5.11 Roughness Data

Roughness data required for a model include estimates of the surface roughness coefficients, or surface friction values, for the channel and the right and left floodplain areas for every cross section in the model. Historically, engineers have used Manning's n values for nearly all floodplain modeling studies.

Estimation of Manning's n

The roughness values assigned to the channel and floodplain of a stream are generally considered to have the most uncertainty of any hydraulic or hydrologic variable in the model. The selection of an n value is as much an art as a science and there is no hard and fast rule that allows the engineer to precisely determine the n value for a specific situation with a high level of confidence. The factors that affect channel roughness include the following:

To collapse all these parameters into a single value is difficult, to say the least. For estimates of the floodplain n, the engineer typically bases the adopted values on vegetation, land use, or both. For channel and especially for floodplain estimates, the time of year is also important. Manning's n varies considerably from summer to winter, when foliage is typically less. The n value should be estimated for the time of year when floods occur.

Sensitivity tests should also be performed to evaluate the effect of varying the value of n on the final results. The engineer's best estimate could easily be 20 percent off from the "true" value of n. Therefore, a conservative analysis of floods could use the upper limit of a range of likely n values. Similarly, a lower range of possible n values could be used where velocity estimates are needed, as in the design of erosion prevention measures such as riprap (rock revetment). A variety of techniques can be applied to the stream reach to assist the engineer in making a determination.

As discussed in the sections that follow, engineers can apply experience, tables, picture comparisons, and the Cowan formula or similar techniques to estimate n values for different channel segments of the study stream. A straight or weighted average of some or all of these techniques can be applied to initially select the channel n. Reasonable adjustments may then be made during the calibration process. For example, floodplain n values can be estimated from tables and modified from aerial photographs showing the locations of vegetation changes.

Judgment/Experience.

Engineers who regularly work on open channel hydraulic studies can develop an intuitive feel for appropriate n values. However, one should never rely on experience or judgment alone, but evaluate n with many different techniques before adopting a value.

Figure 5.14 (USACE, 1996) displays the results of querying several classes held by the USACE's Waterways Experiment Station and attended by hydraulic personnel of varying experience. The participants were asked to view a series of slides showing different rivers and streams and to estimate the channel n value by judgment alone. The figure illustrates the variation of the estimates.

Figure 5.14 Uncertainty of Manning's n value estimates based on estimated mean values.

Selecting a value of Manning's n of 0.06 from the figure, which might represent the average estimate for one site, yields a standard deviation of approximately 0.022. This deviation means that one-third of the estimators felt the actual value was either less than 0.04 or more than 0.08. This example shows that even experienced hydraulic personnel can look at the same river channel and estimate significantly different values of n.

The author has conducted numerous open channel hydraulics classes and workshops, with the participants ranging from experienced hydraulic engineers to undergraduate civil engineering students. Even employing the procedures described in the following paragraphs, the average estimate of Manning's n tended to be conservative; that is, higher than the known value. The author's experience has been that estimates of Manning's n varies widely among engineers and generally tends to be overestimated for channel situations. Using some of the techniques discussed in the following sections can lead to a more defensible estimate.

Table Lookup.

Through site visits, the study reach (channel and floodplain) can be described and then compared to standard descriptions of channel and floodplain conditions defined in different hydraulics texts. The most used values for Manning's n are shown in Table 5.7 (Chow, 1959). This table displays maximum, minimum, and normal values of n for a variety of man-made and natural channels, for floodplains, and for rivers of varying width. The channel n values are primarily for streams with less than 100-ft (30-m) top width at flood stage. For streams wider than this, the effects of vegetation, geometry changes, and so on are somewhat less, and Manning's n usually falls in a narrower range. Sediment grain size and channel bed forms may be more important in the estimate of Manning's n for larger streams.

Table 5.7 Values of Manning's n for a variety of man-made and natural channels .
Type of Channel and Description	Minimum	Normal	Maximum
A. Closed conduits flowing partly full
A-1. Metal
a. Brass, smooth	0.009	0.010	0.013
b. Steel
1. Lockbar and welded	0.010	0.012	0.014
2. Riveted and spiral	0.013	0.016	0.017
c. Cast iron
1. Coated	0.010	0.013	0.014
2. Uncoated	0.011	0.014	0.016
d. Wrought iron
1. Black	0.012	0.014	0.015
2. Galvanized	0.013	0.016	0.017
e. Corrugated metal
1. Subdrain	0.017	0.019	0.021
2. Storm drain	0.021	0.025	0.030
A-2. Nonmetal
a. Lucite	0.008	0.009	0.010
b. Glass	0.009	0.010	0.013
c. Cement
1. Neat, surface	0.010	0.011	0.013
2. Mortar	0.011	0.013	0.015
d. Concrete
1. Culvert, straight and free of debris	0.010	0.011	0.013
2. Culvert, with bends, connections, and some debris	0.011	0.013	0.014
3. Finished	0.011	0.012	0.014
4. Sewer with manholes, inlet, etc., straight	0.013	0.015	0.017
5. Unfinished, steel form	0.012	0.013	0.014
6. Unfinished, smooth wood form	0.012	0.014	0.016
7. Unfinished, rough wood form	0.015	0.017	0.020
e. Wood
1. Stave	0.010	0.012	0.014
2. Laminated, treated	0.015	0.017	0.020
f. Clay
1. Common drainage tile	0.011	0.013	0.017
2. Vitrified sewer	0.011	0.014	0.017
3. Vitrified sewer with manholes, inlet, etc.	0.013	0.015	0.017
4. Vitrified subdrain with open joint	0.014	0.016	0.018
g. Brickwork
1. Glazed	0.011	0.013	0.015
2. Lined with cement mortar	0.012	0.015	0.017
h. Sanitary sewers coated with sewage slimes, with bends and connections	0.012	0.013	0.016
i. Paved invert, sewer, smooth bottom	0.016	0.019	0.020
j. Rubble masonry, cemented	0.018	0.025	0.030
B. Lined or built-up channels
B-1. Metal
a. Smooth steel surface
1. Unpainted	0.011	0.012	0.014
2. Painted	0.012	0.013	0.017
b. Corrugated	0.021	0.025	0.030
B-2. Nonmetal
a. Cement
1. Neat, surface	0.010	0.011	0.013
2. Mortar	0.011	0.013	0.015
b. Wood
1. Planed, untreated	0.010	0.012	0.014
2. Planed, creosoted	0.011	0.012	0.015
3. Unplaned	0.011	0.013	0.015
4. Plank with battens	0.012	0.015	0.018
5. Lined with roofing paper	0.010	0.014	0.017
c. Concrete
1. Trowel finish	0.011	0.013	0.015
2. Float finish	0.013	0.015	0.016
3. Finished, with gravel on bottom	0.015	0.017	0.020
4. Unfinished	0.014	0.017	0.020
5. Gunite, good section	0.016	0.019	0.023
6. Gunite, wavy section	0.018	0.022	0.025
7. On good excavated rock	0.017	0.020
8. In irregular excavated rock	0.022	0.027
d. Concrete bottom float finished with sides of
1. Dressed stone in mortar	0.015	0.017	0.020
2. Random stone in mortar	0.017	0.020	0.024
3. Cement rubble masonry, plastered	0.016	0.020	0.024
4. Cement rubble masonry	0.020	0.025	0.030
5. Dry rubble or riprap	0.020	0.030	0.035
e. Gravel bottom with sides of
1. Formed concrete	0.017	0.020	0.025
2. Random stone in mortar	0.020	0.023	0.026
3. Dry rubble or riprap	0.023	0.033	0.036
f. Brick
1. Glazed	0.011	0.013	0.015
2. In cement mortar	0.012	0.015	0.018
g. Masonry
1. Cemented rubble	0.017	0.025	0.030
2. Dry rubble	0.023	0.032	0.035
h. Dressed ashlar	0.013	0.015	0.017
i. Asphalt
1. Smooth	0.013	0.013
2. Rough	0.016	0.016
j. Vegetal lining	0.030	...	0.500
C. Excavated or dredged
a. Earth, straight and uniform
1. Clean, recently completed	0.016	0.018	0.020
2. Clean, after weathering	0.018	0.022	0.025
3. Gravel, uniform section, clean	0.022	0.025	0.030
4. With short grass, few weeds	0.022	0.027	0.033
b. Earth, winding and sluggish
1. No vegetation	0.023	0.025	0.030
2. Grass, some weeds	0.025	0.030	0.033
3. Dense weeds or aquatic plants in deep channels	0.030	0.035	0.040
4. Earth bottom and rubble sides	0.028	0.030	0.035
5. Stony bottom and weedy banks	0.025	0.035	0.040
6. Cobble bottom and clean sides	0.030	0.040	0.050
c. Dragline excavated or dredged
1. No vegetation	0.025	0.028	0.033
2. Light brush on banks	0.035	0.050	0.060
d. Rock cuts
1. Smooth and uniform	0.025	0.035	0.040
2. Jagged and irregular	0035	0.040	0.050
e. Channels not maintained, weeds and brush uncut
1. Dense weeds, high as flow depth	0.050	0.080	0.120
2. Clean bottom, brush on sides	0.040	0.050	0.080
3. Same, highest stage of flow	0.045	0.070	0.110
4. Dense brush, high stage	0.080	0.100	0.140
D. Natural streams
D-1. Minor streams (top width at flood stage < 100 ft)
a. Streams on plain
1. Clean, straight, full stage, no rifts or deep pools	0.025	0.030	0.033
2. Same as above, but more stones and weeds	0.030	0.035	0.040
3. Clean, winding, some pools and shoals	0.033	0.040	0.045
4. Same as above, but some weeds and stones	0.035	0.045	0.050
5. Same as above, lower stages, more ineffective slopes and sections	0.040	0.048	0.055
6. Same as 4. but more stones	0.045	0.050	0.060
7. Sluggish reaches, weedy, deep pools	0.050	0.070	0.080
8. Very weedy reaches, deep pools, or floodways with heavy stand of timber and underbrush	0.075	0.100	0.150
b. Mountain streams, no vegetation in channel, banks usually steep, trees and brush along banks submerged at high stages
1. Bottom: gravels, cobbles, and few boulders	0.030	0.040	0.050
2. Bottom: cobbles with large boulders	0.040	0.050	0.070
D-2. Flood plains
a. Pasture, no brush
1. Short grass	0.025	0.030	0.035
2. High grass	0.030	0.035	0.050
b. Cultivated areas
1. No crop	0.020	0.030	0.040
2. Mature row crops	0.025	0.035	0.045
3. Mature field crops	0.030	0.040	0.050
c. Brush
1. Scattered brush, heavy weeds	0.035	0.050	0.070
2. Light brush and trees, in winter	0.035	0.050	0.060
3. Light brush and trees, in summer	0.040	0.060	0.080
4. Medium to dense brush, in winter	0.045	0.070	0.110
5. Medium to dense brush, in summer	0.070	0.100	0.160
d. Trees
1. Dense willows, summer, straight	0.110	0.150	0.200
2. Cleared land with tree stumps, no sprouts	0.030	0.040	0.050
3. Same as above, but with heavy growth of sprouts	0.050	0.060	0.080
4. Heavy stand of timber, a few down trees, little undergrowth, flood stage below branches	0.080	0.100	0.120
5. Same as above, but with flood stage reaching branches	0.100	0.120	0.160
D-3. Major streams (top width at flood stage > 100 ft). The n value is less than that for minor streams of similar description, because banks offer less effective resistance
a. Regular section with no boulders or brush	0.025	...	0.060
b. Irregular and rough section	0.035	...	0.100

Picture Comparison.

In the author's experience, comparing photographs of the study stream to similar streams whose channel n value has been determined may be the most accurate method for estimating n, unless gage information for the site is available. The USGS publishes reference material that allows comparison of a wide range of channel conditions to the study stream. The USGS photos are all for sites where discharge measurements have been taken. For recorded site information, all geometry and discharge variables are (theoretically) known, and the only unknown variable-Manning's n-is calculated.

The USGS (Barnes, 1987) publishes a very useful book referencing stream sites around the United States where channel n has been computed from measured geometry and discharge data. Figures 5.15 and 5.16 show two of the sites from that publication. For the stream in Figure 5.16, the n value varied with depth in two floods as follows. A flow of approximately 65 ft3/s (1.84 m3/s) with a depth of about 1 ft (0.3 m) resulted in n = 0.073, while a discharge of 1200 ft3/s (34 m3/s) with a depth of 3-4 ft (0.9-1.2 m), (the approximate channel capacity), had a measured n = 0.045. Changes in channel depth change the channel n value. For flood discharges, however, the channel n is often considered fairly constant and represented by the channel n at channel capacity conditions. In addition to photographs, other data such as cross-section and reach geometry, discharges, flow depths, and descriptions of reaches provide useful information with which to compare the site under study. Other publications (Fasken, 1963; Hicks and Mason, 1991) give similar visual displays, descriptions, and estimates of n.

Cowan's Equation.

This formula (Cowan, 1956) is very useful for deriving an analytic estimate of channel n. The formula attempts to assess the various components that comprise the overall estimate of channel n. Cowan developed his procedure from studying 40 to 50 small- to moderate-size channels, so the procedure is questionable for streams with a hydraulic radius exceeding about 15 ft (4.6 m). The formula is


where	n0	=	the portion of the n value that represents the channel material in a straight, uniform smooth reach
	n1	=	the additional value added to correct for the effect of channel surface irregularities
	n2	=	the additional value for variations in shape and size of the channel cross section through the reach
	n3	=	the additional value for obstructions (such as beaver dams, debris dams, stumps, downed trees, and root wads extending into the channel)
	n4	=	the additional value for vegetation in the channel
	m5	=	the correction factor for the meandering of the channel

Figure 5.17 illustrates variations for n1 and n2 and Table 5.8 gives the range of values for use with Cowan's formula. In selecting the values for the various parameters, the engineer must take care not to double count conditions already considered in selecting earlier estimates. For instance, it is not uncommon to tend to include vegetative effects in the estimation of both n3 and n4, when it should really only be considered in n4. Further information on applying Cowan's formula may be found in Chow, 1959 and in FHWA, 1984. The latter publication also presents an additional method similar to Cowan's.

Figure 5.15 Two views of Indian Fork Creek below Atwood Dam, near New Cumberland, Ohio.

Table 5.8 Range of values of coefficients for use in Cowan's equation.
Channel Conditions	Values
Material Involved	Earth	n0	0.020
Rock cut	0.025
Fine gravel	0.024
Coarse gravel	0.028
Degree of Irregularity	Smooth	n1	0.000
Minor	0.005
Moderate	0.010
Severe	0.020
Variations of Channel Cross Section	Gradual	n2	0.000
Alternating occasionally	0.005
Alternating frequently	0.010-0.015
Relative Effect of Obstructions	Negligible	n3	0.000
Minor	0.010-0.015
Appreciable	0.020-0.030
Severe	0.040-0.060
Vegetation	Low	n4	0.005-0.010
Medium	0.010-0.025
High	0.025-0.050
Very high	0.050-0.100
Degree of Meandering	Minor	m5	1.000
Appreciable	1.150
Severe	1.300

Example 5.6 Development of Manning's n for a channel.

Use Table 5.7 and Cowan's Equation 5.4 to estimate Manning's n for Indian Fork Creek, shown in Figure 5.15, for bankfull flow conditions. Compare the estimates to the actual value of 0.026 determined by the USGS for this site.

Table 5.7 is used to find a written description that compares well with Indian Fork Creek. From the photograph, the creek appears to be a natural stream less than 100 ft wide (between bank stations) at flood stage, flowing in a floodplain. Therefore it falls on Table 5.7 in the D-1a stream category (natural streams, minor streams, streams on plain). For this classification, there are eight subcategories. From the picture of the stream in Figure 5.15, Category 1 (clean, straight, full stage, no rifts or deep pools) seems appropriate. Thus, the range of potential n values for the channel is 0.025-0.033, with a normal value of 0.03. A slightly more conservative estimate could be a Category 2, which increases the estimates of n by 0.005-0.007, with a normal value of 0.035.

The use of Cowan's Equation requires an estimate of separate n factors for different channel conditions:

n0 - Channel material. Based on the written description for the Indian Fork Creek channel material (clay), the value for earth material (0.02) is appropriate.

n1 - Degree of irregularity. In reviewing the available channel cross sections for the short reach of creek, each section is smooth from bank to bank, with no undulations. Thus, a rating for this category would be "smooth" (0.000).

n2 - Variations of channel cross section. In reviewing the available channel cross sections, each is U-shaped, with no significant change in cross-section shape between sections. A rating of "gradual" (0.000) appears appropriate.

n3 - Relative effect of obstructions. From the pictures, there appear to be limited or no obstructions. Some exposed tree roots may be seen. A rating of "negligible" (0.000) or "minor" (0.01-0.015) appears appropriate. Select a compromise value of 0.005.

n4 - Vegetation. Some minor vegetation is present along the bank line. A rating of "low" (0.005-0.1) appears adequate. Use a value of 0.005.

m5 - Degree of meandering. Since there is no meandering for this short reach, a rating of "minor" (1.000) is appropriate.

Because this reach of stream is very short compared to a normal reach of stream that would be studied, it is not unusual to have zero values for different categories within Cowan's Equation. For studies involving several thousand feet of channel, most of the different categories could have positive values, or variations in values. The study stream could be subdivided into reaches and different values of channel n computed or estimated for separate reaches.

For this example, both estimates gave the same result-a situation that is not typical. Both estimates exceeded the measured value of n obtained by the USGS by 0.004, or 15%, a situation that is rather typical, based on the author's experience. If only the modeler's experience is used to estimate channel n, the estimate likely would have been higher yet, as compared to the 0.03 values obtained from the two techniques used in this example. Reasonable modifications in the selected values making up the estimate with Cowan's equation could be made to evaluate the variation in possible channel n, such as is given in Table 5.7 (0.025-0.033). As seen, the USGS measurement is near the lower range of possible n values. This variation further indicates the need for sensitivity tests to evaluate the effect of the Manning's n estimate.

Calibration to Gage Data.

Where discharge data have been recorded at a stream gage site, the calibration of n to reproduce known stages from published discharges represents the most accurate method of determining n for a study stream. This technique is especially desirable when one or more significant floods have been recorded, thereby allowing a more defensible estimate of the floodplain n. Even a year or so of gage records, with only in-channel flows recorded, are useful. A bankfull discharge, which is often taken as a 1- to 2-year average recurrence interval flood event, could be used to calibrate a value of n for the channel. If the value of n for the channel can be adequately estimated from these data, only the floodplain roughness needs be determined, by comparison with other criteria or data. Overbank roughness is generally considered to be less difficult to estimate than channel roughness and may have less effect on the overall flood discharges than does the channel roughness, if the channel carries the majority of the flood discharge. The floodplain n values may be initially estimated from the prevailing vegetation, using multiple values of n in overbank areas where vegetation and roughness change significantly. The overbank roughness values are adjusted within allowable limits to approximately reproduce the known stage for the measured discharge.

Even with known roughness data, one should not expect a perfect match of the data between the model's output and the known river data. As mentioned previously in this chapter, discharge estimates may carry significant error and the actual and measured discharges could differ by 5 percent or more. This difference could easily translate into a computed water-surface elevation difference of 0.5 ft (0.15 m) or more.

Also, a stage reading can be faulty. The tube containing the device that records changes in water level is often attached to a bridge pier, a location that could experience rapidly varied flow conditions rather than gradually varied flow. The acceleration of flow into the bridge opening can cause the water surface to be significantly lower under the bridge. The recorded depth could then be less than the actual depth immediately upstream or downstream of the bridge, because of the flow acceleration. A gradually varied flow program may not be able to properly match this rapidly varied flow situation. During the 1993 flood on the Missouri River near its mouth, the reading on the stage recorder (located on a bridge pier) measuring river levels at St. Charles, Missouri, was as much as 2 ft (0.6 m) below the water level a short distance both upstream and downstream of the gage location. Velocities up to 18 ft/s (5.5 m/s) resulted in a severe drawdown at the gage site. The gage was moved to a new site a short distance downstream of the bridge following the 1993 flood to eliminate this problem for future stage measurements (Coleman, 2001). Although this much drawdown is unusual, several inches to a foot (0.1-0.3 m) are not unusual under rapidly varied flow conditions. In general, calibration of the model to reproduce known elevations at the gage site to within 0.5 ft (0.2 m) is considered acceptable (FEMA, 1985).

Engineers can apply experience, table lookup, picture comparisons, and the Cowan or similar technique to estimate n values for different channel segments of the study stream. An average of all techniques can be applied, or the engineer can develop a weighting of some or all of these methods to initially select the channel n. Reasonable adjustments may then be made during the calibration process. For example, floodplain n values can be estimated from table lookup and changed from aerial photographs showing the locations of vegetation changes. The channel and floodplain n values can then be adjusted during calibration runs until the engineer is satisfied with the results. Calibration to recorded stage and discharge data is desirable, however actual data are often not available, especially for small streams. Section 5.14 addresses additional calibration methods when gage data do not exist.

Other Techniques to Estimate n

Several other methods have been developed to assist in the estimate of Manning's n for certain types of channels. Although these techniques are generally less often used than those of the preceding sections, the engineer should not overlook their applicability to the study reach. These methods include the use of an equivalent roughness value (k) and specific equations derived for certain categories of stream.

Equivalent Roughness (k).

The value k represents the average roughness height in the channel or overbank area that affects flow movement. The advantage of using this approach is that it results in changing n values with depth of flow. Chow (Chow, 1959) states that k for river channels ranges from 0.1-3 ft (0.03-0.9 m) and accounts for particle size as well as channel bed forms and other factors. The equation to compute n for a selected k value used in HEC-RAS (USACE, 2002) is

where	n	=	Manning's roughness value (dimensionless)
	R	=	the hydraulic radius (ft)
	k	=	the equivalent roughness height (ft)

Equation 5.5 is in English units; for metric units, the constant 1.486 is replaced with 1 and the constant 32.6 is replaced with 18. A constant value for k results in a changing value of n with depth, perhaps a better reflection of what is occurring in the prototype river. Values for k may be entered directly into HEC-RAS and the program computes n based on these estimates.

Other Methods.

Limerinos (Limerinos, 1970) developed an equation relating n as a function of the hydraulic radius and the D84 bed material particle size. The equation was based on tests of 11 streams with bed material ranging from small gravel to medium-size boulders. The D84 reference is for a particle size of the bed material, in feet, that equals or exceeds that of 84 percent of the particle sizes found in the sample and that represents one standard deviation from the mean particle size.

Jarrett (Jarrett, 1984) developed an equation for high-gradient streams, defined as invert slopes ranging from 0.2-4 percent and hydraulic depths from 0.5-7 feet. Based on 75 data sets obtained from 21 different stream locations, the equation is applicable for main channels having stable bed and bank materials ranging from gravels to cobbles and boulders. The equation relates n to friction slope and hydraulic radius, with channel invert slope used where the friction slope is unknown. Limerinos' and Jarrett's equations should be limited to streams having characteristics similar to those used to develop the expressions. Additional methods for computing n are presented in Chapter 11.