extrapolation of rating curve

HYDROLOGY PROJECTTechnical Assistance

EXTRAPOLATION OF RATING CURVE

• WHY:– GAUGING DOES NOT COVER FULL RANGE OF

FLOW

– CALIBRATION AT HIGH FLOW IS DIFFICULT:* OCCURS INFREQUENTLY

* SHORT DURATION

– AT HIGH STAGES A DIFFERENT CONTROL MAY EXIST (FLOODPLAIN, DIFFERENT ROUGHNESS)

• WHERE:– EXTRAPOLATION AT STATE DATA

PROCESSING CENTRE

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HIGH FLOW EXTRAPOLATION

• METHODS:

– DOUBLE LOG PLOT METHOD

– STAGE-AREA/STAGE-VELOCITY METHOD

– THE MANNING’S EQUATION APPROACH

– THE CONVEYANCE SLOPE METHOD

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DOUBLE LOG PLOT METHOD

• CONDITIONS:– HYDRAULIC AND GEOMETRIC

CHARACTERISTICS DO NOT CHANGE BEYOND MEASURED RANGE

• IMPLICATION:– POWER TYPE RATING CURVE FITTED TO THE

LAST (HIGHEST) SEGMENT WILL BE CONSIDERED APPLICABLE TO EXTRAPOLATED RANGE AS WELL

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X-SECTION KHAMGAON, 1997

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HYDROLOGY PROJECTTechnical AssistanceOHS - 5


STAGE-AREA/STAGE-VELOCITY METHOD

• USE:– TO EXTRAPOLATE RATING CURVE BEYOND

MEASURED RANGE BASED ON:* MEASURED STAGE-X-SECTIONAL AREA RELATION

* EXTRAPOLATED STAGE-VELOCITY PLOT

• NOTE:– ASSUMPTION IS THAT STAGE-VELOCITY PLOT

CAN EASILY BE EXTRAPOLATED SINCE RATE OF INCREASE OF VELOCITY AT HIGHER STAGES DIMINISHES RAPIDLY

– FROM A HYDRAULIC POINT OF VIEW ASSUMPTION DOUBTFULL SINCE U::R^2/3

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ILLUSTRATION OF STAGE-AREA/STAGE-VELOCITY

METHOD

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MANNING’S EQUATION METHOD

METHOD– K* = f(h) PLOTTED

FROM DISCHARGE MEASUREMENTS

– K* BECOMES APPROX. CONSTANT FOR h>>

– K* WITH Ar AND Rr FROM MEASUREMENTS EXTRAPOLATED

– FLOOD PLAIN TREATED BY MANNING EQUATION

– S CAN BE ESTIMATED FROM TOPOSHEETS

2/13/2 SRKu m

3/2*

3/2*

2/1*

R

uK

RKu

SKK m

fpriver

fpfpfpmfp

rrriver

QQQ

SRAKQ

RAKQ

2/1

,

3/2*

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MANNING’S EQUATION METHOD

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CONVEYANCE-SLOPE METHOD

• METHOD:– CONVEYANCE AND

ENERGY SLOPE ARE EXTRAPOLATED SEPARATELY

– A AND R FROM FIELD SURVEY

– Km ESTIMATED IN FIELD

– K EXTRAPOLATED

– S FOLLOWS FROM (Q/K)2 VERSUS h

– EXISTING S-TENDENCY EXTRAPOLATED

3/2

2/1

2/13/2

ARKK

with

KSQ

or

SARKQ

m

m

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INTERPRETATION OF WETTED PERIMETER

FLOOD PLAINRIVER

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EXTRAPOLATION WITH HYMOS

• FIRST:– COMPUATATION OF GEOMETRIC AND

HYDRAULIC QUANTITIES IN MEASRED RANGE

• NEXT:– PLOT OF FOLLOWING PARAMETERS AS f(h)

* SURFACE WIDTH

* WETTED PERIMETER

* X-SECTIONAL AREA

* HYDRAULIC RADIUS

* AR2/3, Q, u, conveyance K, AND S

• FINALLY:– K EXTRAPOLATED AND S ASYMPTOTICALLY

EQUAL TO BEDSLOPE: Q = KS1/2 OHS - 17


Computation of cross-sectional parameters

Station : KHAMGAON Date : 1997 1 1

Section 1

Left bound -160.00 m, right bound .00 m from initial point Water boundaries included

K-Manning: 30.0, Sqrt(S).K-Manning: .4135

Stage Width Wetted Area Hydraulic A*R**2/3 Q Perimeter radius m m m sq-m m m**(8/3) m3/s

516.00 .000 .000 .000 .000 .00 .00 516.50 .000 .000 .000 .000 .00 .00 517.00 7.143 7.738 .715 .092 .15 .06 517.50 19.545 20.182 7.605 .377 3.97 1.64 518.00 45.568 46.233 25.858 .559 17.55 7.26 518.50 102.278 102.988 60.973 .592 42.99 17.78 519.00 106.139 106.976 113.077 1.057 117.34 48.52 519.50 121.428 122.344 168.385 1.376 208.34 86.16 520.00 125.143 126.195 230.063 1.823 343.33 141.98 520.50 128.714 129.903 293.527 2.260 505.44 209.01 521.00 142.500 143.755 360.636 2.509 665.84 275.34

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Section 2

Left bound .00 m, right bound 220.00 m from initial point Water boundaries included



516.00 205.888 207.247 999.412 4.822 2852.65 1572.84 516.50 218.718 220.220 1106.445 5.024 3245.72 1789.57 517.00 220.000 222.033 1216.253 5.478 3779.44 2083.84 517.50 220.000 223.033 1326.253 5.946 4353.09 2400.13 518.00 220.000 224.033 1436.253 6.411 4956.52 2732.84 518.50 220.000 225.033 1546.253 6.871 5588.60 3081.34 519.00 220.000 226.033 1656.253 7.327 6248.32 3445.08 519.50 220.000 227.033 1766.253 7.780 6934.71 3823.54 520.00 220.000 228.033 1876.253 8.228 7646.93 4216.23 520.50 220.000 229.033 1986.253 8.672 8384.14 4622.70 521.00 220.000 230.033 2096.253 9.113 9145.61 5042.54

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Section 3

Left bound 220.00 m, right bound 420.00 m from initial point Water boundaries included



516.00 .000 .000 .000 .000 .00 .00 516.50 2.222 2.741 .300 .110 .07 .03 517.00 6.337 6.975 2.440 .350 1.21 .50 517.50 36.820 37.559 8.071 .215 2.90 1.20 518.00 72.393 73.180 39.330 .537 26.00 10.75 518.50 77.712 78.592 76.856 .978 75.72 31.31 519.00 110.209 111.137 121.607 1.094 129.13 53.40 519.50 132.517 133.496 180.508 1.352 220.72 91.27 520.00 144.521 145.595 251.050 1.724 361.00 149.28 520.50 147.822 149.043 324.136 2.175 544.09 224.99 521.00 177.389 178.710 401.567 2.247 688.91 284.88

Stage Discharge/section >>> Total Discharge 516.00 .00 1572.84 .00 1572.84 516.50 .00 1789.57 .03 1789.60 517.00 .06 2083.84 .50 2084.40 517.50 1.64 2400.13 1.20 2402.97 518.00 7.26 2732.84 10.75 2750.84 518.50 17.78 3081.34 31.31 3130.43 519.00 48.52 3445.08 53.40 3547.00 519.50 86.16 3823.54 91.27 4000.97 520.00 141.98 4216.23 149.28 4507.48 520.50 209.01 4622.70 224.99 5056.70 521.00 275.34 5042.54 284.88 5602.76

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extrapolation of rating curve

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