Bankfull Hydraulic Geometry Relationships for

North Carolina Streams

William A. Harman¹, Gregory D. Jennings¹, Jan M. Patterson¹,

Dan R. Clinton¹,Louise O. Slate, Angela G. Jessup²,

J. Richard Everhart and Rachel E. Smith¹

Abstract

Bankfull hydraulic geometry relationships, also called regional curves, relate bankfull stream channel dimensions to watershed drainage area. This paper describes results of bankfull hydraulic geometry relationships developed for North Carolina Piedmont streams. Gage stations were selected with a minimum of 10 years of continuous or peak discharge measurements, no major impoundments, no significant change in land use over the past 10 years, and less than 20% impervious cover in the watershed. To supplement data collected in gaged watersheds, stable reference reaches in un-gaged watersheds were also included in the study. Cross-sectional and longitudinal surveys were measured at each study reach to determine channel dimension, pattern, and profile information. Log-Pearson Type III distributions were used to analyze annual peak discharge data for USGS gage station sites. Power function relationships were developed using regression analyses for bankfull discharge, channel cross-sectional area, mean depth, and width as functions of watershed drainage area. The bankfull return interval for the gaged watersheds ranged from 1.1 to 1.8, with a mean of 1.4 years. Continuing work will expand this database for the North Carolina Mountains, Piedmont, and Coastal Plain physiographic provinces.

Key Words: Hydraulic Geometry, Regional Curve, Bankfull, Flood Frequency Analyses
 
 

Introduction

Stream channel hydraulic geometry theory developed by Leopold and Maddock (1953) describes the interrelations between dependent variables such as width, depth and area as functions of independent variables such as watershed area or discharge. These relationships can be developed at a single cross section (at-a-station) or across many stations along a reach (Merigliano, 1997). Hydraulic geometry relationships are empirically derived and can be developed for a specific river or watershed in the same physiographic region with similar rainfall/runoff relationships (FISRWG, 1998).

Hydraulic geometry relationships are often used to predict channel morphology features and their corresponding dimensions. This paper describes the process used in North Carolina to develop hydraulic geometry relationships at the bankfull stage. Results for the rural Piedmont physiographic region are presented. Bankfull hydraulic geometry relationships, also called regional curves, were first developed by Dunne and Leopold (1978) and related bankfull channel dimensions to drainage area. Gage station analyses throughout the United States has shown that the bankfull discharge has an average return interval of 1.5 years or 66.7% annual exceedence probability (Dunne and Leopold, 1978; Leopold, 1994). A primary purpose for developing regional curves is to aid in identifying bankfull stage and dimension in un-gaged watersheds and to help estimate the bankfull dimension and discharge for natural channel designs (Rosgen, 1994).
 
 

Field Indicators of Bankfull Stage

The correct identification of the bankfull stage in the field can be difficult and subjective (Williams, 1978; Knighton, 1984; and Johnson and Heil, 1996). Numerous definitions exist of bankfull stage and methods for its identification in the field (Wolman and Leopold, 1957; Nixon, 1959; Schumm, 1960; Kilpatrick and Barnes, 1964; and Williams 1978). The identification of bankfull stage in the humid Southeast is especially difficult because of dense understory vegetation and long history of channel modification and subsequent adjustment in channel morphology. It is generally accepted that bankfull stage corresponds with the discharge that fills a channel to the elevation of the active floodplain. The bankfull discharge is considered to be the channel forming agent that maintains channel dimension and transports the bulk of sediment over time. Field indicators include the back of point bars, significant breaks in slope, changes in vegetation, the highest scour line, or the top of the bank (Leopold, 1994). The most consistent bankfull indicators for streams in the rural Piedmont of North Carolina are the highest scour line and the back of the point bar. It is rarely the top of the bank or the lowest scour or bench.

Study Area

North Carolina contains three major physiographic provinces: Mountains, Piedmont, and Coastal Plain. Because rainfall/runoff relationships vary by province and land cover, separate bankfull hydraulic geometry relationships are being developed for rural, suburban, and urban areas for each physiographic region (total of 9 regional curves). It may be necessary to further stratify the data for unique areas such as high rainfall areas in the Mountains and the Sandhills bordering the Piedmont and Coastal Plain. To date, data collection efforts have focused on the rural Piedmont and Mountains.

Figure 1: North Carolina map showing physiographic provinces with gaged and un-gaged study reaches.

USGS gage stations were identified with at least 10 years of continuous or peak discharge measurements, no major impoundments, no significant change in land use over the past 10 years, and less than 20% impervious cover over the watershed area. To supplement data collected in gaged watersheds, stable reference reaches in un-gaged watersheds were also selected for data collection using the same criteria. Figure 1 shows the relative locations of gaged and un-gaged study reaches.

Methodology

Data Collection

The following gage station records were obtained from the United States Geological Survey: 9-207 forms, stage/discharge rating tables, annual peak discharges, and established reference marks. At the gage, bankfull stage was flagged upstream and downstream of the gage station using the field indicators listed above. Once a consistent indicator was found, a cross-sectional survey was completed at a riffle or run near the gage plate. Temporary pins were installed in the left and right banks, looking downstream. The elevations from the survey were related to the elevation of a gage station reference mark. Each cross section survey started at or beyond the top of the left bank. Moving left to right, morphological features were surveyed including top of bank, bankfull stage, lower bench or scour, edge of water, thalweg, and channel bottom (Harrelson et al., 1994; U.S. Geological Survey, 1969). From the survey data, at-a-station bankfull hydraulic geometry was calculated.

For each reach, a longitudinal survey was completed over a stream length equal to at least 20 bankfull widths (Leopold, 1994). Longitudinal stations were established at each bed feature (heads of riffles and pools, maximum pool depth, scour holes, etc.). The following channel features were surveyed at each station: thalweg, water surface, low bench or scour, bankfull stage, and top of bank. The slope of a line fitted through the bankfull stage indicators was compared to a line of best fit through the water surface points. Leopold (1994) used this technique to verify the feature as bankfull if the two fitted lines were parallel and consistent over a long reach. The longitudinal survey was carried through the gage plate to obtain the bankfull stage. Using the current rating table and bankfull stage, the bankfull discharge was determined. The stream was classified using the Rosgen (1994) method.

Data Analyses

Log-Pearson Type III distributions were used to analyze annual peak discharge data for the USGS gage station sites. Procedures outlined in USGS Bulletin #17B Guidelines for Determining Flood Flow Frequency were followed (U.S. Geological Survey, 1982). USGS recommends Log-Pearson distributions because the log transformation removes positive skew from the data. Generalized skew coefficients and corresponding mean square errors for the Blue Ridge/Piedmont and Coastal Plain are 0.195 and 0.038, respectively (Pope, 1999). For this study, a range of exceedance probabilities from 0.9950 to 0.0100 was chosen. This range represents recurrence intervals between 1.005 and 100 years, with focus between the 1 and 2 year recurrence interval. The annual exceedance probability was calculated as the inverse of the recurrence interval. Exceedance probabilities were plotted as functions of corresponding calculated discharge measurements on log-probability paper, and a regression line was fit to the data. The bankfull discharge recurrence interval was then estimated from the graph.

Ungaged stream reaches were also surveyed to provide points in watersheds with relatively small drainage areas. To obtain a bankfull discharge (Q) estimate, at the stable ungaged watersheds, Manning’s equation was used as:

where R = hydraulic radius, A = cross sectional area, S = average channel slope or energy slope, and n = roughness coefficient estimated using the bankfull mean depth and channel bed materials. Flood frequency analyses was not completed on ungaged streams.
 
 

Results and discussion

The at-a-station hydraulic geometry relationships for bankfull discharge, cross-sectional area, width, and mean depth as functions of watershed area for the rural Piedmont of North Carolina are shown in Figures 3a-d. These relationships represent 10 USGS gage stations and 3 un-gaged reaches ranging in watershed area from 0.2 to 128 mi². The best-fit regression equations and upper and lower 95% confidence limits are shown for each relationship. The power function regression equations and corresponding coefficients of determination are:

Q_bkf = 66.57 Aw ^0.89; (R² = 0.97) (2)