Extrapolation of Stage Discharge Rating Curve

An accurate stage–discharge relationship is necessary for design to evaluate the interrelationships of flow characteristics (depth and discharge)

The stage-discharge relationship also enables you to evaluate a range of conditions as opposed to a preselected design flow rate.

Continuous measurement of discharge in a river is a very costly, time-consuming, and impractical exercise, especially during floods.

Usually, to overcome limitations to continuous discharge measurement, observed stage data is converted into river discharge using a stage-discharge relationship, commonly known as the rating curve.

Rating curve is considered as an epitome of all the channel characteristics

1. Project title Extrapolation of Stage Discharge Rating Curves of Ranikhola and Busuk-khola Rivers in Sikkim Submitted by, Mr . Biswajit Dey (33/AE/16) Ms. Najima Debbarma (23/AE/16) Under the Supervision of Dr. Santosh Rangrao Yadav, Assistant Professor (SWCE) (Senior Scale) JULY , 2020 COLLEGE OF AGRICULTURAL ENGINEERING & POST HARVEST TECHNOLOGY, Ranipool-737135, Sikkim, India

2. INTRODUCTION Rating Curve Extrapolation of Rating Curve Objective Methods Results Discussion and Conclusions CONTENTS

3. An accurate stage–discharge relationship is necessary for design to evaluate the interrelationships of flow characteristics (depth and discharge) The stage-discharge relationship also enables you to evaluate a range of conditions as opposed to a preselected design flow rate. Continuous measurement of discharge in a river is a very costly, time consuming and impractical exercise especially during floods. Usually , to overcome limitations to continuous discharge measurement, observed stage data is converted into river discharge by means of a stage-discharge relationship, commonly known as the rating curve. R ating curve is considered as an epitome of all the channel characteristics Introduction 3

4. a graph of discharge versus stage Rating curve, also known as stage–discharge curve, is a graph showing the relation between the water height (stage), and the volumetric flow-rate (discharge). A mathematical representation of stage‐discharge relationships Used to transform the observed stages into the corresponding discharges. RATING CURVE 4

5. 5

6. Extrapolation of stage discharge rating curves − Shifts in discharge ratings. Extrapolation is an act of inferring an unknown from something that is known. T he extension of a rating curve, or range of values by inferring unknown values from trends in the known data . 6

7. Extrapolation of stage discharge rating curves 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) Continuous measurement of discharge in a river is a very costly, time consuming and impractical exercise especially during floods. WHERE: Extrapolation at state data processing centre 7

8. To establish a stage – discharge equation that enables to extrapolate the h-Q curves OBJECTIVE 8

9. Stages are easy to measure as compared to the measurement of discharge in rivers. Developing a rating curve entails two steps. The first step involves measuring stage and the corresponding discharges in the river and establishing a relationship. For the second stage, stage of river is measured and discharge is calculated by using the established relationship . Stage is measured by reading a gauge installed in the river. METHODS Cont.… 9

10. How Rating Curves are Constructed - I Record stage (depth) during an interesting runoff event Measure velocity across the channel (or structure) Compute discharge as product of the flow area and velocity Cross Section – Measure V at different stations. Q= S VA Wading during flow Boat mounted for deeper/faster water 10 Cont.…

11. How Rating Curves are Constructed - II Stage and measured discharge recorded for several different flow events A curve is fitted to these event pairs, and that curve is the “Rating Curve” 11 Cont.…

12. Typically, a rating curve is a single log-linear equation . The equation form is a power curve: ……..(1) Taking log on both sides : ……(2) Where, , , Alternatively, by regressing X on Y in Eq. (1).   METHODS Cont.… 12

13. METHODS Stage, h(m) Discharge, Q(m 3 /s) a(m) h-a X = Log(h-a) Y= LogQ XY X² Y² 2 2.48 0.026 1.974 0.295 0.394 0.116 0.087 0.156 2.1 2.5 0.026 2.074 0.317 0.398 0.126 0.100 0.158 2.11 2.4 0.026 2.084 0.319 0.380 0.121 0.102 0.145 2.2 2.74 0.026 2.174 0.337 0.438 0.148 0.114 0.192 2.21 3.31 0.026 2.184 0.339 0.520 0.176 0.115 0.270 13

14. From the table ∑X = 11.456 ∑Y = 25.610 ∑XY = 11.455 ∑X 2 = 4.855 ∑Y 2 = 29.184 (∑X) 2 = 131.247 (∑Y) 2 = 655.872 N = 28 RESULTS Cont.… 14 ……..(1) ……(2)  

15. From the table C r = antilog b = 0.034 The required stage-discharge relation is correlation coefficient   RESULTS 15

16. RESULTS 16 Stage-discharge rating curve for the Ranikhola river at Ranipool bridge (Arithmetic)

17. RESULTS 17 Stage-discharge rating curve for the Ranikhola river at Ranipool bridge (Logarithmic)

18. RESULTS 18 Stage-discharge rating curve for the Busuk-khola river at Jalipool bridge (Arithmetic)

19. RESULTS 19 Stage-discharge rating curve for the Busuk-khola river at Jalipool bridge (Logarithmic)

20. From the table DISCUSSION 20 The higher R 2 values (0.988 and 0.989) indicate that there exist perfect statistical correlation

21. CONCLUSIONS The developed equations may be used to estimate flow discharges in the two selected rivers for the measured stages at Ranipool and Jalipool bridge cross-sections respectively. Conversely , the high stages may also be estimated for the design discharge values at the two study sites that may be used for purposes like design of the water harvesting structures on the rivers, pico -hydropower plant design and feasibility studies, etc. Whereas low stages may also be estimated for lean period discharges in the rivers useful in studies on environmental impact/ flow assessment, viability of biotic species in the streams, irrigation water availability in the lean period, etc.

22. THANK YOU for kind attention! questions are welcome 22