ESTABLISHING STAGE-DISCHARGE RELATION (1)

1
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 CURVE

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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)

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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
qc(ha)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 .1507E02 595.95 600.00
-594.025 2.531 .2263E02 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
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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

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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

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CONTROL CONFIGURATION IN NATURAL CHANNEL
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SECTION CONTROL
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CHANNEL CONTROL (1)
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BACKWATER EFFECT
?hx
?h0
Lx
S
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CHANNEL CONTROL (2)

• 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 ltlt 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

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ARTIFICIAL CONTROL
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SHIFTING CONTROLS

• SHIFTING CONTROLS RESULT FROM
• SCOUR AND FILL IN AN UNSTABLE CHANNEL
• GROWTH AND DECAY OF AQUATIC WEEDS
• OVERSPILLING AND PONDING IN AREAS ADJOINING THE
  RIVER
• REQUIRES
• LARGE GAUGING EFFORT AND MAINTENANCE COST TO
  OBTAIN RECORD OF ADEQUATE QUALITY

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FITTING RATING CURVES (1)

• SIMPLE RATING CURVE
• DISCHARGE DEPENDS ON
• STAGE ONLY
• COMPLEX RATING CURVE
• DISCHARGE DEPENDS ON
• STAGE,
• AND
• SLOPE OF ENERGY LINE
• OR
• RATE OF CHANGE OF STAGE WITH TIME

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FITTING OF RATING CURVES (2)

• POSSIBLE CAUSE(S) OF SCATTER IN STAGE-DISCHARGE
  PLOT
• STATION AFFECTED BY VARIABLE BACKWATER
• UNSTEADY FLOW EFFECTS
• SCOURING/SEDIMENTATION OF BED
• CHANGES IN VEGETATION CHARACTERISTICS
• OBSERVATIONAL ERRORS

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PERMANENT CONTROL
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VARIABLE BACKWATER (1)
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VARIABLE BACKWATER (2)
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UNSTEADY FLOW
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RIVER BED CHANGES
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EFFECT OF VEGETATION
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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

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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

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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

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FITTING OF SINGLE CHANNEL SIMPLE RATING CURVE (3)

• RELATION BETWEEN POWER TYPE RATING
• CURVE 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 5/3

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FITTING OF SINGLE CHANNEL SIMPLE RATING CURVE (4)

• 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 ltblt3 (TYPICALLY)
• COMPOUND b gt 5 ( ,,
  )

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FITTING OF SINGLE CHANNEL SIMPLE RATING CURVE (5)

• 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

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TRIAL AND ERROR PROCEDURE FOR a

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ARITHMETIC PROCEDURE TO DETERMINE a

• JOHNSON PROCEDURE
• SELECT AT LOWER AND UPPER END OF ESTIMATED RATING
  CURVE Q1 AND Q3 WITH CORRESPONDING h1 AND h3
• DETERMINE (Q2)2 Q1.Q3 and h2 f(Q2)
• SO Q1/Q2 Q2/Q3
• AND (h1a)/(h2a)
  (h2a)/(h3a)
• YIELDING a (h22-h1h3)/(h1h3-2h2)

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RATING CURVE SEGMENTS

• NUMBER AND RANGES
• DETERMINED BY DISTINCT CHANGES IN THE
  CROSS-SECTION AND HENCE CAN BE IDENTIFIED FROM
  GEOMETRY OF CROSS-SECTION OF CONTROL SECTION
• CAN ALSO BE IDENTIFIED FROM DOUBLE LOGARITHMIC
  PLOT OF STAGE VERSUS DISCHARGE, SHOWN AS A
  DISTINCT BREAK (plot h-a1 vs Q)
• APPLY SOME OVERLAP WHEN FITTING PARAMETERS FOR
  EACH SEGMENT
• SPLIT UP A SEGMENT IF CURVATURE IS CONSIDERABLE
  TO AVOID ODD b-VALUES

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RATING CURVE SEGMENTS (2)
BREAK IN RATING CURVE
CONTROL SECTION PROFILE
BRIDGE SECTION PROFILE
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FITTING OF SINGLE CHANNEL SIMPLE RATING CURVE (8)
h1
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DETERMINATION OF RATING CURVE COEFFICIENTS (1)

• PER SEGMENT (FOR POWER TYPE Q c(ha)b)
• FIRST AN ESTIMATE FOR a IS MADE BY
• COMPUTERISED JOHNSON METHOD
• OR FORCED BY USER
• NEXT THE POWER b AND COEFFIENT c ARE ESTIMATED BY
  LEAST SQUARES METHOD ON THE LOGARITHMS OF Q AND
  (ha)
• PREVIOUS STEPS ARE REPEATED (IF a IS DETERMINED
  BY JOHNSON METHOD) TO OPTIMISE THE VALUES FOR a,
  b AND c, LEADING TO A MINIMUM LEAST SQUARES FOR
  VALUES OF a WITHIN 1 m OF FIRST ESTIMATE

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DETERMINATION OF RATING CURVE COEFFICIENTS (2)
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DETERMINATION OF RATING CURVE COEFFICIENTS (3)
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DETERMINATION OF RATING CURVE COEFFICIENTS (4)
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DETERMINATION OF RATING CURVE COEFFICIENTS (5)
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DETERMINATION OF RATING CURVE COEFFICIENTS (6)

• FINALLY THE VALUES FOR b AND c FOLLOW FROM ? AND
  ?
• b ?
• AND
• c 10?

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SEGMENT-2
BREAK
SEGMENT -1
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Analysis of stage-discharge data Station name
KHED Data from 1997 8 23 to 1997 10
29 Single channel
Given boundaries for computation of rating
curve(s) interval lower bound upper bound nr.
of data 1 583.000 587.000
42 2 586.500 590.000
5 Power type of equation qc(ha)b is used
Boundaries / coefficients lower bound upper
bound a b c 583.00
586.77 -583.710 .993 .1944E03
586.77 590.00 -582.335 2.225
.2147E02 Number W level Q meas Q comp
DIFf Rel.dIFf Semr M
M3/S M3/S M3/S 0/0 0/0
49 589.750 1854.496 1854.495 .001
.00 7.71 50 588.470 1228.290
1216.384 11.906 .98 4.68 51
587.270 753.580 749.389 4.191 .56
5.69 52 587.120 673.660 699.630
-25.970 -3.71 6.20 53 586.600
553.930 557.757 -3.827 -.69 6.67
54 586.320 509.230 504.075 5.155
1.02 6.46 55 585.620 357.030
369.666 -12.636 -3.42 5.83 56
585.410 319.860 329.279 -9.419 -2.86
5.60 57 584.870 226.080 225.272
.808 .36 4.86 58 584.660
190.650 184.735 5.915 3.20 4.49
..............................................
............... 94 583.760 7.950
9.908 -1.958 -19.76 3.65 Overall
standard error 7.530 Statistics per
interval Interval Lower bound Upper bound Nr.of
data Standard error 1 583.000
586.765 42 7.88 2
586.765 590.000 4 2.74
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STANDARD ERROR OF ESTIMATE IN STAGE-DISCHARGE
RELATION
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UNCERTAINTY IN RATING CURVE FIT

• STAGE-DISCHARGE EQUATION IS A LINE OF BEST FIT TO
  THE MEASUREMENTS
• THE CURVE PROVIDES A BETTER ESTIMATE THAN ANY OF
  THE INDIVIDUAL MEASUREMENTS
• POSITION OF THE LINE IS ALSO SUBJECT TO
  UNCERTAINTY
• STANDARD ERROR OF THE MEAN RELATIONSHIP Smr

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CONFIDENCE LIMITS OF RATING CURVE

• Where
• t Student t-value at 95
• probability
• Pi ln(hi a)
• S2P variance of P
• If n 25
• the Smr ? 20 Se
• indicating the advantage of
• using the curve over the
• individual measurements

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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

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COMPOUND CHANNEL RATING CURVE (1)
hf
hr
Br
B
Qriver (hrBr)(Kmrh2/3S1/2 and Qfp
hf(B-Br)(Kmf hf 2/3S1/2 Qtotal Qriver Qfp
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COMPOUND CHANNEL RATING CURVE (2)
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COMPOUND CHANNEL RATING CURVE (3)

• 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

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COMPOUND CHANNEL RATING CURVE (4)

• COMPUTATIONAL PROCEDURE (2)
• LAST WATER LEVEL RANGE IS USED TO FIT THE CURVE
  FOR THE FLOOD PLAIN FLOW Qf ALONE
• HENCE
• h lt BANKFULL
• Q c1(h a1)b1
• h ? BANKFULL
• Q c1(h a1)b1 c2(h
  a2)b2

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RATING CURVE WITH BACKWATER CORRECTION

• NO UNIQUE STAGE-DISCHARGE CURVE
• WHEN
• 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

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BACKWATER EFFECT
?hx
?h0
Lx
S
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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 ltlt 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

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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 SLOPE

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BACKWATER CORRECTION (1)

• 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

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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

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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 curve

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CONSTANT FALL METHOD
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CONSTANT FALL RATING
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CONSTANT FALL COMPUTATIONAL PROCEDURE

• 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

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CONSTANT FALL METHOD WITH HYMOS (1)
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CONSTANT FALL METHOD WITH HYMOS
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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.

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NORMAL FALL METHOD FOR BACKWATER CORRECTION (2)
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NORMAL FALL METHOD FOR BACKWATER CORRECTION (3)
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NORMAL FALL METHOD FOR BACKWATER CORRECTION (4)
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NORMAL FALL METHOD FOR BACKWATER CORRECTION (5)

• 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

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NORMAL FALL METHOD FOR BACKWATER CORRECTION

• 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

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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

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RATING CURVE WITH UNSTEADY FLOW CORRECTION (2)

• 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)

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RATING CURVE WITH UNSTEADY FLOW CORRECTION (3)

• CORRECTION REQUIRED IF FACTOR (11/cS0.?h/?t)1/2
  lt 0.95 OR gt1.05
• 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

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EXAMPLE UNSTEADY FLOW CORRECTION(1)
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EXAMPLE UNSTEADY FLOW CORRECTION(2)
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EXAMPLE UNSTEADY FLOW CORRECTION(3)
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EXAMPLE UNSTEADY FLOW CORRECTION(4)
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EXAMPLE UNSTEADY FLOW CORRECTION(5)
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UNSTEADY FLOW WITH HYMOS(BEFORE CORRECTION)
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UNSTEADY FLOW WITH HYMOS(WITH CORRECTION)
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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

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SHIFTING CONTROL (3)INDETERMINATE Q-h
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SHIFTING CONTROL (4)ALTERNATIVE u-R PLOT
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SHIFTING CONTROL (5)APPROACHES

• FOUR POSSIBLE APPROACHES
• FITTING A SIMPLE RATING CURVE BETWEEN SCOUR
  EVENTS
• VARYING THE SHIFT PARAMETER
• APPLICATION OF STOUTS SHIFT METHOD
• FLOW DETERMINED FROM DAILY GAUGING

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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

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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

Qc1(ha1)b1
Q c1(ha1?a)b1
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SHIFTING CONTROL (8)STOUTs 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
  ?hs
• ?ht ARE USED TO CORRECT RATING

hr (Qm/c)1/b - a
?h hr - hm
?ht f(?hi, ?hj)
Qt c1(ht?hta1)b1
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SHIFTING CONTROL(9)STOUTs METHOD (2)
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SHIFTING CONTROL (10)STOUTs 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

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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

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