ESTABLISHING STAGE-DISCHARGE RELATION (1) WHY A STAGE-DISCHARGE RELATION? –FLOW IS THE VARIABLE...

HYDROLOGY PROJECTTechnical Assistance

ESTABLISHING STAGE-DISCHARGE RELATION (1)

• WHY A STAGE-DISCHARGE RELATION?– FLOW IS THE VARIABLE OFTEN REQUIRED FOR

HYDROLOGICAL ANALYSIS

– CONTINUOUS MEASUREMENT OF FLOW USUALLY IMPRACTICAL OR PROHIBITIVELY EXPENSIVE

– STAGE OBSERVATIONS CONTINUOUSLY OR AT REGULAR SHORT TIME INTERVALS

– STAGE OBSERVATION COMPARATIVELY EASY AND ECONOMICAL

– RELATION BETWEEN STAGE AND DISCHARGE CAN BE ESTABLISHED:

* THE DISCHARGE RATING CURVEOHS - 1


ESTABLISHING STAGE-DISCHARGE RELATION (2)

GENERAL:– RATING CURVE ESTABLISHED BY

CONCURRENT MEASUREMENTS OF STAGE h AND DISCHARGE Q COVERING EXPECTED RANGE OF RIVER STAGES AT SECTION OVER A PERIOD OF TIME

– IF Q-h RATING CURVE NOT UNIQUE, THEN ADDITIONAL INFORMATION REQUIRED ON:

* SLOPE OF WATER LEVEL (BACKWATER)

* HYDROGRAPH h(t) (UNSTEADY FLOW)

– Q-h EXTRAPOLATION MAY BE REQUIRED TO COVER FULL RANGE OF STAGES

– RATING EQUATION IS USED TO TRANSFORM h(t) INTO Q(t)OHS - 2


Stage-Discharge Relationship

Discharge (cumecs)2,0001,8001,6001,4001,2001,000800600400200

Wat

er L

evel

(m+m

.s.l)

599

598

597

596

595

594

OHS - 3


Analysis of stage-discharge data Station name : CHASKMAN Data from 1997 1 1 to 1997 12 30 Single channel Gauge Zero on 1997 7 29 = .000 m Number of data = 91 Power type of equation q=c*(h+a)**b is used

Boundaries / coefficients lower bound upper bound a b c

594.00 595.19 -592.170 9.709 .7147E-03 595.19 595.95 -593.866 2.770 .1507E+02 595.95 600.00 -594.025 2.531 .2263E+02

Number W level Q meas Q comp DIFf Rel.dIFf Semr M M3/S M3/S M3/S 0/0 0/0

1 594.800 9.530 8.541 .989 11.58 3.75 2 595.370 36.480 46.661 -10.181 -21.82 2.12 3 596.060 127.820 136.679 -8.859 -6.48 2.90 4 596.510 231.400 226.659 4.741 2.09 2.06 5 598.080 738.850 783.019 -44.169 -5.64 3.63 6 597.700 583.340 610.359 -27.019 -4.43 3.03 Overall standard error = 5.904 Statistics per interval Interval Lower bound Upper bound Nr.of data Standard error 1 594.000 595.192 38 7.20 2 595.192 595.950 27 5.24 3 595.950 600.000 26 4.84

OHS - 4


THE STATION CONTROL

GENERAL:– THE SHAPE, RELIABILITY AND STABILITY OF

THE Q-h RELATION ARE CONTROLLED BY A SECTION OR REACH OF CHANNEL AT AND/OR D/S OF GAUGING STATION = STATION CONTROL

– ESTABLISHMENT OF Q-h RELATION REQUIRES UNDERSTANDING OF NATURE AND TYPE OF CONTROL AT A PARTICULAR STATION

– ESTABLISHING A Q-h RELATION IS NOT SIMPLY CURVE FITTING

OHS - 5


TYPES OF STATION CONTROLS

• CHARACTER OF RATING CURVE DEPENDS ON TYPE OF CONTROL, GOVERNED BY:– GEOMETRY OF THE CROSS-SECTION

– PHYSICAL FEATURES OF THE RIVER D/S

• STATION CONTROLS CLASSIFIED IN MANY WAYS:– SECTION and CHANNEL CONTROLS

– NATURAL and ARTIFICIAL CONTROLS

– COMPLETE, COMPOUND and PARTIAL CONTROLS

– PERMANENT and SHIFTING CONTROLS OHS - 6


CONTROL CONFIGURATION IN NATURAL CHANNEL

OHS - 7


SECTION CONTROL

OHS - 8


CHANNEL CONTROL (1)

OHS - 9


FITTING RATING CURVES (3)

MAIN CASES:– SIMPLE RATING CURVE

* SINGLE CHANNEL

* COMPOUND CHANNEL

– RATING CURVE WITH BACKWATER CORRECTION:

* NORMAL FALL

* CONSTANT FALL

– RATING CURVE WITH UNSTEADY FLOW CORRECTION

– RATING CURVE WITH SHIFT ADJUSTMENT

OHS - 22


FITTING SINGLE CHANNEL SIMPLE RATING CURVE (1)

TO BE CONSIDERED:

– EQUATIONS USED

– PHYSICAL BASIS EQUATION PARAMETERS

– DETERMINATION OF DATUM CORRECTION

– NUMBER AND RANGE OF RATING SEGMENTS

– DETERMINATION OF RATING CURVE COEFFICIENTS

– ESTIMATION OF UNCERTAINTY IN RATING CURVE

OHS - 23


FITTING SINGLE CHANNEL SIMPLE RATING CURVE (2)

• EQUATIONS:– PARABOLIC TYPE:

Q = c2(h + a)2 + c1(h + a) +c0

– POWER TYPE:

Q = c(h + a)b

log Q = log c + b log(h + a),

Y = A + BX

OHS - 24


FITTING OF SINGLE CHANNEL SIMPLE RATING CURVE (3)

RELATION BETWEEN POWER TYPE RATINGCURVE AND MANNING EQUATION

MANNING:

Q = KmAR2/3S1/2

FOR RECTANGULAR X-SECTION:

A = B.H R H

MANNING: Q KmBS1/2.H5/3

POWER: Q = c(h + a)b

SO: c = KmBS 1/2 h + a = H and b = 5/3OHS - 25



• POWER b IN POWER TYPE RATING CURVE VARIES WITH SHAPE OF CROSS-SECTION:

– RECTANGULAR: b = 1.7

– TRIANGULAR: b = 2.5

– PARABOLIC: b = 2.0

– IRREGULAR: 1.2 <b<3 (TYPICALLY)

– COMPOUND: b > 5 ( ,, )

OHS - 26



DATUM CORRECTION a:

Q = c(h + a)b so: Q = 0 for a = - h

METHODS TO DETERMINE a:

– TRIAL AND ERROR

– ARITHMETIC PROCEDURE

– COMPUTER-BASED OPTIMISATION

OHS - 27


FITTING OF RATING CURVES IN HYMOS

FOLLOWING STEPS ARE REQUIRED:* SELECT THE REQUIRED PERIOD AND STATION

* CHECK THE MAXIMUM RANGE OF WATER LEVELS IN THE TIME PERIOD

* INSPECT THE AVAILABLE STAGE DISCHARGE DATA TOGETHER WITH A REPRESENTATIVE CROSS-SECTION OF THE CONTROL

* IDENTIFY THE BREAKS IN THE SCATTER PLOT

* ELIMINATE OUTLIERS IF UNRELIABLE (MIND OTHER REASONS FOR SCATTER!!!)

* SELECT EQUATION TYPE AND ‘a’ FORCED OR FREE

* SELECT THE INTERVALS WITH OVERLAPS TO FORCE INTERSECTIONS

* INSPECT THE PLOT AND THE TABULAR OUTPUT

* REPEAT IF RESULT IS UNSATISFACTORY

* SAVE THE CURVE PARAMETERS IF ACCEPTABLE OHS - 44


COMPOUND CHANNEL RATING CURVE (1)

B

Br

hfhr

Qriver = (hrBr)(Kmrh2/3S1/2

and

Qfp = hf(B-Br)(Kmf hf 2/3S1/2

Qtotal = Qriver + Qfp

OHS - 45



OHS - 46



• COMPUTATIONAL PROCEDURE (1):– FIRST THE RATING CURVE IS FITTED FOR THE

MAIN CHANNEL UP TO BANKFULL LEVEL

– THIS CURVE IS EXTENDED TO RIVER STAGES ABOVE BANKFULL LEVEL = Qr

– ABOVE BANKFULL LEVEL:

OBSERVED FLOWS Qobs ARE CORRECTED FOR MAINCHANNEL FLOW Qr TO OBTAIN FLOOD PLAIN FLOW ONLY = Qf:

Qf = Qobs - Qr

OHS - 47



COMPUTATIONAL PROCEDURE (2):– LAST WATER LEVEL RANGE IS USED TO FIT

THE CURVE FOR THE FLOOD PLAIN FLOW Qf

ALONE

HENCE:– h < BANKFULL:

Q = c1(h + a1)b1

– h BANKFULL

Q = c1(h + a1)b1 + c2(h + a2)b2

OHS - 48


Rating curve (compound channel)

Rating Curve Measurements

Discharge (m3/s)600550500450400350300250200150100500

Wat

er L

evel

(m+M

SL

)53

52

51

50

49

48

47

46

45

OHS - 49


RATING CURVE WITH BACKWATER CORRECTION

NO UNIQUE STAGE-DISCHARGE CURVEWHEN

STATION CONTROL IS AFFECTED BY OTHER CONTROLS DOWNSTREAM

CAUSES:* FLOW REGULATION D/S

* LEVEL IN MAIN RIVER OR TRIBUTARY AT CONFLUENCE

* WATER LEVEL IN RESERVOIR D/S

* VARIABLE TIDAL EFFECT

* D/S CONSTRICTION WITH VARIABLE CAPACITY DUE TO WEED GROWTH

* RIVERS WITH RETURN OF OVERBANK FLOW

OHS - 50


BACKWATER EFFECT

S

Lx

h0

hx

OHS - 51


CHANNEL CONTROL

EXTENT OF CHANNEL CONTROL:– FIRST ORDER APPROXIMATION OF

BACKWATER EFFECT (rectangular channel):

at x = 0: h0 = he + h0

at x = Lx: hx = he +hx

Backwater: hx = h0.exp[(-3.S.Lx)/(he(1-Fr2)]

Froude: Fr2 = u2/(gh) often << 1

Manning: Q = KmBhe5/3S1/2

So with q = Q/B: he = {q/(KmS1/2)}3/5

ln(hx/h0) = -3.S.Lx/he

at: hx/h0 = 0.05: Lx = he/S OHS - 52


BACKWATER

VARIABLE BACKWATER:CAUSES VARIABLE ENERGY SLOPE FOR THE

SAME STAGE

HENCE:DISCHARGE IS A FUNCTION OF BOTH STAGE

AND OF SLOPE:

SLOPE-STAGE-DISCHARGE RELATION

GENERALLY:ENERGY SLOPE APPROXIMATED BY WATER

LEVEL SLOPEOHS - 53


BACKWATER CORRECTION (1)

ASRKQ m2/13/2

• FALL BETWEEN MAIN AND AUXILIARY STATION TAKEN AS MEASURE FOR SURFACE SLOPE

• m = MEASURED• r = REFERENCE• S = SLOPE• F = FALL • VALUE OF POWER P

THEORETICALLY 0.5

p

r

m

p

r

m

r

m

F

F

S

S

Q

Q

OHS - 54


BACKWATER CORRECTION (2)

• TWO PROCEDURES FOR BACKWATER CORRECTION:

– CONSTANT FALL METHOD* STAGE-DISCHARGE RELATION IS AFFECTED BY

BACKWATER AT ALL TIMES

– NORMAL (OR LIMITING) FALL METHOD* STAGE-DISCHARGE AFFECTED ONLY WHEN THE

FALL REDUCES BELOW A GIVEN VALUE

OHS - 55


CONSTANT FALL METHOD• MANUAL PROCEDURE

– SELECT AN AVERAGE FALL, CALLED THE REFERENCE FALL Fr

– CREATE A RATING CURVE h-Qr WHERE:

Qr = Q/(Fm/Fr)

– CREATE A SECOND RELATION FOR

Qm/Qr = f(Fm/Fr)

– USE SECOND RELATION TO UPDATE Qr AND THE STAGE-DISCHARGE RELATION h-Qr, etc.

• USE: Q = Qr(Fm/Fr)p with Fm from observations

Fr from procedure

Qr from rating curveOHS - 56


CONSTANT FALL METHOD

OHS - 57


CONSTANT FALL RATING

OHS - 58


CONSTANT FALL COMPUTATIONAL PROCEDURE

p

m

rmr F

FQQ

FITTING:– FIRST A REFERENCE

FALL IS SELECTED

– A RATING CURVE IS FITTED BETWEEN h AND Qr

– VALUE OF p IS OPTIMISED

USE:– FOR GIVEN h AND FALL

Fm, Qr AND Fr FROM THE STORED INFORMATION

– DISCHARGE FROM SECOND RELATION

p

r

mr F

FQQ

OHS - 59


CONSTANT FALL METHOD WITH HYMOS (1)

OHS - 60


CONSTANT FALL METHOD WITH HYMOS

OHS - 61


NORMAL FALL METHOD FOR BACKWATER CORRECTION (1)

MANUAL PROCEDURE:– PLOT STAGE AGAINST DISCHARGE AND MARK

THE BACKWATER FREE MEASUREMENTS

– FIT A RATING CURVE FOR THE BACKWATER FREE MEASUREMENTS: Qr-h RELATION

– PLOT FALL VERSUS STAGE AND DRAW A LINE FOR THE NORMAL OR LIMITING FALL Fr

– COMPUTE Qm/Qr AND Fm/Fr FOR EACH OBSERVATION AND DRAW AVERAGE CURVE

– ADJUST THE CURVES BY HOLDING TWO CONSTANT AND PLOTTING THE THIRD, ETC.

OHS - 62



OHS - 63



OHS - 64



OHS - 65



USE OF THE PROCEDURE WITH h AND Fm

GIVEN:

– READ Fr FROM Fr - h CURVE

– CALCULATE Fm/Fr

– READ Q/Qr FROM Qm/Qr - Fm/Fr RELATION

– READ Qr FROM Qr - h RELATIONSHIP

– MULTIPLY Q/Qr WITH Qr TO COMPUTE Q

OHS - 66


NORMAL FALL METHOD FOR BACKWATER CORRECTION

p

m

rmr Q

QFF

/1

• COMPUTATIONAL PROCEDURE:– COMPUTE

BACKWATER FREE RATING CURVE

– DERIVE Fr FROM Fm, Qm AND Qr

– FIT PARABOLA TO Fr - h DATA

– OPTIMISE PAR. p

• USE:– WITH ABOVE

REATIONS FOR Qr-h AND Fr-h APPLY LAST EQUATION

2hchbaFr

p

r

mr F

FQQ

OHS - 67


RATING CURVE WITH UNSTEADY FLOW CORRECTION (1)

• NOTE:– WATER SURFACE SLOPE ON FRONT SIDE OF

FLOOD WAVE STEEPER THAN ON BACK SIDE

– DISCHARGE PROPORTIONAL WITH ROOT OF SLOPE

• HENCE:– FOR THE SAME STAGE, THE DISCHARGE IS

LARGER FOR RISING STAGES THAN FOR FALLING STAGES

– RATING CURVE HAS TO BE ADJUSTED TO ACCOMMODATE FOR THESE EFFECTS

OHS - 68



dt

dh

ScQQ rm

0

11

Qm = measured discharge

Qr = steady state discharge

c = flood wave celerity

S0 = bed slope (energy slope for steady flow)

dh/dt = change of h per unit of time

Procedure:

– trial Qr - h relation is established from measurements where

dh/dt = 0

– compute 1/cS0 and fit a relation for 1/cS0 = f(h)

dtdh

QQ

Scrm

/

1)/(1 2

0

2

0

1chhba

Sc

OHS - 69



• CORRECTION REQUIRED IF FACTOR (1+1/cS0.h/t)1/2 < 0.95 OR >1.05

• CORRECTION FACTOR HIGH WHEN:– BED SLOPE IS SMALL

– CELERITY IS SMALL h/t IS LARGE

• USE:– OBTAIN Qr VIA Qr-h FROM OBSERVED h

– OBTAIN 1/cS0 VIA 1/cS0-h FROM OBSERVED h

– OBTAIN h/t FROM HYDROGRPAH

– APPLY JONES FORMULA TO COMPUTE ACTUAL (UNSTEADY) FLOW OHS - 70


EXAMPLE UNSTEADY FLOW CORRECTION(1)

OHS - 71



OHS - 72



OHS - 73



OHS - 74



OHS - 75


UNSTEADY FLOW WITH HYMOS(BEFORE CORRECTION)

OHS - 76


UNSTEADY FLOW WITH HYMOS(WITH CORRECTION)

OHS - 77


SHIFTING CONTROL (1)

• CONSIDERATION:– A STABLE CONTROL IS A DESIRABLE

PROPERTY OF A GAUGING STATION

– ALLUVIAL STREAM-BEDS ARE NOT STABLE DUE TO SILTATION AND SCOUR (MOVING DUNES AND BARS)

– AS A CONSEQUENCE THE STAGE-DISCHARGE RELATION WILL VARY

– EXTENT AND FREQUENCY OF VARIATION DEPENDS ON:

* TYPICAL BED MATERIAL SIZE

* FLOW VELOCITIES

OHS - 78

HYDROLOGY PROJECTTechnical AssistanceOHS - 79


SHIFTING CONTROL (3)INDETERMINATE Q-h

OHS - 80


SHIFTING CONTROL (4)ALTERNATIVE: u-R PLOT

OHS - 81


SHIFTING CONTROL (5)APPROACHES

• FOUR POSSIBLE APPROACHES:

– FITTING A SIMPLE RATING CURVE BETWEEN SCOUR EVENTS

– VARYING THE SHIFT PARAMETER

– APPLICATION OF STOUT’S SHIFT METHOD

– FLOW DETERMINED FROM DAILY GAUGING

OHS - 82


SHIFTING CONTROL (6)SIMPLE RATING BETWEEN EVENTS

• USE:– WHERE RATING SHOWS LONG PERIOD OF

STABILITY

– WHERE SUFFICIENT GAUGINGS PER PERIOD ARE AVAILABLE

– WHERE SHIFTS IN RATING ARE EASILY IDENTIFIABLE:

* PLOT DATA WITH DATE

* FLOOD EVENTS CAUSE CHANGE

* NOTES IN THE FIELD RECORD BOOK ON REASONS FOR SHIFT

OHS - 83


SHIFTING CONTROL(7)VARYING SHIFT PARAMETER

• USE:– WHERE RATING SHOWS

PERIODS OF STABILITY BUT INSUFFICIENT DATA ARE AVAILABLE FOR NEW RATING

– THEN PARAMETER “a” IS ADJUSTED AS SHOWN LEFT:

hr = rated h for Qm

hm = observed stage for

Qm

CHECK APPLICABILITY

OF a FOR FULL OR

PARTIAL RANGE OF h

nhha m

n

ir /)(

1

Q = c1(h+a1+a)b1

Q=c1(h+a1)b1

OHS - 84


SHIFTING CONTROL (8)STOUT’s METHOD (1)

PROCEDURE:– FIT A MEAN RELATION

FOR ALL POINTS IN PERIOD

– DETERMINE hr FROM Qm

– DETERMINE h FOR INDIVIDUAL MEAS.

– DETERMINE ht BY LINEAR INTERPOLATION BETWEEN h’s

ht ARE USED TO CORRECT RATING

hr =(Qm/c)1/b - a

h = hr - hm

Qt = c1(ht+ht+a1)b1

ht = f(hi, hj)

OHS - 85


SHIFTING CONTROL(9)STOUT’s METHOD (2)

OHS - 86


SHIFTING CONTROL (10)STOUT’s METHOD (3)

• WHEN:– GAUGING IS FREQUENT

– MEAN RATING IS REVISED PERIODICALLY

– IF PREVIOUS METHODS DO NOT APPLY

• ASSUMPTION:– SHIFTS GRADUAL CHANGES IN RATING

• DRAWBACK:– ERRORS IN MEASUREMENT ARE MIXED

DEVIATIONS DUE TO SHIFTS IN CONTROL

– INDIVIDUAL MEASUREMENT ERRORS HAVE SEVERE CONSEQUENCES DIFFERENT FROM ORDINARY RATING CURVE

OHS - 87


SHIFTING CONTROL (11)DAILY GAUGING

• WHEN:– IF BROAD SCATTER IS AVAILABLE NEITHER

FROM BACKWATER NOR FROM SCOUR

– CALCULATED SHIFT IS ERRATIC

– HENCE WHEN NON OF OTHER PROCEDURES APPLY

• NOTE:– IMPORTANT PARTS OF THE HYDROGRAPH

MAY BE MISSED

– BETTER TO RELOCATE THE STATION UNLESS URGENT NEED

OHS - 91

ESTABLISHING STAGE-DISCHARGE RELATION (1) WHY A STAGE-DISCHARGE RELATION? –FLOW IS THE VARIABLE...

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Transcript of ESTABLISHING STAGE-DISCHARGE RELATION (1) WHY A STAGE-DISCHARGE RELATION? –FLOW IS THE VARIABLE...