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ESTABLISHING STAGE-DISCHARGE RELATION (1)

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Title: 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

OHS - 1
2
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
3
OHS - 3
4
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
OHS - 4
5
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
6
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
7
CONTROL CONFIGURATION IN NATURAL CHANNEL
OHS - 7
8
SECTION CONTROL
OHS - 8
9
CHANNEL CONTROL (1)
OHS - 9
10
BACKWATER EFFECT
?hx
?h0
Lx
S
OHS - 10
11
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

OHS - 11
12
ARTIFICIAL CONTROL
OHS - 12
13
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

OHS - 13
14
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

OHS - 14
15
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

OHS - 15
16
PERMANENT CONTROL
OHS - 16
17
VARIABLE BACKWATER (1)
OHS - 17
18
VARIABLE BACKWATER (2)
OHS - 18
19
UNSTEADY FLOW
OHS - 19
20
RIVER BED CHANGES
OHS - 20
21
EFFECT OF VEGETATION
OHS - 21
22
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
23
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
24
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
25
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

OHS - 25
26
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 ( ,,
    )

OHS - 26
27
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

OHS - 27
28
TRIAL AND ERROR PROCEDURE FOR a

OHS - 28
29
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)

OHS - 29
30
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

OHS - 30
31
RATING CURVE SEGMENTS (2)
BREAK IN RATING CURVE
CONTROL SECTION PROFILE
BRIDGE SECTION PROFILE
OHS - 31
32
FITTING OF SINGLE CHANNEL SIMPLE RATING CURVE (8)
h1
OHS - 32
33
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

OHS - 33
34
DETERMINATION OF RATING CURVE COEFFICIENTS (2)
OHS - 34
35
DETERMINATION OF RATING CURVE COEFFICIENTS (3)
OHS - 35
36
DETERMINATION OF RATING CURVE COEFFICIENTS (4)
OHS - 36
37
DETERMINATION OF RATING CURVE COEFFICIENTS (5)
OHS - 37
38
DETERMINATION OF RATING CURVE COEFFICIENTS (6)
  • FINALLY THE VALUES FOR b AND c FOLLOW FROM ? AND
    ?
  • b ?
  • AND
  • c 10?

OHS - 38
39
SEGMENT-2
BREAK
SEGMENT -1
OHS - 39
40
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
OHS - 40
41
STANDARD ERROR OF ESTIMATE IN STAGE-DISCHARGE
RELATION
OHS - 41
42
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

OHS - 42
43
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

OHS - 43
44
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
45
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
OHS - 45
46
COMPOUND CHANNEL RATING CURVE (2)
OHS - 46
47
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

OHS - 47
48
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

OHS - 48
49
OHS - 49
50
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

OHS - 50
51
BACKWATER EFFECT
?hx
?h0
Lx
S
OHS - 51
52
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

OHS - 52
53
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

OHS - 53
54
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

OHS - 54
55
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
56
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

OHS - 56
57
CONSTANT FALL METHOD
OHS - 57
58
CONSTANT FALL RATING
OHS - 58
59
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

OHS - 59
60
CONSTANT FALL METHOD WITH HYMOS (1)
OHS - 60
61
CONSTANT FALL METHOD WITH HYMOS
OHS - 61
62
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
63
NORMAL FALL METHOD FOR BACKWATER CORRECTION (2)
OHS - 63
64
NORMAL FALL METHOD FOR BACKWATER CORRECTION (3)
OHS - 64
65
NORMAL FALL METHOD FOR BACKWATER CORRECTION (4)
OHS - 65
66
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

OHS - 66
67
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

OHS - 67
68
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
69
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)

OHS - 69
70
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

OHS - 70
71
EXAMPLE UNSTEADY FLOW CORRECTION(1)
OHS - 71
72
EXAMPLE UNSTEADY FLOW CORRECTION(2)
OHS - 72
73
EXAMPLE UNSTEADY FLOW CORRECTION(3)
OHS - 73
74
EXAMPLE UNSTEADY FLOW CORRECTION(4)
OHS - 74
75
EXAMPLE UNSTEADY FLOW CORRECTION(5)
OHS - 75
76
UNSTEADY FLOW WITH HYMOS(BEFORE CORRECTION)
OHS - 76
77
UNSTEADY FLOW WITH HYMOS(WITH CORRECTION)
OHS - 77
78
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
79
OHS - 79
80
SHIFTING CONTROL (3)INDETERMINATE Q-h
OHS - 80
81
SHIFTING CONTROL (4)ALTERNATIVE u-R PLOT
OHS - 81
82
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

OHS - 82
83
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
84
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
OHS - 84
85
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
OHS - 85
86
SHIFTING CONTROL(9)STOUTs METHOD (2)
OHS - 86
87
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

OHS - 87
88
OHS - 88
89
OHS - 89
90
OHS - 90
91
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
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