# Hydrodynamic Drivers of Dissolved Oxygen Variability within a Tidal Creek in Myrtle Beach, South Carolina

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}watershed [5].

## 2. Field Observations

## 3. Analytical Methods

#### 3.1. Quality Control

^{®}(v3.7.15, Onset Computer Corporation, Bourne, MA, USA) and the calibration DO measurements made with the YSI. These corrections were performed bi-weekly with calibration DO measurements taken at the start and end interval. Additionally, consecutive DO percent saturation measurements differing by more than 20% were considered erroneous and removed from the data set. This threshold removed clear outliers within the time series.

#### 3.2. Tidal Range, Currents, and Discharge

_{f}and Q

_{e}), calculated over the rising and falling tides, respectively. Current velocity, $\overline{u}$, measured by the Vector at Site B, is the mean of the measured velocities over a burst-interval (i.e., 5-min) and is assumed to be homogeneous over the cross-section when computing discharge.

#### 3.3. Reynolds Shear Stress

#### 3.4. Pearson Correlation Analysis

## 4. Results and Discussion

^{−5}m/s and thus are considered negligible.

_{R}) indicates either the sampling interval or the period of time the data were averaged prior to the correlation if C

_{R}is greater than the sampling interval. The data is segmented and correlated over each segment, then the correlation coefficients are averaged over all possible segments at each lag. This segment is referred to as the correlation time interval (C

_{I}) (Table 2).

_{I}= 14 days) from September 2017 through June 2018 reveals a weak but statistically significant relationship (R = 0.277, 1.5 day-lag). DO concentration was downsampled to a 12-h time interval (C

_{R}) to match the resolution of the tidal range time series. The C

_{I}of this DO concentration time series and tidal range captures variations in dissolved oxygen and tidal range occurring over timescales longer than a tidal cycle. A direct relationship with a lag of 1.5 days between tidal range and dissolved oxygen concentrations indicates that an increase in tidal range precedes an increase in DO concentration. This finding suggests higher tidal ranges result in a net increase in DO concentrations within the system over time.

^{5}m

^{3}(total ebb discharge over May was 2.58 × 10

^{7}m

^{3}) while the average flood discharge per tidal cycle was 9.97 × 10

^{4}m

^{3}(total flood discharge over May was 5.68 × 10

^{6}m

^{3}). This result as well as the strong correlation between discharge and tidal range (R = 0.754 for flood Q; R = 0.977 for ebb Q) indicates that the creek system is not storing water (at least during this time) and other sources entering the creek (e.g., rainfall, runoff, and groundwater) likely lead to the larger water export on ebb.

^{2}. Positive ${R}_{S}$ is generally observed during flood currents (averaging 0.186 N/m

^{2}) and negative ${R}_{S}$ with ebb currents (averaging −0.049 N/m

^{2}), so positive mean ${R}_{S}$ indicates larger ${R}_{S}$ on flood tides overall. While these results indicate that ${R}_{S}$ magnitude is flood dominated, like the discharge, variations in sampling volume location within the water column possibly affected the asymmetric cycles in observed ${R}_{S}$ [13].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Morris, J.T.; Sundareshwar, P.V.; Nietch, C.T.; Kjerfve, B.; Cahoon, D.R. Sea Level of Coastal Wetlands to Ristng Responses. Ecology
**1992**, 83, 2869–2877. [Google Scholar] [CrossRef] - Kirwan, M.L.; Megonigal, J.P. Tidal wetland stability in the face of human impacts and sea-level rise. Nature
**2013**, 504, 53–60. [Google Scholar] [CrossRef] [PubMed] - Brinson, M.M. Strategies for assessing the cumulative effects of wetland alteration on water quality. Environ. Manag.
**1988**, 12, 655–662. [Google Scholar] [CrossRef] - Saiz-Salinas, J.I.; Gonzalez-Oreja, J.A. Stress in estuarine communities: Lessons from the highly-impacted Bilbao Estuary (Spain). J. Aquat. Ecosyst. Stress Recover.
**2000**, 7, 43–55. [Google Scholar] [CrossRef] - Hoffnagle, B.L. Linking Water Quality and Beach Morphodynamics in a Heavily Impacted Tidal Creek in Myrtle Beach, South Carolina. Master’s Thesis, Coastal Carolina University, Conway, SC, USA, 2015. [Google Scholar]
- Voulgaris, G.; Meyers, S.T. Temporal variability of hydrodynamics, sediment concentration and sediment settling velocity in a tidal creek. Cont. Shelf Res.
**2004**, 24, 1659–1683. [Google Scholar] [CrossRef] - Trowbridge, J.H. On a Technique for Measurement of Turbulent Shear Stress in the Presence of Surface Waves. J. Atmos. Ocean. Technol.
**1998**, 15, 290–298. [Google Scholar] [CrossRef] - Trowbridge, J.H.; Geyer, W.R.; Bowen, M.M.; Williams, A.J. Near-Bottom Turbulence Measurements in a Partially Mixed Estuary: Turbulent Energy Balance, Velocity Structure, and Along-Channel Momentum Balance. J. Phys. Oceanogr.
**1999**, 29, 3056–3072. [Google Scholar] [CrossRef] - Feddersen, F.; Trowbridge, J.H.; Williams, A.J. Vertical Structure of Dissipation in the Nearshore. J. Phys. Oceanogr.
**2007**, 37, 1764–1777. [Google Scholar] [CrossRef] - Thorpe, S. The Turbulent Ocean; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Elgar, S.; Raubenheimer, B.; Guza, R.T. Quality control of acoustic Doppler velocimeter data in the surfzone. Meas. Sci. Technol.
**2005**, 16, 1889. [Google Scholar] [CrossRef] - Barnhardt, W.A. (Ed.) Coastal Change Along the Shore of Northeastern South Carolina—The South Carolina Coastal Erosion Study; U.S. Geological Survey Circular 1339: Reston, VA, USA, 2009.
- Pastore, D.M. Hydrodynamic Drivers of Dissolved Oxygen Variability Within a Highly Developed Tidal Creek. Master’s Thesis, Coastal Carolina University, Conway, SC, USA, 2018. [Google Scholar]
- Fagherazzi, S.; Hannion, M.; Odorico, P.D. Geomorphic structure of tidal hydrodynamics in salt marsh creeks. Water Resour. Manag.
**2008**, 44. [Google Scholar] [CrossRef] - Svendsen, I.A. Introduction to Nearshore Hydrodynamics; World Scientific Publishing Co. Pte. Ltd.: Hackensaack, NJ, USA, 2006. [Google Scholar]
- Dean, R.G.; Dalrymple, R.A. Water Wave Mechanics for Engineers and Scientists; Liu, P., Ed.; World Scientific Publishing Co. Pte. Ltd.: Hackensaack, NJ, USA, 1991. [Google Scholar]
- Troup, M.L.; Fribance, D.B.; Libes, S.M.; Gurka, R.; Hackett, E.E. Physical Conditions of Coastal Hypoxia in the Open Embayment of Long Bay, South Carolina: 2006–2014. Estuaries Coasts
**2017**, 40, 1576–1591. [Google Scholar] [CrossRef] - Aubrey, D.G.; Speer, P.E. A study of non-linear tidal propagation in shallow inlet/estuarine systems Part I: Observations. Estuar. Coast. Shelf Sci.
**1985**, 21, 185–205. [Google Scholar] [CrossRef] - O’Laughlin, C.; Van Proosdij, D.; Milligan, T.G. Flocculation and sediment deposition in a hypertidal creek. Cont. Shelf Res.
**2014**, 82, 72–84. [Google Scholar] [CrossRef] - Dronkers, J. Tidal asymmetry and estuarine morphology. Neth. J. Sea Res.
**1986**, 20, 117–131. [Google Scholar] [CrossRef] - Blanton, J.O.; Lin, G.; Elston, S.A. Tidal current asymmetry in shallow estuaries and tidal creeks. Cont. Shelf Res.
**2002**, 22, 1731–1743. [Google Scholar] [CrossRef] - Cimbala, J.M.; Çengel, Y.A. Essentials of Fluid Mechanics: Fundamentals and Applications; McGraw-Hill Higher Education: New York, NY, USA, 2008. [Google Scholar]
- Marusic, I.; McKeon, B.J.; Monkewitz, P.A.; Nagib, H.M.; Smits, A.J.; Sreenivasan, K.R. Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues. Phys. Fluids
**2010**, 22, 065103. [Google Scholar] [CrossRef]

**Figure 1.**(

**A**) satellite image of the southeastern United States with emphasis on the Long Bay area, located between North Carolina (NC) and South Carolina (SC). The location of the study area is approximated by the red “x” and the state border is defined by the light blue line; (

**B**) aerial photo of Singleton Swash tidal creek showing the most dynamic area of the swash between the waterline and beach dune as well as the surrounding watershed. Measurement locations for this study are also labeled as Site A, Site B, and Site C.

**Figure 2.**(

**A**) along-channel and (

**B**) cross-channel view of the Vector, seating, and frame at low tide. The Vector is approximately centered across the channel width.

**Figure 3.**(

**A**) sample time series of all three velocity components on 6 May 2018 beginning at 16:00, where the along-channel velocity (u) is blue, the across-channel velocity (v) is red, and the vertical velocity (w) is yellow; (

**B**) power spectral density of along-channel velocity in (

**A**), exhibiting a peak at a frequency within the approximate timescales for wind waves (~1 Hz). Such a record would be excluded from calculation of Reynolds shear stresses (see Section 3.3).

**Figure 4.**Sample time series of percent (%) saturation of dissolved oxygen at Site B over a period of 15 days. Daylight hours (x) begin at 6:00 a.m. and end at 8:00 p.m. and non-daylight hours (x) range from 8:00 p.m. to 6:00 a.m. Regions of light blue denote times during spring tide while the grey denotes periods of neap tide.

**Figure 5.**(

**A**) time series of along-channel current velocity ($\overline{u}$) measured by the ADV during the May, 2018 deployment; (

**B**) power spectral density (PSD) of current velocity ($\overline{u}$) shown in (

**A**). The highest spectral peak occurs at a period of 12.5 h.

**Figure 6.**Time series of Reynold shear stress (${R}_{S}$) calculated from velocity measurements recorded by the ADV over the May deployment.

**Figure 7.**Bi-plot of principal components one and two resulting from a PCA on variables: current speed ($\left|\overline{u}\right|$), Reynolds shear stress magnitude ($\left|{R}_{S}\right|$), tidal range, and dissolved oxygen (DO). Blue lines represent loading of each variable onto each principle component. Principle component one and two represent 74% and 19% of the dataset variance, respectively.

**Table 1.**Time series used in Equation (4) for both correlation variables (p, q), sampling period (T), location of the measurement corresponding to each variable, and the instrument used to perform the measurement.

p | q | T (Days) | Location of Measurements (p/q) | Instruments (p/q) |
---|---|---|---|---|

Tidal Range (m) | Tidal Range (m) | 131 | Site A/Site C | HOBO water level logger/HOBO water level logger |

Tidal Range (m) | Max Flood Current (m/s) | 31 | Site A/Site B | HOBO water level logger/Vector |

Tidal Range (m) | Max Ebb Current (m/s) | 31 | Site A/Site B | HOBO water level logger/Vector |

Tidal Range (m) | Flood Discharge (m^{3}) | 31 | Site A/Site B | HOBO water level logger/Vector |

Tidal Range (m) | Ebb Discharge (m^{3}) | 31 | Site A/Site B | HOBO water level logger/Vector |

Reynolds Shear Stress (N/m^{2}) | $\overline{u}$ (m/s) | 31 | Site B/Site B | Vector/Vector |

Dissolved Oxygen (% saturation) | Reynolds Shear Stress (N/m^{2}) | 31 | Site B/Site B | HOBO DO logger/Vector |

Dissolved Oxygen (% saturation) | Flood Discharge (m^{3}) | 31 | Site B/Site B | HOBO DO logger/Vector |

Dissolved Oxygen (% saturation) | Ebb Discharge (m^{3}) | 31 | Site B/Site B | HOBO DO logger/Vector |

Dissolved Oxygen (% saturation) | $\overline{u}$ (m/s) | 31 | Site B/Site B | HOBO DO logger/Vector |

Dissolved Oxygen (% saturation) | Tidal Range (m) | 271 | Site A/Site A | HOBO DO logger/HOBO water level logger |

Dissolved Oxygen (% saturation) | Wind Speed (m/s) | 31 | Site B/Apache pier | HOBO DO logger/Met station |

**Table 2.**Correlated parameters (p and q; Equation (4)) with the corresponding maximum correlation coefficients, upper and lower 95% confidence intervals (lower: CI

_{L}; upper: CI

_{H}), lag time, correlation time series resolution (C

_{R}), and correlation time interval (C

_{I}).

p | q | R | 95% Cl_{L} | 95% CI_{H} | Lag (Hours) | C_{R} (Hours) | C_{I} (Days) |
---|---|---|---|---|---|---|---|

Tidal Range (m) | Flood Q (m^{3}) | 0.754 | 0.62 | 0.89 | 0 | 12.00 | 30.0 |

Tidal Range (m) | Ebb Q (m^{3}) | 0.977 | 0.96 | 0.99 | 0 | 12.00 | 30.0 |

Tidal Range Site A (m) | Tidal Range Site C (m) | 0.981 | 0.98 | 0.98 | 0 | 12.00 | 14.0 |

Tidal Range (m) | Max Flood Current (m/s) | 0.927 | 0.92 | 0.93 | 0 | 1.00 | 1.0 |

Tidal Range (m) | Max Ebb Current (m/s) | 0.842 | 0.83 | 0.85 | 0 | 1.00 | 1.0 |

Reynolds Shear Stress (N/m^{2}) | $\overline{u}$ (m/s) | 0.434 | 0.40 | 0.46 | 0 | 0.25 | 0.5 |

Dissolved Oxygen (% saturation) | $\overline{u}$ (m/s) | −0.511 | −0.55 | −0.47 | 1.75 | 0.25 | 2.0 |

Dissolved Oxygen (% saturation) | Flood Q (m^{3}) | 0.608 | 0.32 | 0.89 | 0 | 12.00 | 10.0 |

Dissolved Oxygen (% saturation) | Ebb Q (m^{3}) | −0.541 | −0.74 | −0.34 | 0 | 12.00 | 10.0 |

Dissolved Oxygen (% saturation) | Wind Speed (m/s) | 0.274 | 0.19 | 0.36 | 1.00 | 0.08 | 14.0 |

Dissolved Oxygen (% saturation) | Reynolds Shear Stress (N/m^{2}) | 0.276 | 0.24 | 0.31 | 0 | 0.25 | 0.5 |

Dissolved Oxygen (% saturation) | Tidal Range (m) | 0.277 | 0.03 | 0.53 | 36 | 12.00 | 14.0 |

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**MDPI and ACS Style**

Pastore, D.M.; Peterson, R.N.; Fribance, D.B.; Viso, R.; Hackett, E.E.
Hydrodynamic Drivers of Dissolved Oxygen Variability within a Tidal Creek in Myrtle Beach, South Carolina. *Water* **2019**, *11*, 1723.
https://doi.org/10.3390/w11081723

**AMA Style**

Pastore DM, Peterson RN, Fribance DB, Viso R, Hackett EE.
Hydrodynamic Drivers of Dissolved Oxygen Variability within a Tidal Creek in Myrtle Beach, South Carolina. *Water*. 2019; 11(8):1723.
https://doi.org/10.3390/w11081723

**Chicago/Turabian Style**

Pastore, Douglas M., Richard N. Peterson, Diane B. Fribance, Richard Viso, and Erin E. Hackett.
2019. "Hydrodynamic Drivers of Dissolved Oxygen Variability within a Tidal Creek in Myrtle Beach, South Carolina" *Water* 11, no. 8: 1723.
https://doi.org/10.3390/w11081723