Measuring Water Velocity and Streamflow in Open-water and Under Ice John Fulton and Steve Robinson U.S. Geological Survey Joe Ostrowski Middle Atlantic.

Measuring Water Velocity and Measuring Water Velocity and Streamflow in Open-water and Under Streamflow in Open-water and Under IceIce

John Fulton and Steve RobinsonJohn Fulton and Steve RobinsonU.S. Geological SurveyU.S. Geological Survey

Joe OstrowskiJoe OstrowskiMiddle Atlantic River Forecast CenterMiddle Atlantic River Forecast CenterNational Weather ServiceNational Weather Service

Dapei WangDapei WangWater Survey of CanadaWater Survey of Canada

OverviewOverview

• Evolution of MethodsEvolution of Methods Water VelocityWater Velocity StreamflowStreamflow

• Open-water and Ice-cover ProjectsOpen-water and Ice-cover Projects RadarRadar AcousticsAcoustics

• The ‘Real Story’ Behind Your Ice RecordThe ‘Real Story’ Behind Your Ice Record

Evolution of MethodsEvolution of Methods

Current-meter methodsCurrent-meter methods


Chapra (1997)Chapra (1997)

)( VxAQ

umaxumax

oz

z

ku

uequationondistributivelocityKarmanvonandtlorlawpowerGeneral ln

1,Pr

*


• Secondary and vertical Secondary and vertical flow components develop flow components develop due to side-wall effectsdue to side-wall effects

• uumaxmax may occur below the may occur below the water surfacewater surface

Darcy, in Proc. Roy. Soc., A (1909)Darcy, in Proc. Roy. Soc., A (1909)

Therefore, we need an “alternative” velocity distribution equation

USGS (1904)

Velocity vs. Water DepthMississippi River Data (Gordon, 1992)

0

5

10

15

20

25

30

35

- 0.200 0.400 0.600 0.800 1.000 1.200

Velocity (mps)

Wat

er D

epth

(m

)

Actual Regression


Information EntropyInformation Entropy (probability-based solution for characterizing the velocity distribution) (probability-based solution for characterizing the velocity distribution)

“y-axis” contains umax

0,1exp11ln, max

hwherehD

y

hD

ye

M

uuequationondistributivelocityChiu M


• uuavgavg = = u umaxmax

• Q = uQ = uavgavg A A

(M) (M) is a measure of a is a measure of a streams “happy place” streams “happy place” and and does not change withdoes not change with flowflow velocityvelocity stagestage channel geometrychannel geometry bed form and materialbed form and material slopeslope alignmentalignment

Relationship between umax and uavg

Skagit River, Washington

uavg = 0.6346umax

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.000 2.000 4.000 6.000 8.000 10.000 12.000

umax (ft/s)

uav

g (f

t/s)

A significant amount of information can be derived from the maximum velocity

NWS Proof-of-Concept StudyNWS Proof-of-Concept Study

ADCPsADCPs

Radar gunsRadar guns

Rating CurveRating Curve

““Actual” Stream FlowActual” Stream Flow

Current-meter Current-meter methodmethod

NWS Proof-of-Concept StudyNWS Proof-of-Concept StudyOpen-waterOpen-water

Steps …Steps …

1.1. y-axisy-axis

2.2. (M)(M)

3.3. uumaxmax or u or uDD

4.4. areaarea

5.5. Q = uQ = uavgavg A = ( A = ( u umax max ) A) A

Ohio River at SewickleyUSGS Data, 12/1938-8/1974

Year

1935 1940 1945 1950 1955 1960 1965 1970 1975

Zy

(ft

)

-1000

-800

-600

-400

-200

0

200

400 Water level below 8 ft G.H.Mean location of y-axis Zy=-695 ft

Zy± ft)

Water level above 8 ft G.H.Mean location of y-axis Zy=-329 ft

Zy±ft)

Ohio River at SewickleyUSGS Data, 12/1938-8/1974

G (ft)

0 5 10 15 20 25

Zy

(ft

)

-1000

-800

-600

-400

-200

0

200

400Water level below 8 ft G.H.Mean location of y-axis Zy=-695 ft

Zy± ft)

Water level above 8 ft G.H.Mean location of y-axis Zy=-329 ft

Zy±ft)

Yen (1998)


Steps …Steps …

1.1. y-axisy-axis

2.2. (M)(M)


4.4. areaarea


Ohio River at SewickleyUSGS Data, 10/1938-8/1974U=Q/A

Umax (ft/s)

0 1 2 3 4 5 6 7 8 9 10

_ U (

ft/s

)

0

1

2

3

4

5

6

7

8

9

10

Water level below 8 ft G.H.Water level above 8 ft G.H.=0.76 (M=3.70)

Yen (1998)


Steps …Steps …

1.1. y-axisy-axis

2.2. (M)(M)


4.4. areaarea


Chiu and others (2001)


Steps …Steps …

1.1. y-axisy-axis

2.2. (M)(M)


4.4. areaarea


Figure 9 Relationship between the Gage Height and Channel Area,

Allegheny River at West Hickory

Area (ft2)

1000 1500 2000 2500 3000 3500 4000

Gag

e H

eigh

t (ft

)2

3

4

5

6

7

8

Allegheny River at West Hickory

Data reported by USGS for the period 6/14/76 to 11/30/93Maximum gage height and area = 6.99 ft and 3754 ft2

Minimum gage height and area = 3.05 ft and 1412 ft2

Note:

r2 = 0.99

Yen (1998)


Steps …Steps …

1.1. y-axisy-axis

2.2. (M)(M)


4.4. areaarea


Ohio River at SewickleyUSGS Data, 10/1938-8/19740.76 (M=3.7)Qest=UmaxAest

Aest=1115(G+16.5)1.02

Qobs (ft3/s)

0 100000 200000 300000 400000

Qes

t (f

t3 /s)

0

100000

200000

300000

400000

Yen (1998)


Discharge Discharge methodmethodss

Current-meter = 210 cfsCurrent-meter = 210 cfs

Rating curveRating curve = 189 cfs= 189 cfs

Entropy Entropy regressregress = 193 cfs= 193 cfs

Entropy Entropy surf velsurf vel = 201 cfs= 201 cfs

s.d. s.d. = 9 cfs= 9 cfs

= 0.58= 0.58

uusurf velocity – ADVsurf velocity – ADV = 2.6 fps = 2.6 fps

uusurf velocity – radarsurf velocity – radar= 2.5 - 2.6 fps= 2.5 - 2.6 fps

Open-waterOpen-waterChartiers Creek at Chartiers Creek at Carnegie, PaCarnegie, PaDrainage area – 257 Drainage area – 257 mimi22

Unregulated systemUnregulated system


Discharge Discharge methodsmethods

Current-meter = 10,800 Current-meter = 10,800 cfscfs

ADCPADCP = 10,130 cfs= 10,130 cfs

Rating curveRating curve = 10,550 cfs= 10,550 cfs

Entropy Entropy regressregress = 10,330 cfs= 10,330 cfs

Entropy Entropy surf velsurf vel = 9,950 cfs= 9,950 cfs

s.d. s.d. = 340 cfs= 340 cfs

= = 0.780.78

uusurf velocity – ADVsurf velocity – ADV = 2.4 fps = 2.4 fps

uusurf velocity – radarsurf velocity – radar= 2.0 - 2.3 fps= 2.0 - 2.3 fps Susquehanna River at Susquehanna River at Bloomsburg, PaBloomsburg, PaDrainage area – Drainage area – 10,560 mi10,560 mi22

Regulated systemRegulated system


Actual vs. Simulated Stream Flow

100

1,000

10,000

100,000

1,000,000

10,000,000

100 1,000 10,000 100,000 1,000,000 10,000,000

Actual Stream Flow (cfs)

Sim

ulat

ed S

trea

m F

low

(cf

s)

Susquehanna R. at Harrisburg, Pa Susquehanna R. at Bloomsburg, Pa

Susquehanna R. at Towanda, Pa Skagit River at Mount Vernon, Wa

Open-waterOpen-waterBasin DAs – 260 to 24,100 Basin DAs – 260 to 24,100 mimi22

Regulated and non-Regulated and non-regulated systemsregulated systems

NWS Proof-of-Concept StudyNWS Proof-of-Concept StudyIce-coverIce-cover

Steps …Steps …

1.1. y-axis and y-axis and (M) (M) established during established during open wateropen water

2.2. uumaxmax along y-axis along y-axis

3.3. areaarea


NWS Proof-of-Concept StudyNWS Proof-of-Concept StudyIce-coverIce-cover

• Red River of the North at Red River of the North at Grand Forks, ND (1984 to Grand Forks, ND (1984 to 2002)2002)

• Open water measurementsOpen water measurements

• Ice measurements were Ice measurements were collected by the North collected by the North Dakota District onDakota District on 01/20/0401/20/04 02/05/0402/05/04 03/02/0403/02/04

• = .596 computed for = .596 computed for open-water used to calculate open-water used to calculate stream flow under ice coverstream flow under ice cover

Relation between maximum velocity and mean channel velocityRed River of the North at Grand Forks, ND (05082500) from

1984 to 2002

0 2 4 6 8 100

2

4

6

feet per second

feet

per

sec

ond

uavg

best_fit

umax umax

STA 84STA 84

QQactact= 463 cfs= 463 cfs

QQobsobs= 476 cfs= 476 cfsdiff = 3%diff = 3%

Nolan, K.M. and Jacobson, Jake, Discharge measurements Nolan, K.M. and Jacobson, Jake, Discharge measurements

under ice cover, USGS WRIR 00-4257under ice cover, USGS WRIR 00-4257

NWS Proof-of-Concept StudyNWS Proof-of-Concept Study

Future Efforts …Future Efforts …

• Partnering with the Partnering with the NWSNWS SRBCSRBC HIFHIF University of WashingtonUniversity of Washington USGS, North Dakota USGS, North Dakota

DistrictDistrict Water Survey of CanadaWater Survey of Canada

• Wind and precipitation Wind and precipitation influencesinfluences

• Flashy conditionsFlashy conditions• Ice conditionsIce conditions• Real-time areasReal-time areas

Project ScopeProject Scope

• EquipmentEquipment SonTek Argonaut-SW & SonTek Argonaut-SW &

SLSL

• Open-channel flow and Open-channel flow and flow under iceflow under ice

• Flow velocity Flow velocity distribution (FVD) modeldistribution (FVD) model

Water Survey of CanadaWater Survey of Canada

Vertical velocity distribution Vertical velocity distribution in open waterin open water

universal-velocity-universal-velocity-distribution lawdistribution law

bed roughness parameter bed roughness parameter y0b to reflect effects of y0b to reflect effects of channel bed roughnesschannel bed roughness

hydraulic parameterhydraulic parameter to to reflect effects of hydraulic reflect effects of hydraulic gradientgradient


Vertical velocity distribution Vertical velocity distribution under ice coverunder ice cover

• ice roughness parameter ice roughness parameter y0i y0i for effects of bottom for effects of bottom surface surface of ice coverof ice cover

• approximated by a two-approximated by a two-layer layer scheme scheme

• lower layer - solely lower layer - solely affected affected by bed roughnessby bed roughness

• upper layer - solely upper layer - solely affected affected by ice roughnessby ice roughness


Chateauguay, Downstream, XS & SW position

-3

-2

-1

0

1

2

-10 0 10 20 30 40 50 60

Tagmark (from IP) m

He

igh

t

m

ADVM SonTek Argonaut-SW @ Chateauguay River

Chateauguay River, QC, Canada two SW installations, 400 m apart SW data: Dec. 03 – May 04

Open flows & Flow under ice cover

upstream site:

flow depth 2-5 m

channel width ~ 85 m

ice cover 12/11/03 to 3/25/04 21:30 downstream site:

flow depth 2-4 m

channel width ~ 40 m

ice cover 1/9/04 9:45 to 3/4 12:00

Chateauguay, Upstream, XS & SW position

-4

-3

-2

-1

0

1

2

-10 0 10 20 30 40 50 60 70 80 90 100

Tagmark (from IP) m

Heig

ht

m


Chateauguay, Discharge w/ SW Data, U/S vs. D/S

0

50

100

150

200

250

300

350

12/1

0

12/2

4

1/7

1/2

1

2/4

2/1

8

3/3

3/1

7

3/3

1

4/1

4

4/2

8

5/1

2

5/2

6

6/9

Dis

ch

arg

e

c

u.m

./s

Q us

Q m/m

Q ds


Measuring Water Velocity and Streamflow in Open-water and Under Ice John Fulton and Steve Robinson U.S. Geological Survey Joe Ostrowski Middle Atlantic.

Documents

u max slide

u max q

open water

u maxu avg

u avg aq

evolution of methods

wall effects u max

u surf velocity adv