Abstract

There exists a rich understanding of channel forms and processes for rivers with unidirectional flows, and for their estuarine components with bidirectional flows. On the other hand, complementary insight on the transitional reach linking these flows has not been well developed. This study highlights analyses of high-resolution, high-accuracy bathymetric surveys along a coastal plain river at 30–94 km upstream of the estuary mouth. The goal of this work was to identify geomorphic indicators of the fluvial-tidal transition channel. Trends with sharp breaks were detected in along-channel variations in depth, hydraulic radius, channel shape, bed elevation, and sinuosity, but cross-section area of flow provided the greatest insight. The transition channel is characterized as a reach with greater than 50% decline in area of flow relative to the background values at the upstream and downstream ends. Further downstream, the river is a mixed bedrock-alluvium system, and a 22 km reach of discontinuous bedrock outcrops has a marked influence on local channel metrics, and corresponding backwater effects on upstream metrics. Despite the confounding effects of bedrock on channel form, the transition channel linking estuarine and fluvial channel segments is apparent as a 13 km geomorphic discontinuity in flow area along a channel reach of relatively uniform width. Finally, it is proposed that bedrock outcrops enhance tidal energy dissipation and influence the position of the fluvial-tidal transition reach, and associated geomorphic and hydrodynamic features.

INTRODUCTION

Along the river continuum, a single channel can transition from fluvial to tidal dominance in flow and sedimentary processes, and in benthic ecology (Dalrymple and Choi, 2007; Jablonski and Dalrymple, 2016). In particular, many coastal river systems experience the combined influence of terrestrial runoff processes and marine storms and tides (e.g., Wright et al., 1973; Bokuniewicz, 1995; Ensign et al., 2013; Sassi and Hoitink, 2013), giving rise to at-a-station flow conditions ranging from unidirectional downstream to bidirectional tidal (e.g., Jay, 1991; Godin, 1999). Coastal plain rivers are especially susceptible to the effects of marine forcing due to their low elevations and low gradient, and they can be expected to have well-developed transition channel reaches that link fluvial- and tidal-dominant conditions (Dalrymple and Choi, 2007). In this context, the fluvial-tidal transition is taken as the geomorphic transition associated with unidirectional to bidirectional dominant flows (after Yankovsky et al., 2012).

Typically, as tidal waves enter the estuary and advance upstream, their amplitudes increase due to upstream channel area convergence (Friedrichs and Aubrey, 1988), and this gives rise to tidal oscillations in stage, and the potential for flow reversals far upstream of both the estuary mouth (Wright et al., 1973; Sassi and Hoitink, 2013) and the zero isohaline (Allen, 1991). However, further upstream, the tidal waves become increasingly distorted due to bottom friction and superposition of fluvial currents (e.g., Godin, 1999), resulting in an asymptotic decline in amplitude (e.g., Jay, 1991). Complete tidal wave dissipation occurs tens to hundreds of kilometers upstream of the coast, at the “tidal limit” (or “head of tide,” “limit of tidal effects,” “tidal length”), which is taken as the upstream limit of measureable tidal oscillations in stage (e.g., Wright et al., 1973; Dalrymple et al., 1992; van den Berg et al., 2007; Ensign et al., 2013; Pittaluga et al., 2015). Since terrestrial runoff, tidal forcing, and storm surge vary with time, the tidal effects on channel form vary along the channel (Wright et al., 1973; Dalrymple and Choi, 2007). For instance, river flow responses to tidal oscillations can vary temporally with local weather effects (<day), dam releases (days), terrestrial flood waves (weeks), seasonal effects (months), or changes in climate (decades). The way in which these conditions translate to tide-influenced channel geomorphology remains largely unexplored (Phillips and Slattery, 2007; Ensign et al., 2014).

Greater insight into fluvial-tidal channel form is needed to help guide or constrain complementary studies of the transition zone, and to provide a context for coastal river system dynamics. A fruitful approach to studying the fluvial-tidal transition would be to combine work on hydrodynamics, sedimentology, land use, watershed dynamics, and geomorphology, because all are intimately coupled. However, such an approach typically is not tractable within the context of a single research project. Nevertheless, new insight on fluvial-tidal transition zone geomorphology can provide benefits to a range of studies. For instance, the research theme of processes and forms associated with the fluvial-tidal transition zone has received a great deal of recent attention (see Ashworth et al., 2015).

Much of what is known about modern fluvial-tidal channel geomorphology comes from a handful of papers. Ashley and Renwick (1983) reported that the transition from fluvial to tidal currents, and the corresponding change in cross-section shape and other metrics, should occur in a gradual manner. However, they did not address the effects of variable bedrock lithology and slope associated with their channel reach crossing the “fall line,” the crystalline bedrock to coastal plain boundary (Ashley et al., 1988). Hence, their channel properties reported as being responsive to fluvial-tidal interactions remain speculative. Gurnell (1997) found systematic channel variations in 122 cross sections along an 18 km channel reach. However, the study site only experienced the effects of the higher tides and no current reversals due to the placement of a downstream weir, and as a consequence, those findings provide limited insight. Further, Gardner and Bohn (1980) and later Ensign et al. (2013) provided a conceptual view on how terrestrial and tidal channel cross sections should differ by highlighting the characteristic change in channel properties due to the onset of tidal effects, with particular emphasis on width. Inokuchi (1989) and later Nittrouer et al. (2011b) examined particle size, channel cross sections, and long profiles of hundreds of kilometers of the lower Mississippi River. Overall, inconsistencies in sediment caliber and bed slope were interpreted as resulting from coastal backwater effects (e.g., Fernandes et al., 2016). Tidal distortion and tidal wavelength effects on channel properties were reported by Wright et al. (1973) and expressed as equilibrium between the tidal prism and equal work per unit channel bed area for the channel of a funnel-shaped estuary. Phillips and Slattery (2008) analyzed long- and cross-channel river profiles to assess the role of topography and antecedent landforms in sediment bottlenecks upstream of the modern fluvial-tidal transition, and their effects on the sediment budget and channel morphology further downstream. These effects were expressed as a systematic decline in channel slope and stream power. Together, these studies show that fluvial-tidal transition systems have a range of dynamic attributes, but few details are known about active channel dimensions and geomorphology.

A noteworthy point about these modern process-based studies is that most are from field sites with rivers that traverse a coastal plain, while the conceptual models published elsewhere to describe transition zone processes, geomorphology, and sedimentary facies were almost exclusively developed for submerged river valleys or funnel-shaped estuaries not necessarily on the coastal plain (e.g., Dalrymple and Choi, 2007; Jablonski and Dalrymple, 2016). This distinction is important because the latter will have stronger upstream channel area convergence (e.g., Dalrymple and Choi, 2007), while the low-gradient coastal plain rivers likely will have more subtle convergence. The ways in which these differences translate to processes, forms, and facies are not well understood, and few data on channel form exist to make a robust comparison.

The purpose of this study was to investigate the modern geomorphic structure of a channel reach that links fluvial-dominated and tidal-dominated river segments in the upper alluvial estuary of a coastal plain river (sensu Savenije et al., 2008). The detailed observations and analyses presented here will help improve our understanding of transition zone morphodynamics, and they will help to support the utility of generalized facies models that are taken to represent average conditions over much longer time scales (e.g., Bokuniewicz, 1995; Blum and Tornqvist, 2000; Cattaneo and Steel, 2003; Phillips and Slattery, 2007; van den Berg et al., 2007; Dalrymple and Choi, 2007; Jablonski and Dalrymple, 2016). Also, given the dynamic nature of the transition channel, it is likely that both process and form respond at time scales commensurate with land-use change, climate change, and sea-level rise (Florsheim et al., 2008). Moreover, with the relative uniformity of the modern southeastern U.S. coastal plain landscape (Hayes, 1994), it is likely that the channel features reported here may apply to many rivers that discharge to the southeastern U.S. Atlantic Bight (Fig. 1), and perhaps to rivers that traverse coastal plains in general, landscapes that occupy 5.7 × 106 km2 worldwide (Colquhoun, 1968). Overall, this work attempts to fill a gap in knowledge of the geomorphic structure of the fluvial-tidal transition channel, and it is driven by the hypothesis: Geomorphic discontinuities define the channel reach linking upstream fluvial-dominant and downstream tidal-dominant parts of the river continuum.

STUDY SITE

The Santee River is one of 20 larger and many smaller rivers that discharge to the Atlantic Ocean along an ∼1400 km section of coast (Fig. 1). The drainage area is ∼38,000 km2, with headwaters in the Blue Ridge and Piedmont Provinces, and it is one of the larger river systems in the southeastern United States (McCarney-Castle et al., 2010). The Santee forms at the confluence of the Wateree and Congaree systems at ∼230 km along channel from the coast, and it flows across the South Carolina Coastal Plain. Further downstream, the Santee bifurcates at the apex of the Santee River delta, ∼22 km inland, giving rise to the North and South Santee distributary channels, and several smaller ones (Fig. 1). Kjerve and Greer (1978) reported that during mean annual discharge, 73% of the flow occurs through the North Santee.

The Santee was dammed in 1942 at ∼150 km from the coast, along channel, and flows were redirected back to the Santee at 77 km (Fig. 1; Kjerve and Greer, 1978). Despite the presence of the dam, sediment flux to the coast is estimated to persist at 0.86 Mt yr–1 (Milliman and Farnsworth, 2005). Also, McCarney-Castle et al. (2010) conducted simulations of sediment flux over 20 yr time intervals to estimate the pre-European, predam, and postdam conditions. The corresponding values are 2.24, 5.80, and 0.81 Mt yr–1, respectively. At this time, it is not known if the channel has attained morphodynamic equilibrium in response to dam effects. However, a comparison of aerial images from 1939 and 2011 indicates that the channel pattern and width have remained relatively stable over 72 yr, except for ∼12 m of widening near the rediversion canal where flows are returned to the system (Fig. 1).

This study is focused on an ∼64 km reach between 30 km and 94 km from the mouth. For clarity, hereafter “mouth” is taken to mean “estuary mouth,” where the estuary meets the ocean (sensu Savenije, 2012). The site was chosen because a U.S. Geological Survey (USGS) gauging station at 59 km upstream of the mouth shows that the reach has intermittent tidal- and non-tidal-dominant flow conditions. The downstream limit of the study reach was set by the position where distributary channels begin, by changes in land cover, and by the presence of dikes along the channel. The upstream limit was set by the position where <0.04 m tidal oscillations were detected during low-flow conditions. Hereafter, unless otherwise noted, all distances are reported as along channel, and relative to the Highway 17A bridge (“Bridge” of Fig. 1) near Jamestown, South Carolina; distances upstream of the bridge are negative. This reference is used because the bridge is easily identified in images, and it precludes arbitrary measures of distance along a complex distributary system (Fig. 1).

Discontinuous outcrops of the Santee Formation (Siple, 1960) were observed along part of the riverbed and banks (Fig. 1), and they consist of indurated gray to buff massive limestone interspersed with layers of weakly cemented lithic limestone, dipping <10° east. In particular, three outcrops of 2–3 km in length occur along the study reach but are limited to downstream of the bridge. The three occurrences of bedrock banks are at 3 km to 7 km, 9 km to 11 km, and 19 km to 22 km (Fig. 1). Hence, in these bedrock-influenced reaches, the channel adjustments to modern conditions have been limited to the alluvial north bank. Bedrock banks were not observed upstream of the bridge despite a determined search. Together, these observations indicate that the lower study reach between 3 km to 22 km can be characterized as a mixed alluvial-bedrock river (Howard, 1998; Turkowski et al., 2008), while further upstream, it is alluvial (Fig. 1).

Tree fall, undermined or leaning trees, and intact trees in the channel indicate that parts of the system are actively shifting or widening, or both, particularly at about −25 km (Fig. 1), where the canal delivers water to the main channel. Bed sediment from 42 grab samples between −12 km and 8 km (Fig. 1) consisted of nearly pure quartz sand with a group average D50 of 0.67 mm. The salinity within 3 km of the bridge was zero during low river discharge (Yankovsky et al., 2012), and Hockensmith (2004) reported that the zero isoline is limited to the distributary channels, within 20 km of the mouth. Therefore, this study reach is part of a tidal freshwater system (e.g., Odum, 1988). There are seven tributaries along the study reach, all with mouth widths <6 m and their respective drainage areas limited to the surrounding floodplain, and their net contributions to flow are assumed to be negligible.

The USGS maintains the Jamestown gauging station at the bridge (#02171700, Fig. 1) with a pressure transducer and velocimeter that record data at 0.25 h intervals; all references to discharge are from this station. The corresponding stage datum is at 0.33 m, with mean high water (MHW), mean sea level (MSL), and mean low water (MLW) at 0.50 m, 0.31 m, and 0.16 m, respectively (relative to North American Vertical Datum of 1988 [NAVD88]). Tidal range at the estuary mouth is ∼1.16 m, with MHW 0.54 m, MSL −0.05 m, and MLW at −0.63 m (NAVD88). Tidal oscillations at the USGS station vary with discharge but range from zero at high flows to 1.3 m under low flows. Mean annual discharge from 1987 to 2005 was ∼311 m3 s–1. For discharges of ∼300 m3 s–1 the semidiurnal, mixed tide range varied but was typically <0.6 m, with highs and lows more strongly developed on spring tides. Yankovsky et al. (2012) reported that a typical flood tide lasts ∼2 h, while the ebb tide lasts ∼6 h, and high-tide velocities appear quasi-steady for 5–6 h, coincident with the duration of the ebb tide. The flood tide or upstream currents may reach 0.3 m s–1, but these peak values are short-lived. The ebb or downstream currents can be much higher, but for frequently occurring annual average discharges, they are ∼0.3 m s–1, comparable to the upstream tidal velocities.

At this study reach, Yankovsky et al. (2012) made simultaneous measurements of velocity profile and stage at two locations (“X” symbols at −4.6 km and 1.5 km in Fig. 1). They found that tidal amplitude did not change between observations sites 6.1 km apart, despite having the water depth and flow area decline by nearly 50% in the upstream direction. They also estimated tidal energy dissipation and reported that the downstream location had a nondimensional tidal velocity that was more than double that from the shallower upstream site. Moreover, they characterized the flow regime as having a substantial phase lag between free surface and velocity fluctuations. These analyses highlight the dominant effect of friction and dissipation over tidal inertial effects, and the larger phase lag at the shallower upstream end, which indicated higher tidal energy dissipation relative to the downstream site. Based on these findings, the local flow conditions in proximity to the bridge (Fig. 1) were characterized as strongly dissipative and weakly convergent (after Lanzoni and Seminara, 1998).

METHODS

Bank-top width was estimated by two methods, from a river survey and from the February 2013 image of Google Earth reflecting high-flow conditions. For the latter, the canopy-to-canopy width was measured at 1 km intervals over an 86 km reach from the mouth to 34 km upstream of the bridge (Fig. 1). Width in places without tree canopy was measured directly from the image; measurements for canopy-covered banks assumed the bank extended 5 m landward. For the bifurcating North and South Santee Rivers, the channel width was taken as the sum of both widths at the corresponding distance (e.g., after Pethick, 1992; Davies and Woodroffe, 2010).

Width was also measured directly at ∼1 km intervals along the study reach, at each cross section. A Trimble R8 global positioning system (GPS) system and a Seafloor SonarMite (Hydrolite-TM) echo sounder were installed on a 5.3-m-long vessel to acquire bathymetry at cross-section sites and along the channel. All data were collected at 1 m spacing with a vessel speed <2 m s–1. The base station for the real-time kinematic survey was part of the South Carolina GPS Virtual Reference Station (VRS) connected through cellular internet connection (Lapine and Wellslager, 2007). The GPS system gives an accuracy of 10 mm ± 1 ppm root mean square error (RMSE) horizontally and 20 mm ± 1 ppm RMSE vertically for static surveys. The soundings for bathymetry ran at 6 Hz with a frequency of 235 kHz, and accuracy was <10 mm (or 0.1% of depth), with a measurement capacity ranging from 0.3 m to 75 m. The VRS-GPS and echo sounder were integrated with a Trimble survey controller TSC2 via wireless connection. A Wilson Electronic Sleek Wireless Signal Booster was used to augment the requisite internet connection to the VRS. All field survey data were referenced to Universal Transverse Mercator 17 North and to NAVD88.

Multiple hydrographic surveys were conducted during 2013; the centerline survey was conducted during flood conditions when the USGS stage was relatively constant. The free surface profile data are presented as water surface elevations averaged over a 20 m reach (σ < 0.014 m) upstream and downstream of each cross-section profile location. Cross-section surveys took place on 11–12 March, 31 August, 17 November, and 20–21 December in 2013. Among these days, river stage varied by 2.2 m, but 41 of the 64 cross sections were surveyed at or about bank-top stage. In most cases, the vertical banks allowed the echo sounder transducer to approach to within 1–2 m. When the banks were more gradual, the hydrographic transect ended at 0.5 m water depth, and cross-section bathymetry was augmented with channel bank surveys acquired with a 5 m stadia rod and handheld leveling scope on the dry bank to the bank tops. All cross-section metrics for bank-top conditions were assessed with WinXSPro (Hardy et al., 2005).

Cross-section area-stage relations were further evaluated by converting area and corresponding stage to a proportion and plotting all curves as values ranging from 0.0 to 1.0. The concave-up curves with stage as the independent variable were well represented with a power function: A = aSb, where A = cross section area (m2), S = stage (m), a = 1, and b is the fitting parameter. This facet of the analysis provides a metric for comparing channel shapes via a “shape factor,” b. The b values ranged from 1.0 to 4.0, corresponding to rectangular to “wide V” shapes, respectively. The along-channel survey data were used to assess river sinuosity (S) expressed as the ratio of channel distance to straight-line distance between points. S was computed over 1-km-long reaches centered about each cross section, or about ten times the average river width (Leopold and Wolman, 1957).

RESULTS

Channel Planform

The 64-km-long study reach has a corresponding valley length of 45 km, giving a sinuosity of 1.42, characteristic of a meandering system. In finer detail, however, the channel has a mix of straight and meandering reaches, and in the meandering segments, there is a mix of irregular and regular patterns, with the latter being more prevalent downstream. The largest meanders are centered at 24 km, near the confluence of the distributaries (Fig. 1). Local kilometer-scale sinuosity, S, varies from 1.0 to 3.8, but 78% of the values are less than 1.2, e.g., from −16 km to 23 km (Fig. 2D).1 Therefore, the middle part of the reach is mostly straight, but beyond that, it is meandering. Given the limited extent of bedrock outcrops, the meandering part of the channel system can be characterized as unconfined. Finally, it is noteworthy that the highest downstream S values coincide with the downstream end of the bedrock outcrops, between 23 km to 27 km (Figs. 1 and 2D).

Channel Width and Depth

The Santee system exhibits a downstream exponential increase in width to the mouth. For instance, the imagery data (Fig. 2A) show that at −3 km, the channel width, w, is 93 m, but at the mouth, 62 km downstream, it is 825 m. The width convergence length, the limit of exponentially decreasing values, is estimated to be at least 94 km (after Savenije, 2012; based on data from Yankovsky et al., 2012). Since the overall study reach extends from 30 km to 94 km inland, it follows that this study reach is in the zone of channel convergence. Upstream convergence in width adheres to the expression y = 6.53 exp(0.092x) + 90, with r2 = 0.94 (Fig. 2A). These data and curve fit provide a broader along-channel context in which to view the overall study. Thus, the study site is mainly along a channel reach of gradually declining width in the upstream direction, especially upstream of the bridge.

There is a 25-km-long section, from −2 km to 23 km, with noteworthy departures in width from the overall exponential trend (Fig. 2A). The locations and values of these departures are comparable in both the image and surveyed values. In particular, both sets of data have two distinct reaches of locally high values, one at −2 km to 13 km and the other at 17 km to 23 km (Fig. 2A). The maximum departure from the trend in Figure 2A for the upstream reach occurs at 5 km with a corresponding width of 213 m, or ∼130 m wider than expected from the exponential fit. The downstream local maximum is at 20 km, and it is 75 m greater than background width. However, along the 4 km reach between these wider sections, width returns to the background trend (Fig. 2A). On the other hand, upstream of these highs, there are relatively nominal fluctuations. Field observations indicate that the aberrant highs in width coincide with the presence of the discontinuous bedrock outcrops (see Fig. 2A), and both coincide with relatively straight parts of the channel (Fig. 2D).

Average depth, d, is taken as the quotient of bank-top cross-section area of flow, A, and surveyed channel width. Values range from 0.8 m to 4.5 m, with a mean of 2.62 ± 0.85 m. Along-channel trends in d reveal two patterns of variability (Fig. 2A). From −34 km to 3 km, d exhibits a weak parabolic-type response with a peak at −17 km. However, a pronounced departure from this trend occurs with an abrupt but persistent shoaling from −14 km to −11 km. Further downstream, the variability has no clear pattern and ranges from 1.2 m to 4.8 m, and the lower values correspond to the presence of bedrock (Fig. 2A). The higher values occur with higher sinuosity S, but not exclusively (Fig. 2D) as with Nittrouer et al. (2011b). Excluding the bedrock reaches and meander effects on depth at the downstream and more tide-influenced part of the reach, d is relatively uniform and remains within a narrow range of ∼2 m. Therefore, the overall downstream trend in d when accounting for bedrock and river-bend effects reveals a 22 km section of increasing average depth followed by a decline over a distance of 17 km and then a 25-km-long relatively uniform section (Fig. 2A).

Long Profile

The center-line riverbed elevations are highly variable, ranging from −9.4 m to 3.1 m (NAVD88). Along the profile, there are several local “deeps” taken as kilometer-scale channel reaches with a 3 m to 6 m departure below the surrounding riverbed (Fig. 2B). The long profile shows a quasi-linear decline in elevation downstream, with an overall slope of 5.7 × 10−5 and r2 = 0.48. The declining trend, however, is interrupted at 3 km to 4 km, where the downstream reach is offset by a 1.3-m-high step (Fig. 2B). The upstream and downstream reaches relative to 3 km have similar trend line fits with slopes of 7.4 × 10−5 and 9.2 × 10−5, respectively, and corresponding r2 of 0.47 and 0.24, respectively. Further, along the upstream reach, the fluctuations in bed elevation are typically less than 2 m, although channel deeps of up to 6 m occur (see −17 km to −13 km; Fig. 2B). In contrast, channel deeps in the downstream reach are longer, and they occur more frequently. For instance, there are ten deeps with more than 5 m of relief in the downstream, whereas upstream, there are two.

Among the types of variability in the profile of riverbed elevation are several “plateaus” or positive-relief structures that have relatively smaller fluctuations along them, and they are ∼1 m to 3 m higher than the surrounding riverbed (Fig. 2B). For instance, there are plateaus from 3 km to 7 km, 9 km to 11 km, and at 19 km to 22 km. Comparable plateau features are not apparent upstream, although a positive-relief structure at −24 km to −22 km resembles a plateau, but the top of this feature has an irregular trend (Fig. 2B). The downstream plateaus coincide with the locations of bedrock outcrops with 2–4 km length (Figs. 2A and 2B), and together they illustrate the effects of a spatially variable occurrence of resistant bedrock on riverbed elevation.

The standard deviations of bed elevation based on a 5 km running mean range from 0.5 m to 1.7 m (Fig. 2B), and the along-channel trend has four distinct attributes. First, in the upstream, there is a net decline from an initial value of 0.7 m at −34 km to the minimum of 0.5 m at −4 km. On this overall decline, there is an extensive “high” of 0.5 m amplitude between −23 km to −8 km, e.g., centered at −17 km. This feature corresponds to the effects of the upstream channel deeps (Fig. 2B). From −4 km, the values increase, and this trend continues to the end of the survey. In particular, at 3 km to 4 km, values increase sharply from 0.5 m to 1.6 m, likely related to bedrock influence. Thereafter, the values tend to increase downstream to a maximum of 1.7 m, albeit with minor interruptions to the trend associated with the bedrock plateaus. These observations demonstrate that the downstream riverbed is more irregular relative to the upstream.

The along-channel thalweg elevations show a typical declining trend with a slope of 1.0 × 10−4 (r2 = 0.78; Fig. 2C), i.e., a factor of ∼10 greater relative to the center-line long profile. Patterns in thalweg elevation show two breaks in slope: one corresponding to the upstream relatively uniform decline to a flat-lying segment at −6 km, and the second transitioning to a highly variable downstream decline at 3 km (Fig. 2C). Over the upstream reach, from −34 km to −6 km, there is an ∼4 m decline, giving a mean slope of 1.5 × 10−4 and r2 = 0.64. This condition is followed by an 8-km-long and relatively flat reach with elevations between −2.3 m and −1.4 m. Further downstream, the data exhibit strong fluctuations that include an 8-km-long deep up to 5 m below the background elevation (centered at 16 km; Figs. 2B and 2C). The highly variable but declining elevation trend from 4 km to 30 km has a slope of 8.2 × 10−5, with relatively poor linear correlation coefficient, r2 = 0.19. As detected in the center-line profile (Fig. 2B), most of the higher thalweg elevations in the downstream reach coincide with bedrock outcrops.

The corresponding water surface profile has two breaks in slope at −2 km and 4 km, and perhaps a third along the lower 4–6 km of the survey (Fig. 2C). The upstream reach from −30 km to −2 km has a linear trend line expression of 3.39–1.72 × 10−4 (r2 = 0.99), while downstream reach, from 4 km to 22 km has a trend of 3.84–6.02 × 10−5 (r2 = 0.98). This break in slope is coincident with the transition to bedrock-influenced channel. Overall, these profile conditions are characteristic of a mild to milder slope transition that typically gives rise to an M1-type free surface profile (e.g., Dingman, 2009), most likely because the bedrock outcrops produce a backwater effect. Following the concepts of Parker (2004), the backwater length L (the upstream distance of channel flows affected by decreased free surface slope) can be estimated as L = Δy/S, where Δy is the induced change in channel flow depth at the transition, and S is the upstream riverbed slope. On the other hand, this estimate indicates that L can be computed as the intersection of the upstream and downstream free surface trend lines. It follows that L = 7.5 km, hence, L extends from bedrock outcrops at 3.5 km to −4 km (Figs. 1 and 2C). Close examination of Figure 2C shows that this backwater reach coincides with a local shoaling or flattening of the channel bed in the corresponding thalweg data (Fig. 2C). Therefore, the shoaling condition induced by backwater effects from the free surface decline in slope is limited to a 7.5 km reach, and this value is a more conservative (longer) estimate than the method of Samuels (1989). Further, using the same Δy/S approach of Yarnell (1934) reveals that the backwater effect of the bridge (Fig. 1) is on the order of 1.3 km. Here Δy is based on the nearest mean depth values upstream and downstream of the bridge (Fig. 2A). The net result is that the bridge backwater effect is less extensive than the bedrock effect. On the other hand, the backwater effect of tides can be expected to extend further upstream (Sassi and Hoitink, 2013) and therefore exert a greater influence on channel geomorphology upstream of the −4 km mark.

In summary, the long profiles from the center line and thalweg (Figs. 2B C) reveal a typical riverbed elevation decline toward the mouth, but with upstream and downstream reaches that have distinctly different attributes. In the upstream, the bed relief is typically smaller and less variable. The downstream reach has nominal slope and kilometer-scale “plateau” features that stand higher than the surrounding riverbed. It is inferred that the plateaus at 3 km to 7 km, 9 km to 11 km, and 19 km to 22 km result from resistant bedrock outcrops. Hence, properties of the lower Santee River channel are influenced by the presence of resistant bedrock, while outside of these reaches, the system is alluvial, and channel properties there can be expected to be more dynamic. Likewise, the long profile of the free surface has a particularly large break in slope that coincides with the bedrock outcrops. This transition is shown as a lower free surface slope over the bedrock reach, and this creates conditions that favor generation of a backwater effect. The backwater length is 7.5 km, and it extends from −3.5 km to 4 km (Figs. 1 and 2C). Therefore, local channel metrics upstream of −4 km likely arise from a combination of fluvial processes and tidal backwater effects.

Channel Cross Sections

Bankfull cross-section area values, A, range from 119 m2 to 554 m2, with a mean of 282 ± 82.7 m2. From −34 km to −16 km, there is a net increasing trend from 115 m2 to 324 m2, respectively (Fig. 2D). On the other hand, there is a net decline at 8 km to 30 km, from 385 m2 to 210 m2, respectively. For the channel reach between these segments, −16 km to 8 km, A is highly variable with a range of 210 m2 to 555 m2. In particular, from −16 km to −14 km, A declines by ∼50% to 207 m2 and remains in this lower range to −10 km (Fig. 2D). From −7 km to −1 km A gradually increases, and from −1 km to 1 km it nearly triples, reaching a peak of 554 m2. Further downstream, from 3 km to 30 km, there is a net decline to 230 m2 (Fig. 2D). Collectively, the data have a trend mimicking y = –x2, but of course the downstream or declining part of this apparent trend is not sustainable because of the effects of the tidal prism on area (e.g., on the coastal plain, A typically increases exponentially downstream; after Friedrichs, 2006). Overall, along-channel A values have a highly variable but convex trend, with peak values occurring at −1 km to 2 km (Fig. 2D).

In order to further characterize the variations in A, a linear trend line was applied to the 18-km-long reach that is furthest upstream (Fig. 2D) and in the alluvial part of the channel, from −34 km to −16 km (r2 = 0.74). The trend line was then extrapolated from −16 km to +4 km. This line fit illustrates how the area of the upstream section of alluvial channel can be expected to change toward the downstream, and with fluvial-dominant conditions (Yankovsky et al., 2012). Between −16 km and −1 km, A values plot substantially lower than this trend line. This result emphasizes the aberrant lower A channel reach. Moreover, this shoaling reach is bounded at the upstream and downstream ends by an ∼50% decline in A that occurs over a <2 km distance (Fig. 2D). Together, these observations reveal a channel reach of substantial and abrupt changes in channel properties.

The hydraulic radius, R, varies from 1.28 m to 4.14 m, with a mean of 2.68 ± 0.59 m, but most values are less than 3.3 m. The pattern of R with distance from upstream to downstream shows an initial increasing trend, followed by high variability likely associated with bedrock outcrops (Fig. 2E). From −34 km to −17 km, there is an increase from 1.3 m to 3.3 m, the sixth highest value. This is followed by consecutively declining values, reaching 2.2 m at −13 km, and a return to 3.1 m at −9 km. From there, the values are 2.5 m to 3.3 m to the 3 km mark, but further downstream, R values range between 1.4 m and 4.2 m and lack a clear trend (Fig. 2E).

Exploring the details of R downstream of the bridge, however, sheds light on the bedrock effects. For instance, the lower values of 1.2 m to 1.7 m coincide exactly with the presence of bedrock outcrops (Fig. 2E). Moreover, the high downstream values of 3.0 m to 4.1 m are coincident with abrupt river widening or deepening, or both (Figs. 1, 2A, 2B, and 2C). Taken together, these observations show that when the bedrock-influenced values are removed, the downstream R values have no clear trend. Therefore, from upstream to downstream, R, or channel efficiency, initially increases and then maintains a quasi-steady range. Downstream of 10 km, however, the full range of variability occurs. As is the case with A, the lowest R values are associated with bedrock outcrops (Fig. 2E).

Another means of assessing channel cross-section properties is with the rating curves of A. In all cases, plots of A as the independent variable versus stage height relative to the local thalweg give a characteristic concave-up trend. The same is true for the nondimensional representation of the same data normalized by each transect’s range of values. The power function fit applied to the nondimensional data allowed the fitted exponent, or shape factor b, to vary, and this provides a more quantitative metric for channel shape. Here, b = 1.0 corresponds to a rectangular channel, and b = 4.0 represents a wide V-shape. Overall, b ranges from 1.16 to 3.06, with a mean of 1.83 ± 0.45.

The trend in b (Fig. 2E) from −34 km to −23 km declines from 1.6 to 1.1, respectively. This is followed by an increase to 1.9 at −9 km, but further downstream, the values remain within a range of 1.5–2.1 to 8 km. Continuing downstream, the values have no particular pattern with distance, and the variability increases but remains within a range of 1.4–3.1. Since the shape factor corresponds to nondimensional channel properties, it follows that the downstream effects of bedrock (Figs. 2A and 2E) do not generate overall aberrant channel shapes. On the other hand, bedrock produces wider and shallower reaches that are rectangular but with a slight V-shape (Figs. 1, 2A, and 2E).

Overall, in going along the channel from upstream to downstream, there were consistent patterns with some metrics, and in some reaches, and high variability in others (Figs. 2B and 2C). Typically, depth, area, and hydraulic radius initially increase toward −17 km. Meanwhile, the upstream b values start with slightly varying lower values from −35 km to −17 km before undergoing a step-like increase where depth, area, and hydraulic radius decline. These trends reach a minimum and then recover, but only area continues to increase substantially to a peak at −1 km. Further downstream from 3 km to 30 km, all variables exhibit the greatest variations. In particular, bed elevation and area have a highly variable but declining trend, while widths remain relatively low. Mean depth, hydraulic radius and the shape factor fluctuate the most, and their respective locally lower values are associated with bedrock outcrops.

Field observations, and the patterns of along-channel width and profile elevation support the view that resistant bedrock affects channel properties at three discrete locations, 3 km to 7 km, 9 km to 11 km, and 19 km to 22 km. The effects of bedrock are clearly apparent in all but two metrics, sinuosity and shape factor. Typically, there are shallower and wider channels in the bedrock reaches. Also, the along-channel bathymetry shows local highs or plateaus that are consistent with the response in thalweg elevation, while channel area, depth, and hydraulic radius are locally depressed. The lower part of the Santee River is a mixed bedrock-alluvium system, and the transition from alluvium to resistant bedrock clearly has an influence on channel metrics. When channel metrics from bedrock segments are removed, the respective trends with distance show reduced scatter. Bedrock also produces a measureable decrease in free surface slope, and this gives rise to a backwater effect from −3.5 km to 4.0 km. Finally, it should be noted that two of the 10 metrics highlighted in Figure 2 were directly computed from cross-section area of flow A, those being the hydraulic radius R, and mean depth d, and therefore can be expected to covary accordingly. The other metrics, however, are independent of A.

DISCUSSION

Tide-influenced rivers typically have cross-section area of flow, A, that increases exponentially toward the coast (e.g., Nichols et al., 1991; Friedrichs, 2006; Savenije, 2012; Nittrouer et al., 2011b). With the Santee River, however, there is an ∼22-km-long discontinuous bedrock reach in which A declines downstream (Fig. 2D). Of course, A cannot decrease indefinitely because the tidal prism must be accommodated with greater A toward the mouth. The declining trend therefore is likely an artifact of bedrock influence. For instance, the trend in A for bedrock sections alone shows a relatively uniform downstream decline, and it appears that this trend is translated onto the juxtaposed alluvial reaches (Fig. 2D). Hence, bedrock can strongly influence alluvial channel properties in low-gradient, seemingly transport-limited coastal plain channels, similar to the Mississippi River, with segments of erosion-resistant but unconsolidated sediment (Nittrouer et al., 2011a). These observations highlight caveats when using simplified one-dimensional process models to help establish morphodynamic equilibrium of tide-influenced river systems (e.g., Pittaluga et al., 2015).

Despite the confounding effects of bedrock on channel properties, Yankovsky et al. (2012) detected a geomorphic response to the fluvial-tidal transition zone. In particular, they identified a section of channel characterized by an abrupt near doubling of A from 1 km to 4 km upstream of the bedrock outcrops, e.g., in the alluvial part of the system (Figs. 1 and 2D). They reasoned that the sharp increase in area is likely associated with the observed rapid tidal energy dissipation, and the high rate of dissipation may correspond to the onset of a fluvial-tidal transition in hydrodynamic processes. Hence, Yankovsky et al. (2012) identified the downstream limit of a fluvial-tidal transition reach as an abrupt increase in A.

The upstream limit of the transition reach also is associated with a sharp change in A. For instance, upstream of −1 km, the A values remain relatively low to −16 km (Fig. 2D). At −17 km, area increases by ∼60%, followed by steadily declining A values in the upstream. It is proposed that the upstream peak in A is associated with the upstream limit of the fluvial-tidal transition zone. Further, the limits of the transition reach coincide with the notable discontinuities in flow depth, hydraulic radius, channel shape, and sinuosity (Figs. 1 and 2). Taken together, these data indicate that the fluvial-tidal transition can be readily identified as a channel reach of substantially lower A with abrupt upstream and downstream boundaries. It is noteworthy that widths at, and on either side of the transition reach are relatively uniform (Fig. 2A).

For the Santee River, it appears that the geomorphic fluvial-tidal transition reach is between −1 km and −17 km (Figs. 1 and 2C). However, the bedrock backwater length, L, has an upstream limit at −4 km. Therefore, the transition reach has a well-defined upstream limit, but the downstream limit is more ambiguous due to the backwater effects. The downstream extent of the fluvial-tidal transition reach may be in the vicinity of −1 km, or it may extend much further downstream. It follows that, the shoaling transition channel reach extends from −17 km to at least −4 km (Figs. 1 and 2C), i.e., at least 13 km long.

Similar along-channel shoaling has been reported for other southeastern U.S. coastal plain rivers. The pattern of interest is a decline in A that persists on the order of tens of kilometers, and the recovery to background values (Figs. 2D and 3). The Potomac River shows such a trend between 75 km and 100 km from the river mouth, and the James River at 60 km to 75 km, respectively (Figs. 3A and 3B; data taken from Friedrichs, 2006). Also, the Altamaha River has a similar pattern at 49 km to 59 km (Fig. 3C). Hence, a 10–30 km channel reach with uncharacteristically lower cross-section area appears to be a recurring feature in some coastal plain rivers of the southeastern United States. It is proposed that this pattern of lower area is a type of geomorphic discontinuity.

Lastly, variations in transition zone A are not necessarily associated with similar or comparable variations in channel width. Since convergence in A has such an important effect on tidal properties up river, including current direction and magnitude (e.g., Langbein, 1963; Wright et al., 1973; Allen, 1991; Friedrichs and Aubrey, 1988; Dalrymple and Choi, 2007), a more meaningful assessment of upstream flood tide tidal prism convergence is best represented through A, and at the very least, one should not rely exclusively on trends in channel width as a proxy for trends in A. In the case of the Santee River, channel width is not a reliable indicator of the fluvial-tidal transition channel.

Conceptual Model

Based on the field observations, and in consideration of the work of Ashley and Renwick (1983), Allen (1991), Gurnell (1997), van den Berg et al. (2007), and Sassi and Hoitink (2013), the following augmentation to the prevailing fluvial-tidal facies model of Dalrymple and Choi (2007), Dalrymple et al. (2012), and Jablonski et al. (2016) is proposed. Of course, the positions of the various attributes of the fluvial-tidal transition vary with time, and so this revised conceptual view is presented as channel properties that develop in response to the recurring channel-forming processes (Fig. 4A). The largest departure from Dalrymple and Choi (2007) is an extensive channel reach where the fluvial and tidal energies are of comparable magnitude (Fig. 4B), as first reported for the Santee River by Yankovsky et al. (2012). Bedrock effects were omitted from this conceptual framework.

Between the tide-influenced fluvial and the fluvial-influenced tidal parts of the system, there exists an abrupt geomorphic discontinuity in A (Fig. 4A). From the upstream extent of tidal oscillations (the tidal limit) to downstream, the transition reach is identified by a local high in flow area, A, followed by a sustained decrease that may persist on the order of tens of kilometers. Further downstream, A abruptly recovers and attains a local peak value, followed by a rapid decline, perhaps related to the onset of rapid tidal energy dissipation, as proposed by Yankovsky et al. (2012). At the upstream local high in A there is the limit of current reversals, or the transition from unidirectional to bidirectional flows. Further downstream, A develops the expected exponentially increasing trend to accommodate the tidal prism (Figs. 2D and 4A), with the salinity limit taken as being proximal to the limit of fluvial influence (Odum, 1988). The channel reach with lower A is taken as the fluvial-tidal transition reach. This generalized conceptual view highlights a geomorphic discontinuity in A, and it results from a simplification of the most salient and transferable features detected in a coastal plain river (Figs. 3 and 4A).

In the absence of bedrock effects, coastal plain riverbed shoaling can be expected to arise from backwater effects due to tides (Sassi and Hoitink, 2013) and the river-to-ocean transition (Fernandes et al., 2016). Santee River tidal oscillations in stage were <0.04 m at −35 km (Fig. 1). Although tidal oscillations can be expected to decline asymptotically further upstream (e.g., Jay, 1991), for practical considerations, it is assumed that the tidal limit is at about −40 km (Fig. 1), or ∼100 km from the mouth. Following the approach of Parker (2004), the backwater length L for the river-ocean transition is up to ∼53 km, using a downstream channel depth of 3.23 m (where average depth is 2.41 ± 0.82 m), and a downstream free surface slope of 6.02 × 10−5 (Figs. 2A and 2C). It follows that the ocean backwater effects may extend up to the middle of the bedrock outcrops. These observations indicate that the abrupt changes in A that define the fluvial-tidal transition upstream of the bedrock outcrops most likely developed in response to tidal backwater effects.

Another facet of the fluvial-tidal transition is that the fluvial and tidal energies of flow frequently attain comparable magnitude. Figure 4B summarizes the distribution of relative flow energy, similar to the conceptual models presented by Dalrymple and Choi (2007), Dalrymple et al. (2012), and Jablonski et al. (2016). There are two noteworthy features of this revised view: (1) There is an extensive reach of nearly equal flow energy conditions (length-scale order tens of kilometers) where each process is ascribed ∼50% of the respective energy budget (after Yankovsky et al., 2012), and (2) the transition to fluvial or tidal dominance is abrupt, as opposed to gradual. For instance, the large changes in cross-section area of flow that define the transition reach occur over relatively short distances (length-scale order kilometers). It is proposed that this transition be referred to as the “fluvial-tidal geomorphic discontinuity.”

Overall, along the Santee River continuum, the fluvial -and tidal-dominant parts of the system are joined by a channel reach of recurring similar fluvial and tidal flow energies, and with distinct shoaling. In particular, the fluvial-tidal discontinuity is on the order of 10% of the total tide-influenced channel length. Within this context, the modern fluvial-tidal transition zone should be characterized as being centered on the channel reach where conditions are such that the frequently occurring downstream river discharges are comparable to upstream tidal discharges, and the transition reach may retain conditions that favor intermittent and short-lived changes in ebb and flood tide dominance that may give rise to conditions favoring sediment accumulation and declining cross-section area. Moreover, the recurring comparable fluvial and tidal energies dictate that the limit of current reversals must reside within the transition reach (Fig. 4).

Finally, the role of bedrock on the fluvial-tidal transition cannot be overlooked, especially since it seems that the presence of bedrock is a recognized feature of low-gradient coastal plain rivers (e.g., Nittrouer et al., 2011a). In the case of the Santee River, it is proposed that the bedrock outcrops contributed to the rapid dissipation of tidal energy over a relatively short bedrock reach. If the bedrock outcrops were not present, the fluvial-tidal geomorphic discontinuity, the tidal limit, and other tidal river features would have occurred further upstream. Hence, tide-influenced coastal plain river features and their respective positions along the channel can be strongly influenced by bedrock conditions that promote the development of backwater effects, and dissipation of tidal energy. The same can be expected for managed or stabilized tide-influenced channels.

CONCLUSIONS

The channel reach linking the fluvial- and tidal-dominant parts of the Santee River has distinct geomorphic features that give rise to a fluvial-tidal geomorphic discontinuity. The discontinuity is ∼10% of the length of the tide-influenced channel, and it is apparent as an abrupt transition in various channel metrics, but cross-section area of flow best depicts the start and end of the transition reach. In particular, from downstream to upstream of the transition reach, the flow area increases from 380 m2 to 550 m2, declines to ∼200 m2, and persists about this value for ∼10 km before increasing to over 300 m2. From there, in the predominantly fluvial part of the system, area declines at ∼20 m2 km–1. The transition reach is at least 13 km long and centered at ∼68 km upstream of the estuary mouth. The downstream extent of the discontinuity is influenced by backwater effects that result from discontinuous bedrock outcrops. Taken together, these observations, combined with an earlier hydrodynamics study (Yankovsky et al., 2012), indicate a need for revisions to the prevailing conceptual models of the fluvial-tidal transition zone. The modern fluvial-tidal transition channel should be characterized as a channel reach with abrupt changes in geomorphic structure. Also, these changes are associated with recurring and comparable upstream and downstream, or fluvial and tidal, discharge or hydrodynamic conditions.

ACKNOWLEDGMENTS

This work was supported by National Science Foundation EAR GLD award number 10-53299 and National Aeronautics and Space Administration (NASA) award number EPSCOR NNX16AR02A. Kyungho Jeon acquired the field data as part of a thesis project, with support from Jeff Ollerhead and Matt Balint. Alexander Yankovsky, Miles O. Hayes, and Allan James provided insightful commentary during the development this manuscript. Reviews by Dale Leckie and one anonymous reviewer helped improve this contribution.

1GSA Data Repository item 2017186, a table of the data presented in Figure 2, is available at http://www.geosociety.org/datarepository/2017 or by request to editing@geosociety.org.
Science Editor: David I. Schofield
Associate Editor: Joan Florsheim
Gold Open Access: This paper is published under the terms of the CC-BY license.

Supplementary data