape of any diel signature, will change over each 12-month period, these “deployment effects” have led us to take a two-phase approach to quantification of periodicity in the water quality indices:

1. Fit periodic regression models to deployment-length segments of data (7-30 days), obtaining graphical and numerical descriptives of tidal and diel signatures, and then
   
2. Analyze deployment-level summaries for annual periodicity, and compare and contrast mean levels between the 55 sites for summaries of interest.
   

Deployments less than 7 days in duration were not used in these analyses. Furthermore, deployments greater than 30 days duration were split into multiple sub-series of duration less than 30 days each. Turbidity (NTU) values crossed several orders of magnitude, so these were transformed to log10 (turbidity +0.5) prior to phase 1 analysis.
Phase 1: Periodic regression models for deployment-level data
Technical details provided in this section are conceptually summarized as an example of the graphical presentation of each deployment’s harmonic model fit in Figure 38 (p. 67). The graphical summaries of each deployment’s data have been captured into PowerpointÒ presentations for each available combination of the 55 sites and 8 variables, and are available for review by contacting Dr. Don Edwards (edwards@math.sc.edu).

Classical harmonic regression techniques model periodicity due to tidal gravitational potential using weighted sums of sine functions whose periods have historically been deduced from the movements of the earth, moon, and sun. These methods have a rich scientific history dating back to the work of Newton and LaPlace in the 17th and 18th centuries, with contributions by Darwin, Lord Kelvin and many others. Our principal references, based on the advice of Blanton (2001), are Defant (1958) and Foreman and Henry (1989), whose recommendations are based on Godin’s (1972) work.

The deep-water tide-generating forces can be grouped into constituents, each of which owns a sine wave in the classical harmonic regression model. The most important constituents are shown in Table 18, modified from Defant (1958, p. 48). There are many other classical tidal constituents, but these are either of much less importance, of longer duration, or are inseparable from the above constituents for series 7-30 days in duration.

Water quality variables are also potentially strongly influenced by solar energy; thus, we introduced a diel term (period = 24 hours), herein referred to as the “D” constituent. Simulation studies conducted during this project, as well as published literature (Foreman & Henry 1989), confirm that this constituent is not distinguishable from K1 or P1 for series 7-30 days in duration because their periods are too similar, nor from K2 or S2, whose periods are approximately or exactly D/2. Subsequently, the deployment-level model extracts four periodic signatures from the data as follows:

1. D (in sum with K1, P1, K2, and S2),
   
2. M2,
   
3. N2, and
   
4. O1.
   

By far the most consistently important among these are D and M2. The additional terms N2 and O1 are rarely of great importance, but the addition of these to the model is theoretically necessary and seemed to lead to better model fits and greater consistency for the D and M2 patterns. The model used here also included a trend term, which would remove the effects of the main long-period constituent Mt and other constituents whose periods are on the order of a few days to a month.

Classical harmonic regression analyses of water level (depth) typically fit the data remarkably well and provide near-perfect predictions. Occasionally, shallow-water settings create complexities in tidal signatures that are not well modeled by a weighted-sum of sine waves using the classical constituents (Defant 1958). Moreover, “noisier” variables like dissolved oxygen and salinity require a much more flexible approach than the classical sine-wave-based models, and there is certainly no reason to believe that the very important diel signature will be well approximated by sine waves for any variable. These considerations, and an unusual abundance of data, have led us to use a nonparametric regression approach to the deployment-level harmonic analyses, using a relatively new statistical technology called “generalized additive models” (Hastie and Tibshirani 1990). For a measurement made at a time t, we can identify the stage of each of the four major cycles: XD, XM2, XN2, and XO1, defining each X to be 0 at midnight on the first day of the data collection. The model hypothesizes that the measured water quality variable Y can be well approximated during the deployment by the sum of a slowly-changing trend term and four smooth, repeating cyclic functions:

Y » f0(t) + fD(XD) + fM2(XM2) + fN2(XN2) + fO1(XO1) (1)

Here, fD, fM2, fN2, and fO1 are smooth but flexible nonparametric “profiles” or “signatures” describing the diel and tidal periodicities in Y, and f0(t) is a term designed to remove within-deployment trend (analogous to using a low-order polynomial with a time series). The above model fits the noisier variables much better than a classical sine-based model, and is very competitive for modeling depth (Winterton 2002). Despite its complexity, it lends itself very well to graphical depiction, which is key for interpretation.

The generalized additive model (1) also lends itself readily to deployment-level numerical descriptives (Table 19). Deployment descriptives were used for studying annual periodicity and site comparisons in phase 2. These quantities are self explanatory except for the “Pure Error” terms, which are the error sum of squares and degrees of freedom from a “saturated” smooth-curve fit.(See PDF for details)

Figure 38 provides a graphical summary of how the model works. Panel (A) depicts the goodness of fit between the observed data and the predicted curve. Panel (B) plots the residuals from the fit of the observed data to the predicted curve, as well as the Root Mean Square for Error (RMSE). Panel (B) is useful for identifying episodic events and irregularities in the data distribution. In this particular example, two to three low-depth events, each approximately 24 hours in duration, were apparent in the plot of the residuals, but were not apparent in panel (A), due to some extent because of differential scaling of the y-axis between these two panels. The x-axis for panels A&B is expressed as days since 1/1/1995, the first date with data in this study. Panel (C) compares the residuals in panel (B) with the predicted 24-hour (diel) signature intended to gauge the influence of solar energy on subsequent water quality parameters. Among deployments lasting 7-30 days in duration, diel signatures were confounded with some of the lesser tidal constituents (K1, P1, K2 and S2). As a result, the “double bump” curve in panel (C) represents the sum of the diel signature and these (usually) small tidal signatures. This shape is atypical and, in this case, probably represents effects of K2 and/or S2 on depth at this site. Panel (D) depicts the main tidal constituent (M2) with a periodicity of 12.42 hours versus the residuals from panel (B). It is especially important to note the occurrence of daily high and low tides in this cycle when interpreting M2 patterns, which are also seen in other variables (i.e., minimum DO during the main tidal cycle). Panels (E) and (F) depict the influence of two other tidal constituents, N2 and O1, with periods 12.66 h and 25.82 h, respectively. Although observed in this example, these constituents were rarely substantial. More examples and suggestions for interpretation of deployment-level plots are provided in the Results section.

Phase 2: Removing Annual Periodicity; Site Comparisons
In phase 2 of the analysis, for each site and variable with at least 30 fitted deployments from phase 1, key numerical summaries of each deployment (Table 20) were checked for presence of an annual (365.24 d) periodicity. Once again, a nonparametric approach was used to estimate the annual signature for each deployment summary across all available site and variable combinations. The p-value of an approximate F-test for significance of the annual periodicity was calculated for each fit. Because these are approximate tests, and because there could be as many as 440 such tests performed for each summary measure, the annual periodicity was considered statistically significant only if the p-value for this test was less than 0.05/500 = 0.0001. In this case, an estimate of the range and mean level of the fitted annual periodic function was computed and a graphical summary created (e.g., Figure 39)

The time series of key summary values (each point corresponds to an analyzed deployment from phase 1) in Figure 39a is presented with respect to the fitted annually periodic nonparametric curve. Residual points plotted by Julian day and the fitted annual curve, with the approximate P-value for the hypothesis of no annual signature (in this case, P is less than 10-12) are presented in Figure 39b. This particular example shows that, for salinity at the Joe Leary Slough site in the Padilla Bay NERR, the diel profile’s variance is typically greater than the main tidal (M2) variance, but the ratio varies seasonally. At this site, diel signals dominate tidal signals in controlling salinity; however, the relative importance of diel signals doubles in winter (ratio » 10) relative to summer (ratio » 5). In the spring months, diel signals continue to be slightly more important influences on salinity than tidal signals; however, in the fall months the two signals are almost equally important (log-ratio » 0).

Because data were not as plentiful for this phase of the analysis, these fitted seasonal curves in some cases are discontinuous from December to January. Also, it appears to us that the approximate F test for annual periodicity is fairly liberal. The remaining aspects of phase 2 involved graphical presentations and comparisons of the mean values of key deployment summary measures between sites.

Figure 39 (see PDF). Annual periodicity in salinity based on the logarithm base 10 of the ratio of Diel to M2 variance at Joe Leary Slough (Padilla Bay NERR), 1995-2000. Panel (A) depicts this log-ratio relative to the sampling period (Jan 1995-Dec 2000), whereas panel (B) depicts the seasonal signal of this log-ratio across all sampling years (p = 1.462e-013).

Results and Discussion
Phase 1, Deployment fits
The following graphs (Appendices 35-39) provide examples of patterns that appeared in the deployment level analyses. These examples are not exhaustive and are included mainly to inspire exploration of the 3-6 year records available in Powerpoint “movies” for each of the 8 variables at 55 NERR sites (with a few exceptions). Specifically, we hope that scientists familiar with the dynamics of any given site(s) will spend time inspecting these Powerpoint images for these site(s) in order to help generate explanations for patterns that may emerge. The images themselves are at times noisy, and fitted curves may not always correspond to real patterns, especially if the residual scatter in a constituent’s plot is substantial. We recommend that any particular pattern in a constituent “signature” be taken seriously only if it recurs in similar form across several consecutive deployments, or across several years at a similar time of year, or if a reasonable scientific explanation for the pattern can be offered.

Phase 2, Removing Annual Periodicity
For site/variable combinations with 30 or more analyzed deployments from phase 1, the key deployment summary measures shown in Table 20 were checked for annual periodicity. Table 21 shows, for each of the 8 variables, the number of sites analyzed and for each key measure the number of sites where annual periodicity was detected at significance level p < 0.0001 (0.05/500). For example, the model R2 for water temperature was found to vary with a repeating annual pattern in only 1 of 45 sites tested. The mean temperature for the fitted values was, in contrast (and not surprisingly), found to be annually periodic for all 45 sites.

Ecological interpretation of Table 21 is difficult. This table is provided to emphasize that mean values of key summary measures may, in some cases, not be representative of a measure for a given site and variable (i.e., if averages of values are strongly seasonal). It is important to note also that a small p-value for this test doesn’t necessarily indicate strong seasonal patterns; with large enough sample sizes, even a minor seasonal pattern may produce a statistically significant result. Fewer analyzed deployments (i.e., smaller sample sizes) may be partially responsible for the smaller pH, turbidity, and specific conductivity values in Table 21. We recommend thorough inspection of the individual deployment plots (e.g., Figure 38), and seasonal plots (e.g., Figure 39) to gain the deepest understanding possible of these water quality variable dynamics at the NERR sites, rather than depending completely on overall averages.

Phase 2, Site Comparisons
All comparisons presented in this section use averages of key deployment summaries as described in Tables 20-21 across all analyzed deployments. The first sub-section, evaluation of model performance, briefly discusses the merits of the GAM approach in characterizing water quality periodicity in the NERR SWMP. The second sub-section, site characteristics, addresses the general patterns observed in the data sets evaluated. The final sub-section deals with the comparison of diel and tidal importance in influencing each of the variables analyzed.

Model Performance
The Generalized Additive Model (GAM) typically provided a better approach for characterizing periodicity in water quality observations at NERR SWMP sites than the harmonic models used in the previous synthesis (Wenner et al. 2001). Data for most site and variable combinations fit the predicted curve very well. Root Mean Square for Error (RMSE) and R-squared values for all site and variable combinations are depicted in Figure 40. Sites with low values of mean R2 or high values of mean RMSE are identified by site abbreviation. Regarding water depth, R2 values were near or above 0.90 for all but 8 sites, which had mean R2 values between 0.65 and 0.8 (Figure 40). For all other variables except turbidity (R2 = 0.4 to 0.8), mean R2 values typically exceeded 0.7.

Sites with little explainable variance (i.e., little natural variation in depth) may have a lower R2 value even if the model predicts the data well. In these instances, RMSE, which measures the accuracy with which individual values would be predicted using the fitted model, provides a better measure of overall model performance than R-squared. For example, in all but five sites, mean RMSE for depth is near or below 0.1 m. Hence, the harmonic regression model at the vast majority of sites typically predicts 95% of depth values to an accuracy of ± 0.2 m, which is twice the RMSE. Average RMSE values for all but four sites were less than 1.5 ppt for salinity, 3 mS/cm for conductivity and £1 mg/l (15% sat) for dissolved oxygen. Average RMSE values for water temperature was less than 1° C at all but two sites and less than 0.2 for pH at all sites. Average RMSE for turbidity at all but four sites was < 0.25 NTU; thus, transformed turbidity at most sites are predicted to an accuracy of ± 0.5 NTU. Applying the anti-log base 10 to this result we obtain 3.16; thus, un-transformed turbidity is predicted at most sites within a multiple of approximately 3 or less. Relative to un-transformed turbidity variation of a factor of 100 in the same deployment, transformed variability is minor and acceptable.

Poor RMSE performance was occasionally observed (Figure 40). Poor RMSE performance for water temperature was observed at Azevedo Pond (Elkhorn Slough NERR), Jug Bay (Chesapeake Bay MD NERR) and Old Woman Creek (State Route 6). Poor RMSE performance for dissolved oxygen was observed for both Elkhorn Slough NERR sites, Jug Bay, and the Tidal Linkage site (Tijuana River Estuary NERR). Poor RMSE performance for salinity and specific conductivity were observed for both South Slough NERR sites, Joe Leary Slough (Padilla Bay NERR), and Lamprey River (Great Bay NERR). Poor RMSE performance for pH was observed for both Weeks Bay NERR sites and Joe Leary Slough. Poor RMSE performance for turbidity was observed at Lower Duplin (Sapelo Island NERR) and station 10 (Jobos Bay NERR)

Site Characteristics
Although the uniqueness of each of the 55 NERR SWMP sites evaluated often inhibited the task of comparing sites, a few general patterns did emerge. For several parameters, the mean value was positively correlated with the average range. Specifically, sites with extreme low or high mean values for salinity (specific conductivity) and water depth also demonstrate relatively small variability in these values.

Figure 41 shows a plot of the mean range of model fitted values versus the mean model fitted value for each of the eight variables, with some of the more extreme points labeled.

• Points at left in each plot represent sites with relatively low mean fitted values for that variable, for example: the Rookery Bay sites for dissolved oxygen; the Wells – Inlet and Padilla Bay – Bayview Channel sites for temperature; the Old Woman Creek – State Route 2, Hudson River, Chesapeake Bay Maryland, and Mullica River – Lower Bank sites for salinity and specific conductivity; the Mullica River – Lower Bank, Wells – Head of Tide, and Delaware – Penrose Branch sites for pH; and the Narragansett Bay, Waquoit Bay, and Wells – Head of Tide sites for turbidity.
  
• Points at right in each plot are sites with relatively high mean fitted value for that variable, for example: the Hudson River – Saw Kill, Wells – Head of Tide, Chesapeake Bay Virginia - Goodwin Islands, and Waquoit Bay – Central Basin sites for dissolved oxygen; the Jobos Bay sites for temperature, salinity, and specific conductivity; The Waquoit Bay, Hudson River – Saw Kill, Elkhorn Slough – North Marsh, Weeks Bay – Weeks Bay, and North Carolina – Masonboro Island sites for pH; and the Old Woman Creek, Delaware, Chesapeake Bay Virginia – Taskinas Creek, and North Inlet – Thousand Acre sites for turbidity.
• Points high on each plot are sites that have the largest range of fitted values for that variable, on average, within their deployments. For example: the Wells – Inlet site for depth; the Elkhorn Slough, Tijuana River – Tidal Linkage and Chesapeake Bay Maryland – Jug Bay sites for DO and/or temperature; the South Slough and Padilla Bay – Joe Leary Slough sites for salinity and temperature; the Mullica River – Lower Bank site for pH; and the Sapelo Island – Lower Duplin site for turbidity.
• Points low on each plot are sites that have the smallest range of fitted values for that variable, on average, within their deployments. For example: the Hudson River – Saw Kill site for dissolved oxygen; the Narragansett Bay, Sapelo Island, and Jobos Bay – 10 sites for temperature; the Old Woman Creek – State Route 2, Hudson River, and Chesapeake Bay Maryland sites for salinity and specific conductivity.
  

Diel vs. Tidal Influence
Discussion of the average relative importance of the diel and tidal cycles examines the average ratios of certain mean squares from the phase 1 analyses (Figures 42-47). Throughout this section, we define the “strength of the diel profile” as the ratio of the diel mean square to the model mean square. When this ratio is large, a substantial proportion of the variation explained by the model (if any) is attributable to the diel profile. Similarly, we define the “strength of the tidal (M2) profile” as the ratio of the M2 mean square to the model mean square. Other tidal constituents (N2 and O1) were not included in the comparisons presented here, as these terms were so often of little importance that their inclusion “watered down” the apparent effects of tide. Sites plotted near the 45° line in each figure represent sites where diel and tidal (M2) forces were equally (if at all) important in influencing the parameter of interest. Points located near the origin correspond to sites for which neither diel nor tidal (M2) components played a substantial role in the model. Where necessary, plotted labels have been shifted slightly for readability.

An overview of the results shows great heterogeneity in tidal vs. diel dominance among these sites; neither tidal (M2) nor diel forces are completely dominant over all sites for any variable. Though there are several notable exceptions for each statement below, it seems apparent that

• More sites are tidally-dominated for depth and salinity than are diel-dominated.
  
• More sites are diel-dominated for dissolved oxygen and temperature than are tidally dominated.
  
• Sites split fairly evenly with respect to tidal vs. diel dominance for pH and turbidity, though less data is available for these variables.
  

This section continues with a detailed discussion of tidal versus diel effects for each variable, on the following pages (Figures 42-47).

Figure 42. (See PDF for details) Diel vs. tidal force influence on water depth, NERR SWMP 1995-2000.

Sites from the same reserve tend to cluster with respect to the importance of diel vs. tidal forces in influencing water depth (Figure 42). The Jobos Bay, Padilla Bay, Weeks Bay, Apalachicola Bay and Tijuana River sites lie above the “equal importance” line, suggesting that water depth is driven more by solar influences than tidal ones at these reserves. The Elkhorn Slough sites straddle the line. Water depth at all other sites seems to be more strongly influenced by tidal forces than diel forces.

Water depth was not strongly influenced by either diel or tidal cycles at four freshwater sites, specifically: both Old Woman Creek NERR sites, Hudson River-Saw Kill, and Delaware Bay-Penrose Branch. These sites also had low average R2 values for depth, as their depth did not vary with any substantial cyclic regularity.

The most extreme sites along both axes in Figure 42 approach or exceed “strength” values of 3. Depth is unusual among the variables in this respect, probably because it is so cleanly cyclic at so many sites. For most other variables, the largest “strength” values are closer to 2.0.

Figure 43. (See PDF for details) Diel vs. tidal force influence on DO (% sat), NERR SWMP 1995-2000.

A handful of sites lie below the 45° line, suggesting that DO (% sat) at these sites is at least somewhat tidally dominated (Figure 43). Sites where DO (% sat) appears to be primarily tidally influenced include both ACE Basin NERR sites and two Great Bay NERR and two Sapelo Island NERR sites (for both of these reserves, remaining sites lie near the line of equal importance). The Hudson River sites at Tivoli Bay (HUDTN and HUDTS) also appear to be tidally-dominated; however, the Hudson River – Saw Kill site lies far to the upper left, making it one of the most extremely diel-dominated sites for DO (% sat). Other sites either lie near the line of equal importance or show a much stronger diel than tidal influence; of these, the Elkhorn Slough, Jobos Bay and Waquoit Bay sites stand out at extreme upper left, along with the Chesapeake Bay Virginia – Goodwin Islands and Tijuana River – Tidal Linkage sites.

Figure 44. (See PDF for details) Diel vs. tidal force influence on water temperature, NERR SWMP 1995-2000.

Not surprisingly, temperature is dominated by diel influences in all but a handful of the sites (Figure 44). The most extreme example of tidal influence on water temperature occurs at Valino Island site (South Slough NERR). Additional sites where temperature seems to be somewhat more tidally driven include the Mullica River – Buoy 126, Wells – Inlet site, and two of the three Great Bay sites (Great Bay and Squamscott River). The third Great Bay site, Lamprey River, lies near the origin in this plot, and so shows no great cyclical pattern in temperature. Sites which are extremely dominated by diel effects for temperature include the Elkhorn Slough – Azevedo Pond and North Marsh sites, and the Jobos Bay and Tijuana River sites.

Figure 45. (See PDF for details) Diel vs. tidal force influence on salinity, NERR SWMP 1995-2000.

Three sites were excluded from this comparison due to shortage of data (Figure 45). Recall that the salinity analyses from phase one should be interpreted cautiously due to frequent freshwater intrusion events that create inconsistencies in the cyclic fluctuations at some sites. A large number of sites lie near the origin in this plot, suggesting that salinity is not very consistently cyclic at these sites. Salinity at a handful of sites seems to be more influenced by diel influences than tidal forces; these sites include the Padilla Bay, Weeks Bay, and Tijuana River sites, and the Jobos Bay – 09 site. Not surprisingly, more sites seem to be tidally-dominated for salinity; among these, the most extreme examples of strong tidal influence on salinity include the Great Bay – Squamscott River site, the South Slough and ACE Basin sites, the Sapelo Island Marsh Landing and Lower Duplin sites, and the Mullica River – Buoy 126 site.

Figure 46. (See PDF for details) Diel vs. tidal force influence on pH, NERR SWMP 1999-2000.

Two sites were excluded from this comparison due to shortage of data, and data on pH were typically only two years in duration, as opposed to 5-6 years for previously discussed variables, so patterns may not be as well defined for pH as for preceding variables (Figure 46). Sites evaluated were almost evenly divided between the tidal- and diel-dominant groups. Sites with strong tidal influence on pH include Hudson River – Tivoli Bay sites, Great Bay - Squamscott River, both ACE Basin sites, the North Inlet – Winyah Bay sites, the South Slough sites, the Wells – Inlet site, and all four Sapelo Island sites. Sites representing the most extreme diel influence on pH include the Hudson River – Sawkill site, the Elkhorn Slough – Azevedo Pond site, The Chesepeake Bay Virginia – Goodwin Island site, and the Padilla Bay, Waquoit Bay, Tijuana River, and Jobos Bay sites.

Figure 47. (See PDF for details) Diel vs. tidal force influence on turbidity, NERR SWMP 1999-2000.

Similar to pH, turbidity data sets spanned a shorter time frame (1999-2000) and were less uniform than data sets for depth, DO, and temperature variables. Four sites are excluded due to lack of data. Figure 47 suggests that there are more tidally dominated sites than diel-dominated ones, but there are a number of sites in both categories. The sites which seem most extremely diel-dominated for turbidity include the Padilla Bay sites as well as the Tijuana River – Tidal Linkage, Weeks Bay – Fish River, Elkhorn Slough – Azevedo Pond, Apalachicola Bay – East Bay Bottom, and Narragansett Bay – Potters Cove sites. Sites which seem most extremely tidally-dominated for turbidity are Great Bay – Squamscott River, South Slough - Winchester Arm, North Inlet – Oyster Landing, and a host of others.

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