## Tuesday, December 15, 2009

### n-values in steep streams

Written by Chris Goodell, P.E., D. WRE

What is a good range of n values for a typical river or stream bed? 0.03?0.045? What about a mountain stream? 0.05? 0.07? Jarrett has a very simple formula that serves as a good check on n values in mountain streams. He developed his equation from 75 observations of streams in Colorado. His streams were composed of bed material ranging from cobbles to small boulders. Range of energy slopes were 0.002 ft/ft to 0.09 ft/ft and range of hydraulic radii were 0.5 to 7 ft.

Jarretts equation is: n = 0.39*(S^0.38)*(R^-0.16), where S is the energy slope and R is the hydraulic radius of the stream (in US Customary length units of feet).  (*Note-the original post had mistakenly listed the equation as 0.47*(S^0.38)*(R^-0.16).  That was incorrect.  The correct equation, as published in "DETERMINATION OF ROUGHNESS COEFFICIENTS FOR STREAMS IN COLORADO" by Robert Jarrett is n = 0.39*(S^0.38)*(R^-0.16).  Sorry about the mistake!)

Using his range of energy slopes and hydraulic radii, you could compute n values from 0.032 to 0.21. Yes, that's 0.21!!! I have had discussions with many class participants of mine who indicate that indeed they are finding n values much higher than traditionally what have been used. We're talking as high as 0.12 to 0.15 in some cases. This definately fits within Jarrett's confines. Partly to blame in this underestimation of n values in steep mountain streams would be the very popular table of n values in Chow. Chow lists mountain streams as having n values from 0.03 (gravels, cobbles, and a few boulders) to 0.07 (cobbles with large boulders). Also, another popular n value predictor, Barnes (USGS), lists it's highest n value stream as Rock Creek near Darby Montana, with an n value of 0.075. Rock Creek is composed of boulders with a d50 of about 220 mm. However, this was measured during a flood. It is likely that the n value is much higher at lower discharges where the bed irregularities have a greater impact on the overall roughness.

I like to use Jarrett's equation whenever I'm dealing with steep mountain streams that fall within (or close to) his experimental range. A little secret here: higher n values helps to stabilize unsteady flow models!

I'm curious to know if anyone out there has comment on this topic. I'd like to know what kinds of n values you all are coming up with for steep streams.

1. Hey there

In Switzerland 2001 a publication from the Federal Office for Water and Geologie about river roughness came out.

They analyzed different type of streams and measured the roughness factor. They found out, that in mountain streams with low flows n values with 0.2 are realistic. If the flow rise the n values falls in the same stream up to a value of 0.05.

So I think Jarretts formula could be realistic because the flow in mountain streams is essential for the n value.

Regards Fabian

Btw. nice Blog

2. Hi Chris
Thanks for your post. Very interesting blog.
In addition to Fabian's comment I'll post the link to the publication from Switzerland. It's in German but at least you can find an English summary with the observed/calculated Strickler roughness's.

greetz from Switzerland
Chris

3. Fabian- thanks for sharing. Do you know how I can get ahold of that paper?

4. @ Chris G.
check my posted link. This is the link to the PDF document from that paper which Fabian mentioned ;)

cheers
Chris

5. Hey Swiss Chris

To understand the publication it’s maybe necessary to say, that the Strickler k value is the reciprocal value of Manning n (n = k^-1).

Fabian

6. Thanks Chris and Fabian! Great stuff...now I have to quickly learn to read German! Just to clarify and avoid confusion for those who are not familiar, Strickler k values are not the same as the k values you can use in RAS to specify roughness (besides using n values). These are equivalent roughness values (sometimes called equivalent sand roughness, or Nikaradse k values). They are quite different from Strickler k values. Chapter 2 in the HEC-RAS Hydraulic Reference Manual talks about Equivalent sand roughness (k) values.

7. The HEC-RAS Reference Manual Table 3-1 provide numbers for mountain streams, these are considerable lower than what Jarrett came up with. Because most my river stream modeling involve dambreaks, flows are rather large, most vegetation will be gone before the peak arives so I tend to use low mannings values (per the reference manual).

8. Simon, this is certainly another good reason to use flow-weighted factors for n values for dam breach modeling. For base flow, use the high n values, then as the dam breach flood arrives, start ramping down the n values (based on discharge). Of course, there is a lot of turbulence (especially near the dam) in a dam breach flood wave-could this increase the n value where the lack of vegetation decreases the n value? This is all very subjective. It would be nice to have some back-up research on this.

9. (This from Bill M.)

For my thesis, I worked on Wheeler Creek which drains Snowbasin ski resort in Utah. I measured flow, surveyed slopes, and 'back calculated' Manning's n. The sites I worked on had slopes in the 4-8% range and Manning's n were generally north of 0.06, sometimes as high as 0.09 for Q2/bankfull type flows.

10. Lisa Hubbard did a dissertation in 1996 that evaluated flow processes in mtn rivers, using the Roaring River in Co for field analysis and evaluating the ability of existing equations to estimate the n values she derived based on field data. She found values at her site of 0.07-0.31 for this 4-8% slope small cobble-boulder stream.

11. Question: I imported n-values from a shape file in GIS. I think this may have removed all culvert or bridge data that I had previously entered, has anyone seen this happen? The ineffective flow areas and expansion/contraction coefficients remained, but actual road surfaces and structures were removed. Is this because I was importing the XS again, even though I only selected manning and none of the other XS attributes to import?

Thanks!

1. I wouldn't have expected you to lose your bridge data the way you re-imported. However, as an extra measure of safety, in addition to limiting the attributes I import, I also like to limit the cross sections I re-import to only the ones that have been changed in GIS.

12. Shouldn't it be: n = 0.39*(S^0.38)*(R^-0.16) ?

1. YES!!! Thanks for catching that. I've made the change to the original post above.

13. I am interested in the Swiss publication mentioned above, but link appears to be gone and there's not much of a citation. All I can deduce is that it was published by the "Bundesamt für Wasser und Geologie". If someone could confirm year (2001) and provide title and/or author that would be helpful.

14. Chris, great information, in the hydraulic reference manual it notes that Jarrett used Cc and Ce of 0.0 and 0.5 in his analysis. Does that mean while running an analysis using his n values that you should set these coeffients to 0.0 and 0.5 respectively?

1. That's a very good question Richard. I would say yes, in theory, however I would be interested to know how sensitive those coefficients are, compared to the n value. In practice, I typically use the standard 0.1 and 0.3 coefficients, and probably still will, but perhaps for calibration, it may make sense to go with 0.0 and 0.5.

15. For those of you looking for the Swiss paper referenced above, it appears to be missing from the website that was referenced. So I've uploaded it here: https://drive.google.com/file/d/0B0bpiyLiUeRXUjBkRTVXUVJ5aEU/view?usp=sharing

16. This comment has been removed by a blog administrator.

17. I am currently doing my master thesis on modelling of flash floods in steep catchments, and came over the article below. This states that in order to sucessfully model flashy events, a shock-capturing algorithm must be used in the 2D-model. I have searched the web and looked through the reference manual of Hec-RAS, but can not find any information about this.

So my question is: Does HEC-RAS 2D have a shock-capturing algorithm like the one described in the paper?

www.mdpi.com/2073-4441/9/9/705/pdf

Best Regards
Sondre

18. Chris，in equation n = 0.39*(S^0.38)*(R^-0.16),R is US Customary？ If i use metric system，can i need to convert Units system？

1. Yes! R is in US Customary units (i.e. feet). Please convert meters to feet before using this equation!

19. Here is a great reference for n in steep channels.
https://www.fs.fed.us/rm/pubs/rmrs_gtr323.pdf