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:
• Bed material and average grain size
• Surface irregularities of the channel
• Channel bed forms (such as ripples, dunes, transition, and plane bed)
• Erosion and depositional characteristics
• Meandering tendencies
• Channel obstructions (downed trees, exposed root wads, beaver dams, debris, and so on)
• Geometry changes between channel sections
• Vegetation along the bankline and in the channel
Figure 5.13 Example of discharge-frequency curves computed with three different techniques.
Section 5.5 Roughness Data 145
To collapse all these parameters into a single value is difficult, to say the least. For esti-mates of the floodplain n, the engineer typically bases the adopted values on vegeta-tion, 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 engineerʹs 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, pic-ture 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. Reason-able adjustments may then be made during the calibration process. For example, floodplain n values can be estimated from tables and modified from aerial photo-graphs 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 tech-niques 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.
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 per-sonnel 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 authorʹs experience has been that estimates of Man-ning’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 con-ditions 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 nor-mal 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
USACE
Figure 5.14 Uncertainty of Manning’s n value estimates based on estimated mean values.
Section 5.5 Roughness Data 147
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
Table 5.7 Values of Manning’s n for a variety of man-made and natural channels (cont.).
Type of Channel and Description Minimum Normal Maximum
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
Table 5.7 Values of Manning’s n for a variety of man-made and natural channels (cont.).
Type of Channel and Description Minimum Normal Maximum
Section 5.5 Roughness Data 149
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),
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 resis-tance
a. Regular section with no boulders or brush 0.025 … 0.060
b. Irregular and rough section 0.035 … 0.100
Table 5.7 Values of Manning’s n for a variety of man-made and natural channels (cont.).
Type of Channel and Description Minimum Normal Maximum
(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 infor-mation 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 ana-lytic 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
(5.4) 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 select-ing 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.
n = (n0+n1+n2+n3+n4)m5
Section 5.5 Roughness Data 151
.
Figure 5.15 Two views of Indian Fork Creek below Atwood Dam, near New Cumberland, Ohio.
(a) Upstream from right bank below section 3. (b) Upstream from right bank at section 2.
(c) Plan view and cross sections.
Figure 5.16 Two views of Provo River near Hailstone, Utah.
Figure 5.17 Examples for variations in Cowan’s n1 and n2 variables.
Section 5.5 Roughness Data 153
w
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 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 undula-tions. Thus, a rating for this category would be “smooth” (0.000).
Table 5.8 Range of values of coefficients for use in Cowan’s equation.
Channel Conditions Values
n2 – Variations of channel cross section. In reviewing the available channel cross sec-tions, 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.
Inserting the estimates into Equation 5.4 yields
n = (0.02 + 0.00 + 0.00 + 0.005 + 0.005) 1.00 = 0.03
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 authorʹs experience. If only the modelerʹs 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 esti-mate with Cowanʹs equation could be made to evaluate the variation in possible chan-nel 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 tech-nique 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 deter-mined, 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 modelʹs output and the known river data. As mentioned previously in this chapter, discharge estimates may carry significant error and the actual and
mea-Section 5.5 Roughness Data 155
sured discharges could differ by 5 percent or more. This difference could easily trans-late 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 experi-ence rapidly varied flow conditions rather than gradually varied flow. The accelera-tion 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 var-ied 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 draw-down 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 eleva-tions 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, flood-plain n values can be estimated from table lookup and changed from aerial photo-graphs showing the locations of vegetation changes. The channel and floodplain n
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, flood-plain n values can be estimated from table lookup and changed from aerial photo-graphs showing the locations of vegetation changes. The channel and floodplain n