Developing Hydraulic Geometry Relationships with Piedmont Reference Reaches

and Testing Urban and Rural Regional Curves

NR 595G Project

Brian Lowther

Introduction

Streams and rivers play an important role in providing fresh water and recreation for the human population; yet the degradation of streams and rivers is at an all time high. More than one-third of streams are classified as impaired or polluted, while freshwater withdrawals prevent major rivers from flowing into the sea year round (Bernhardt et al., 2005). The National Research Council (1992) defined stream restoration as the “various techniques used to replicate the hydrological, morphological, and ecological features that have been lost in a stream due to urbanization, farming, or other disturbance.” Traditionally, stream restoration has relied on straightening, widening, deepening, and hardening banks and channels, as well as, forcing streams to have static stream geometry to control erosion and protect private and public lands. Recent developments in the approach to stream restoration has led to the use of a natural-channel approach that is based on computational models and equations.

Over the past decade, the natural channel design approach has been adopted by the natural resource management organizations in North Carolina. This design approach uses regional relationships for bankfull channel dimensions and reference reach geometry data. Much of the need for restorations in North Carolina is due to degradation of streams from channelization, dredging, and loss of riparian vegetation. This results in incised streams with unstable banks and features, as well as, poor habitats. Options for restoring these incised streams include: construction of a new stable channel at the floodplain elevation, enhancement of the floodplain at the existing channel elevation, or stabilization of streambanks already in place. Procedures for natural channel design include analog, empirical, and analytical methods. In order to implement the natural channel design training in geomorphology, hydrology and engineering is needed, as well as, an understanding of principles from multiple disciplines, such as fishery biology and plant science. An important part of natural channel design is finding stable streams in order to use them as references for design parameters. The reference reach is used to develop natural channel design criteria from measured morphological relations associated with the bankfull stage for a specific stable stream type (Rosgen, 1998).

These reference reaches have developed a stable dimension, pattern, and profile such that, over time, channel features are maintained and the stream system neither aggrades nor degrades (Rosgen, 1996). This restoration approach relies on the accurate identification of the bankfull channel dimension and discharge. Hydraulic geometry relationships that relate bankfull stream channel dimensions and discharge to watershed drainage area are therefore useful tools for stream restoration design. Dunne and Leopold (1978) first developed hydraulic geometry relationships, also called regional curves, for the bankfull stage.

Over a hundred reference reaches have been used for stream restoration projects in the past few years. Data has been collected on North Carolina streams by engineering firms and the Ecosystem Enhancement Program (EEP) and is currently applied to restoration projects across North Carolina. This paper will focus on reference reach validation, hydraulic geometry relationships, and comparison of created relationships to previously developed equations.

Hydraulic geometry relationships are often used to predict channel morphology features and their corresponding dimensions. Hydraulic geometry relationships for streams throughout North Carolina vary with hydrology, soils, and extent of development within a watershed (Doll et al., 2002). Therefore, it is necessary to develop curves for various levels of development in each hydrophysiographic region. 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) (Harman et al., 1999). Both urban and regional curves have been developed for the Piedmont region (Harman et al. 1999, and Doll et al., 2002). Doll et al. (2002) focused on quantifying the effect of urbanization of the watershed on channel size. The study found an increase in bankfull average width and depth with an increase in urbanization. Both these studies use a wide range of channel sizes to develop good regression equations of hydraulic geometry relationships in the Piedmont of North Carolina.

For this study, survey data will be collected at each selected reference reach. Then a geographic information system (GIS) program, ArcMap, will be used to locate and map the streams. Additional software, ArcHydro, will be used to delineate the watersheds. The different watersheds will be evaluated to find the percent of impervious area in each drainage area. The data from the reference reaches will be used to test whether or not similar regression equations can be created for these piedmont reference streams as well as how well the developed equations for urban and rural streams predict the actual streams channel dimensions.

Method and Materials

Field Survey and Calculations

Over the past summer, reference reaches from the EEP projects were visited and assessed for reference reach quality. The sites were evaluated focusing on correct pattern, profile, and dimension for a reference reach. The primary factor used to eliminate sites was bankfull not at the top of the bank (incision) and a secondary reason was poor bank conditions. The length of the reach was walked and then given a score using a rapid assessment score sheet (see Appendix). Field visits were conducted to verify location of the reference reach, evaluate current condition, and obtain permission to survey the site. Selected sites were surveyed and documented. The locations reference reaches are shown in Figure 1.

Figure 1: North Carolina map showing physiographic provinces and reference reach sites.

At each site, a Total Station survey was completed with a team of 3 or 4. The survey involved two parts: longitudinal profile of the channel and measuring the channel cross-sections. The longitudinal survey was completed over a stream length equal to at least 20 bankfull widths (Leopold, 1994). Points were taken at the morphological features: thalweg (channel bottom), edge of water, bankfull stage, and top of bank. The thalweg was divided into identified distinct features: riffle, run, pool, and glide. Many of the streams were too small to have distinct runs and glides. Cross-sections were taken at riffles and pools where clear bankfull indicators were present. The inlet and outlet points of the reach were recorded using a handheld GPS.

In order to accurately calculate the bankfull cross-sectional area it was important to correctly identify bankfull. It is generally accepted that bankfull stage corresponds with the discharge that fills a channel to the elevation of the active floodplain (Harmen et al., 1999). 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 (Harman et al., 1999).

Bankfull hydraulic geometry was calculated from the survey data at each riffle cross section. Width, depth, cross-sectional area and hydraulic radius were calculated using the cross-section survey data. Figure 2 shows a sample riffle cross-section that was used for the calculations. The values were averaged for each reach.

Figure 2: Sample Cross-Section Graph for an Unnamed Tributary of Lake Raleigh

To obtain a bankfull discharge (Q) estimate, at the stable ungaged watersheds, Manning’s equation was used as:

Q = 1.4865 AR^2/3 S^1/2 / n

where R = hydraulic radius, A = cross sectional area, S = average channel slope, and n = roughness coefficient (Harmen et al., 1999). The slope was calculated using longitudinal survey data for each reach. In order to find the roughness coefficient for each reach a pebble count was conducted on each cross section. These measurements were taken in a zigzag method along the cross section within the restored stream. Individual particle measurements were taken along the intermediate axis of all particles (or estimated for very small particles) according to protocols developed by Wolman (Leopold et. al, 1964). Particle sizes may be recorded on a worksheet and cumulative frequency calculated. The 84^th percentile was found and used along with the hydraulic radius in the Limerinos (1970) equation to find Manning’s n value:

n = 0.0926 R^1/6 / 1.16 + 2.0 log₁₀ ( R / d₈₄)

where n = Manning’s n value, R = hydraulic radius, ft and d₈₄ = the particle size, ft, which 84 percent of the sediment mixture is finer.

GIS and ArcHydro

As stated earlier, GIS and ArcHydro were used to locate the streams, find drainage areas, and calculate impervious area for each reach. The EEP provided stream, and road vector shape files, which originally came from the North Carolina Center for Geographic Information and Analysis, in cooperation with the North Carolina Division of Water Quality. Digital elevation models (DEMs) for Alamance, Chatham, Franklin, Guilford, Orange, and Wake Counties were obtained from the North Carolina Floodplain Mapping Program (NCFPM, 2003). This DEM has a 20-foot resolution created from high-resolution Light Detection and Ranging (LIDAR) data. USGS topologic maps downloaded at the NCDOT site were used in order to reference where stream was located (USGS, 2001). All the data was projected to NAD 1983 State Plane North Carolina FIPS 3200 Feet. The first step was to create a new layer for the GPS points of each stream. GPS points were added to ArcMap as a layer file that included inlet and outlet points for 17 different reaches. However, data was only completed for 12 streams. County data was clipped for each stream’s drainage area by exporting the DEM data and creating a new file.

The DEM was then processed using ArcHydro to delineate the watershed boundary for each stream. The Batch Terrain Preprocessing tool was used for watershed delineation and stream extraction. This tool was ideal in this situation because it does a number of steps at once. The Fill command was used to process each DEM. The default settings were used to determine number of accumulated grid cells that represents the source of a stream channel and stream threshold. The default for the stream threshold was set to 1% of the cells. For more consistency a value can be added as the number of grid cells instead of a percent. After running the Fill command the temporary files were added; cat, fac, fdr, fil, lnk, shdrelief, str, DrainagePoint, DrainageLine, Catchment, and AdjointCatchment. The point delineation tool was used to find the watershed for the outlet of the stream by clicking on the outlet GPS point and then snapping to the stream network. The drainage area was converted from square feet to square Kilometers.

The land use data was downloaded in order to find the percent of impervious area for each watershed (NLCD, 2001). Natural Resource Conservation Service (NRCS) guidelines were used along with the metadata from the National Land Cover Database to assign an impervious cover percentage to each land use (NRCS, 1986). To calculate the percent impervious for each watershed, data was first clipped using the extract by mask tool to all the watersheds and then exported for each stream. The average impervious area values used for the land uses were:

National Land Cover Database	Average Impervious
Developed, Open Space	12%
Developed, Low Intensity	38%
Developed, Medium Intensity	65%
Developed, High Intensity	85%

Table 1: Percent Impervious for NLCD Land Use

These land use percentages were then used to estimate the impervious percentage for each stream’s watershed.

Results

Table 2 summarizes field measurements and hydraulic geometry data for each reference reach. The streams were broken into two categories based on the percent impervious of the watershed. Piedmont streams with greater than 10 percent impervious surface in their drainage area (Schueler, 1995) were considered urban, which was also used to develop the urban curves (Doll et al., 2002).

Name	Shape Area (km^2)	Bkf XSEC Area, Abkf (sq m)	Discharge (cms)	Width, Wbkf (m)	Mean Depth, Dbkf (m)	Wetted Perimeter (m)	Hydraulic Radius (m)	Slope (%)	Roughness Coefficient, n	D84	Impervious Surface Percentage
Rural
UT to UT to Billy's Creek	0.4	1.3	2.19	3.2	0.4	4.2	0.2	1.52	0.021	49.75	0.00%
UT to Varnals Creek	1.1	1.5	2.28	4.21	0.4	5.7	0.6	1.70	0.026	75.74	0.09%
Ut to Lake Raleigh	0.2	1.1	2.91	3.5	0.3	4.1	0.0	3.62	0.029	28.37	0.38%
Morgan Creek	21.3	6.2	8.54	10.1	0.6	6.6	0.3	0.56	0.029	85.84	0.72%
Landrum Creek	5.4	1.3	1.02	4.2	0.3	4.7	0.2	0.76	0.031	113.56	0.90%
UT to Cane Creek A3	2.2	2.8	4.78	5.5	0.5	6.7	0.9	0.90	0.032	43.80	1.58%
MidPines	3.3	2.6	3.81	4.7	0.5	6.5	0.3	0.46	0.031	23.88	5.43%
UT to Lake Wheeler	0.9	1.6	3.22	3.2	0.5	4.9	1.1	0.63	0.047	7.39	5.47%
Urban
Terrible Creek	6.0	2.5	2.91	5.9	0.4	4.0	0.1	0.49	0.033	45.00	12.65%
UT to SW BeaverDam	0.7	1.7	3.22	3.8	0.5	6.5	0.0	1.43	0.021	39.93	14.81%
UT to Lake Jeanette	0.3	2.2	4.90	5.8	0.4	11.3	1.9	0.95	0.037	7.08	20.93%
Abbots Farm	1.7	2.0	3.24	5.9	0.4	4.9	0.2	1.18	0.038	31.53	22.80%

Table 2: Watershed Data

The relationships for bankfull discharge, cross-sectional area, width, and mean depth as functions of watershed area for the reference reaches in the Piedmont of North Carolina are shown in Figure 3. The graphs were created similarly to that developed by Harmen et al. (1999) and Doll et al. (2002) in order to directly compare the results of the regression equations. The data was graphed on a log scale and a trend line was added. Graph 1 shows the data and the trend line. The low R² value illustrates that the line does a poor job of predicting a trend. This could be explained by that fact that these are all small streams that are close in size.

Figure 3: Hydraulic Geometry Relationships of: (a) Bankfull Cross-Sectional Area, (b) Discharge, (c) Width, and (d) Depth Compared to Watershed Area for Reference Reaches in the North Carolina Piedmont.

Results from the data show a poor regression fit due to lack of significant variation in stream size. The low coefficients of determination indicate these power functions explain a low percentage of the variability of the four hydraulic geometric variables.

The data was then used to test relationships developed for rural and urban streams by Harmen et al. (1999) and Doll et. al. (2002) that have high r² values. The relationships are shown below:

Rural Curves

A_bkf = 1.08 A_w ^0.67 r² = 0.95

Q_bkf = 1.32 A_w ^0.71 r² = 0.97

W_bkf = 3.14 A_w ^0.36 r² = 0.91

D_bkf = 0.38 A_w ^0.29 r² = 0.86

Urban Curves

A_bkf = 3.02 A_w ^0.65 r² = 0.95

Q_bkf = 4.77 A_w ^0.63 r² = 0.94

W_bkf = 5.43 A_w ^0.33 r² = 0.88

D_bkf = 0.54 A_w ^0.33 r² = 0.87

Q_bkf = bankfull discharge in cubic meters per second (cms), Aw = watershed drainage area in square kilometers (sq km), A_bkf = bankfull cross-sectional area in square meters (sq m), W_bkf = bankfull width in meters (m), and D_bkf = bankfull mean depth in meters (m) (Doll et al., 2002).

Tables 3-6 shows the results of estimating area, discharge, width, and depth with the urban and rural curves. To compare the results for the different curves, the percent error was calculated to find the error for each curve compared to the measured value and the percent difference was calculated to see the difference between the urban and rural curves.

Name	Area (m^2)	Urban Curve Estimate	Rural Curve Estimate	Urban	Rural
Rural				Percent Error	Percent Error	Percent Difference
UT to UT to Billy's Creek	1.27	1.56	0.55	22.93	-56.92	96.20
UT to Varnals Creek	1.51	3.27	1.17	117.35	-22.08	94.44
UT to Lake Raleigh	1.08	0.91	0.32	-15.47	-70.86	97.46
Morgan Creek	6.24	22.04	8.38	253.47	34.38	89.82
Landrum Creek	1.32	9.07	3.35	587.70	154.40	91.99
UT to Cane Creek A3	2.78	5.08	1.85	83.01	-33.50	93.39
MidPines	2.56	6.62	2.42	158.04	-5.47	92.75
UT to Lake Wheeler