Date: Mon, 4 Jul 2022 00:36:14 -0600 (MDT) Message-ID: <1019826268.1992.1656916574015@IGSKAHCMVSLAP20.cr.usgs.gov> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_1991_70368920.1656916574014" ------=_Part_1991_70368920.1656916574014 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html How to translate Surface-water Velocities into a Mean-vertical o= r mean-channel Velocity

# How to translate Surface-water Velocities into a Mean-vertical or m= ean-channel Velocity

Regardless of the method (LSPIV or velocity radars) used to meas= ure surface-water velocities, computing a discharge requires:

• Mean-channel velocity
• Cross-sectional area

This post offers methods for translating surface-water velocities into a= mean-vertical (uvertical) or mean-channel (uavg) velocity either directly (USGS Surface-water M= ethod, Probability Concept) or indirectly (Index Velocity Rating). Future p= osts will address steps for (1) assessing the quality of surface-waters sca= tterers, (2) correcting for wind drift, which can bias measurements and alt= er surface-water velocities, (3) schemes for filtering instantaneous veloci= ty measurements, (4) computing area, and (5) computing real-time discharge.=

It is important that when reporting uavg, the method should account for the velocity distribution that exists at = the transect or cross-section-of-interest. For example, if the maximum velo= city occurs at the water surface, a logarithmic or or power law can be assu= med; however, if the maximum velocity occurs below the water surface, a non= -standard velocity distribution equation (e.g., Chiu velocity equation) sho= uld be used.

Direct Measurement:

USGS Surface-water Method for estimating the mean-vertical v= elocity

If surface-water velocities (uD) are measured direct= ly (LSPIV or velocity radars) and at multiple stations (25-30) from the lef= t edge of water (LEW) to the right edge of water (REW), uvert= ical at a station can be computed using equation 1:

• uvertical =3D uD x coefficient (typ= ically ranging from .84 to .90)            &n= bsp;                     =         Eq. 1

This assumes the vertical-velocity profile can be characterized by a log= arithmic or 1/6th or 1/7th power law (Muell= er, 2013). Rantz et al. (1982) and Turnipseed and Sauer (2010) recommend a = coefficient is necessary to convert a surface-water velocity to a = uvertical; however, these coef=C2=ADficients are generally = difficult to determine reliably because they may vary with stage, depth, an= d position in the measur=C2=ADing cross section. Experience has shown that = the coefficients generally range from about 0.84 to about 0.90, depending o= n the shape of the vertical-velocity curve and the proximity of the vertica= l to channel walls, where secondary currents may develop causing the maximu= m velocity to occur below the water surface. During these conditions, the c= oefficient can exceed unity (1.0). Larger coefficients are generally associ= ated with smooth streambeds and normally shaped vertical-velocity curves; w= hereas, smaller coefficients are associated with irregular streambeds and i= rregular vertical-velocity curves.

In many instances, the velocity distribution is non-standard or the maxi= mum velocity occurs below the water surface. In these cases, an alternative= velocity distribution equation is needed to translate a surface-water velo= city into a uavg (Chiu, 1989; Chiu a= nd Tung, 2002; Fulton and Ostrowski, 2008) or uvertical=  (Guo and Julien, 2008; Jarrett, 1991; Kundu and Ghoshal, 2012; W= iberg and Smith, 1991; Yang et al., 2006).

Probability Concept Method for estimating the mean-channel v= elocity

The Probability Concept was pioneered Chiu (1989) and offers an eff= icient platform for computing uavg a= t a cross-section-of-interest. Two parameters, =CF=95 an= d the maximum-instream velocity (umax), are needed to c= ompute uavg. The variable =CF=95=  is derived by measuring point velocities along a very im= portant and single vertical as a function of depth beginning = at the channel bottom and concluding at the water surface or by collec= ting pairs of uavg and umax for a variety of flow conditions. The vertical is called the "= y-axis" and all data collection efforts should focus on that station, which= is that vertical that contains the maximum information content (minimum ve= locity, maximum velocity, and depth) to derive the parameters umax, =CF=95, h/D used to compute u= avg (equations 2 and 3). Research suggests (Chiu = et al., 2001; Fulton and Ostrowski, 2008; Fulton et al., in preparation) th= e location or stationing of the y-axis is generally stable for a given tran= sect and does not vary with changing hydraulic conditions including variati= ons in stage, velocity, flow,  flow, channel geometry, bed form and ma= terial, slope, or alignment; however, field verification of these parameter= s must be conducted periodically and a stage-area rating m= ust be maintained. The y-axis rarely coincides with the thalweg in ope= n or engineered channels. Computing =CF=95 is accom= plished through a Python or R-script (will provide link); umax can be computed or measure= d directly using LSPIV or velocity radars.

• uD =3D umax/M x ln [1+ (eM-1)= x 1/(1-h/D) x  exp(1- 1/(1- h/D)]          &= nbsp;                    =        Eq. 2

• =CF=95 =3D uavg / umax                     &nb= sp;                     &= nbsp;                    =                     &nbs= p;                     &n= bsp; Eq. 3

Where =CF=95 =3D function of M (2 to 5.6) and gen= erally ranges from .58 to .82 and

umax  =3D maximum in-stream velocity

uavg =3D mean-channel velocity

M =3D entropy parameter and is related to =CF=95 =3D e/ (eM-1) -1/M<= /em>

uD =3D surface-water velocity

h/D =3D location of umax below the water surface at = the y-axis/water depth at the y-axis

##### Indirect Measurement:

Index Velocity Rating for estimating the mean-channel veloci= ty

The protocol for establishing index velocity ratings are described by Le= vesque and Oberg (2012) where an index such as uD&= nbsp;can be paired to a measured discharge for a variety of flow conditions= .

##### References

Chiu, C.-L., and Tung, N.C., 2002. Velocity and regularities in open-cha= nnel flow. Journal of Hydraulic Engineering, 128 (94), 390-398.

Chiu, C.-L., Tung, N.C., Hsu, S.M., and Fulton, J.W., 2001, Comparison a= nd assessment of methods of measuring discharge in rivers and streams, Rese= arch Report No. CEEWR-4, Dept. of Civil & Environmental Engineering, Un= iversity of Pittsburgh, Pittsburgh, PA.

Chiu, C.-L., 1989, Velocity distribution in open channel flow, Journal o= f Hydraulic Engineering, 115 (5), 576-594.

Fulton, J.W., Cederberg, J.R., Best, H.R., Fulford, J.M., Mills, J.T., J= ones, M.E., and Bjerklie, D.M., in preparation, SWOT-based Ri= ver Discharge: Ground-truthing using the Probability Concept and Continuous= -wave Velocity Radars.

Fulton, J.W. and Ostrowski, J., 2008, Measuring real-time streamflow usi= ng emerging technologies: Radar, hydroacoustics, and the probability concep= t, Journal of Hydrology 357, 1=E2=80=9310.

Guo, J. and Julien, P.Y., 2008, Application of the Modified Log-Wak= e Law in Open-Channels, Journal of Applied Fluid Mechanics, 1 (2), 17-23.

Jarrett, R.D., 1991, Wading measurements of vertical velocity profiles, = Geomorphology, 4, 243-247.

Kundu, S. and Ghoshal, K., 2012, Velocity Distribution in Open Channels:= Combination of Log-law and Parabolic-law, World Academy of Science, Engine= ering and Technology, International Journal of Mathematical, Computational,= Physical, Electrical and Computer Engineering, 6 (8), 1234-1241.

Levesque, V.A. and Oberg, K.A., 2012, Computing discharge using the inde= x velocity method: U.S. Geological Survey Techniques and Methods 3=E2=80=93= A23, 148 p.
(Available online at http://pubs.usgs.gov/tm/3a= 23/).

Mueller, D., 2013, extrap, Software to assist the selectin of extrapolat= ion methods for moving-boat ADCP streamflow measurements, Computers & G= eosciences, 54, 211-218.

Rantz, S.E. and others, 1982. Measurement and computation of streamflow:= Volume 1. Measurement of stage and discharge. Water-Supply Paper 2175, U.S= . Geological Survey.

Turnipseed, D.P. and Sauer, V.B., 2010, Discharge measurements at gaging= stations: U.S. Geological Survey Techniques and Methods book 3, chap. A8, = 87 p. (Also available at http://pubs.usgs.gov/tm/tm3-a8/= ).

Wiberg, P.L. and Smith, J.D.,  1991, Velocity distribution and bed = roughness in high-gradient streams, Water Resources Research, 27 (5), 825-8= 38.

Yang, S.-Q., Xu, W.-L., and Yu, G.-L., 2006, Velocity distribution in gr= adually accelerating free surface flow, Advances in Water Resources, 29, 19= 69-1980.

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