Fig 1.
Conceptual schematic of progressive, mixed, and standing waveforms.
Schematic of relationships between stage (S) and discharge (Q) (first row) and between stage-rate-of-change (dS/dt) and discharge (second row) through time, for progressive (a, d), mixed (b, e), and standing (c, f) waveforms. Thicker line and right y-axes represent Q(t), thinner lines and left y-axes represent S(t) or dS(t)/dt. Absolute magnitude of phase offset (| ϕ |) between S and Q is the space between the dashed lines. The figure was composed using MATLAB from a hypothetical dataset.
Fig 2.
Locations of the tidal rating curve model validation and application sites.
The 12 tidal USGS gauges available nationally with appropriate data for validation were located throughout the eastern US (circles in a) [51]. The ten original model application sites were on the Mission (triangles in b,c) and Aransas (squares in b, d) Rivers of the Texas Gulf Coastal plain, distributed throughout the tidal freshwater zone of each river [16]. Elevation data, watershed boundaries, and river lines were obtained from U.S. Geological Survey, National Geospatial Program [52]. The Texas state and U.S.A. country outline was obtained from the U.S. Census Bureau [53]. Both the National Geospatial Program and the U.S. Census Bureau provide public access to their data sets. Data visualized using ESRI ArcGIS software.
Fig 3.
Range of tidal fourier transform magnitudes vs. velocity phase offsets (ϕ) across sites.
Site labels are the same as those in Table 1. To enable comparison among sites, the Relative Tidal Signal Magnitude represents the maximum power spectrum magnitude observed during each site’s FFT analysis. Although the variable is unitless, this variable serves as a proxy for the maximum tidal harmonic amplitude (i.e., larger magnitudes ~ larger amplitudes). However, this metric is used for illustration purposes and aides in the graphical differentiation of each site, but the variable does not completely represent the multiple important tidal harmonics at each site. Visualization created using MATLAB software.
Table 1.
List of sites used for validation and testing of the tidal rating curve model.
Table 2.
Tidal rating curve model coefficients (k1, k2, k3, k4, standard errors, and t-statistics) for the validation and test sites under baseflow conditions.
Fig 4.
Comparison of observed and modeled discharge at two standing wave sites.
Example comparisons of baseflow discharge data from M-A site A3 observed by ADP surveys (a) and at the USGS Crystal River gauge (b) versus discharges modeled by the tidal rating curve method. The solid line represents the 1:1 ratio. Predictions at site A3 exhibited R2 = 0.94, while predictions at the USGS Crystal River site displayed R2 = 0.97. Visualization created using MATLAB software.
Table 3.
Summary of Mission-Aransas sites’ discharge (m3 s-1) during baseflow, storm, and overall conditions from July 2015 –July 2017.
Fig 5.
Example regressions of tilt current meter velocities to ADP-measured discharges.
Example linear regressions of tilt current meter (TCM) velocities to ADP-measured discharge at Aransas river sites A3 (a) and A4 (b). Gray dashed lines indicate zone of TCM velocity magnitudes less than the 0.02 m s-1 reliable detection limit. In each figure panel, circles marking empirical observations are transparent; thus, darker circles denote overlap of observations. Dashed lines represent 95% confidence bounds of the regression. Visualization created using MATLAB software.
Fig 6.
Elliptical relationships between stage, stage-rate-of-change, and discharge.
Discharge (Q) relationships to stage (S, left column) or stage-rate-of-change (, right column) at five of the tidal USGS sites during two weeks of baseflow, with points colored by the other variable (
, left; S, right). An ideal progressive-wave system would exhibit linear Q(S) and an ideal standing-wave system would exhibit linear Q (
). Sites are: (a-b) Shark River, (c-d) Connecticut River, (e-f) Halls River, (g-h) Crystal River, (j-k) Plum Island River (see Table 1). The Shark, Halls, and Plum Island Rivers measured stage relative to a zero MSL datum, hence positive and negative stage; the Connecticut and Crystal Rivers used a lower datum. Data for these rivers was obtained from USGS NWIS [50] and visualized via MATLAB.