I was recently party to a discussion on analysing ADCP velocity profiles in order to develop suitable alpha coefficients for wider use with surface velocity. I'm aware there is a lot of work happening in this area, and a lot of historical evidence already collected, so won't dwell on that, but it did remind me that I'd like evidence (empirical or theoretical) of velocity profiles in a super critical concrete channel. In this situation it is very difficult to measure flow using current meters or ADCPs, and there are possibly some concerns with edge effects, air bulking etc. I have since received some material from Ray Maynard, and I understand he may have joined this forum so I'll let him speak to that. The other thing I'd like to encourage is the production of a handbook of alpha coefficients, rather like the texts for estimating Mannings n, versions of which have been released by the USGS, The Swiss National Hydrography Service, and our own New Zealand version.

Regards,

Martin Doyle, Tasman District Council, New Zealand.

## 4 Comments

## Engel, Frank

From Elizabeth Jamieson:

Hi Martin,

Welcome to confluence and the surface velocity work group (or Surf Board), and thanks for posting your comment.

I agree that the production of a handbook of alpha coefficients would be very useful and something we should be working towards. Just yesterday I did a comparison measurement (hand-held LSPIV and FlowTracker), and the % difference in LSPIV discharge from the reference FlowTracker discharge varied greatly with the choice of alpha; by -18 % for alpha = 0.7 to +17 % for alpha = 1, so the final discharge was very sensitive to alpha in this case. (And an alpha = 0.85 brought the LSPIV discharge within 1% of the reference measurement!).

Liz

## Engel, Frank

Yes, welcome Martin, thanks for chiming in. We are starting to add affiliated members of the International Community to this website, so if you are interested let us know (Perhaps Kenney, Terry A. has already been talking with you?).

The alpha coef. guidebook would be a useful tool. In general, we have been suggesting that for typical conditions, it is useful to differentiate non-flood conditions from flood conditions. We have suggested (anecdotally) that alpha = 0.85 is an acceptable assumption for non flood flows, and alpha = 1.0 acceptable for flood flows. Of course, having a measurement of alpha is superior. In similar work, we are finding that alpha can be related to other measurable factors (in my case water level):

This is a figure I'll be presenting at HMEM on some preliminary findings.

PS- I will likely move this comment & discussion into the Surface Velocity Public Forum

## Alexandra Lavictoire

The latest Surfboard Webinar on Surface Velocity Radars introduced a new Phi coefficient used to relate surface velocity to discharge. This generated a renewed discussion on alpha coefficients between myself and Elizabeth Jamieson. Since the selection of alpha significantly affects the final LSPIV discharge estimate (as shown in Liz's sensitivity analysis above), we are trying to determine how to measure our own alpha coefficients as opposed to using the suggested 0.85.

Engel, Frank:

I was wondering if you could share more details about the graphs you posted above? We are curious to know how alpha was computed from the ADVM measurements (and possibly also from ADCP measurements)? We have ADCP velocity profiles and are hoping we could determine an alpha coefficient from these profiles.

Based on your graph, it also looks like the change in alpha over water level is significant enough to warrant computing a site specific range of alpha values. We would be curious to know if you have observed this at other sites or relationships between alpha and other factors?

Thanks!

Alexandra Lavictoire, Environment Canada, Ottawa.

## Engel, Frank

Alexandra Lavictoire & Elizabeth Jamieson: Excellent questions. For the graphs posted above, I used the cell data from an uplooking ADVM to fit a power law velocity profile of the form:

whereusing the exponent

uis the velocity at distance from the channel bottom;_{ij}uis the shear velocity;_{*i}αis a coefficient;_{i}zis a value based on roughness;_{0i}mis an exponent;iis the index for the profile; andjis the index for the depth cell in a profile. The ADVM was performing a 1 minute average velocity measurement. The alpha parameter (k-index in the literature) was computedm, as:For each velocity profile sample from the ADVM, alpha was computed with the equation above and. As you mention, I found that alphawas stage-dependent, but at least for this site (simple geometry) the relationship was linear, so I was able to develop relationship between the alphaparameter and ADVM flow depth using linear regression. I suspect that for many sites, alpha changes with stage, but I do not have very much data to verify this as of yet.

Practically, I solved for alpha by adapting Dave Mueller's Extrap program to work with supplied velocity profile data. In my case, the ADVM was recording 1-minute data, and I wanted to average the profiles to 5 minute increments, associated with the LSPIV videos (I acknowledge that the videos are recorded at 30 second

discretesamples and I'm averaging ADVM data over 5 minutes, but the fits can be pretty noisy if you don't). In matlab-code, it looked like this:Basically, the function extrapADVM is normal extrap, with some tweaks I made to read in the data as I had constructed it. I can share that via email if desired.

From early on I have advocated that the best approach is to

measurealpha if at all possible. Was I had hoped is that alpha would be site specific, but "rate-able". That was the case for the channel geometry and conditions at Boneyard Creek. We need to test this further for other locations and conditions. In practice, the alpha values at Boneyard varied from about 0.78 to 0.95.