HYDROLOGY Lecture 8 Measurements-2 Assoc.Prof. dr.tarkan erdik

1. Rating Curve Rating curve shows the stage-discharge relation of a stream cross-section

Control section is a cross-section where rating curve is obtained Control section is a cross-section where rating curve is obtained. Narrow and deep cross sections are preferred. Power function Q=K(h-ho)n Lineer function Logarithmic scale Logarithmic scale

Rating curve might change due to change of control section Rating curve might change due to change of control section. Dredging, vegetation, bridge construction and sedimentation are possible reasons. Once or twice a year a check must be made, especially after floods. Extrapolation must be made at high waters

The rating curve equation is given below The rating curve equation is given below. The red ones in the equation are constants and they are obtained at the control section. Question: How can we find the constants in red if we measure Q and h at the certain control section? Reply: we have to logarithmically transform both of the axes

Q=K(h-ho)n Log Q=Log K + n Log(h-ho) Lets denote Log Q=Y, Log K=a, Log(h-ho)=x Y=a+nx This is a lineer equation

Example: The following measurements are made at the gaging station below h (m) 0.2 0.3 0.4 0.5 0.6 0.8 1 1.5 2 2.5 Q (m3/s) 6.9 9.9 15.2 22.5 32 66 116 279 486 720

n=2.58 Log K =1.7977 K=101.7977 =63 Q=63(h- -0.2)2.58 =63(h+0.2)2.58

Please calculate the discharge if stage is 2.8m Q=63(2.8+0.2)2.58 =1073 m3/s

Daily streamflows are plotted versus time to obtain the hydrograph. 0 6 12 24 24 hour Time (Hour) Periodicity is observed

Computation of Daily Flows When stage is measured once, a,b,c represent measurements on the previous day, that day and the next day When stage is measured twice. Measurement at 8:00 on the next day Measurement at 16:00 on that day Measurement at 16:00 on previous day Measurement at 8:00 on that day

1.Estimation of Flows at Ungaged Sites Flows at an ungaged site of a stream are estimated using the data at anoter site on the same stream or on a neighboring stream. In order to do that you have to make an assumption flows are proportional to the drainage areas of the sites. Flood sicharges can be estimated assuming that they are proportional to An, where n<1 (such as n=0.2-0.7).

2. Flow Duration Curve Flow duration curve is obtained by plotting the flows on the vertical axis, and the percentage of time the flow is equal to or exceeeds a certain value on the horizontal axis (t1+t2)/T Percentage of time Q t1 t2 Discharge (m3/s) Time

Discharge that is exceeded in %25 of time Discharge that is exceeded in %50 of time Discharge that is exceeded in %90 of time The discharge in 50% of time can be taken when calculating firm energy of HEPP

Example: Please calculate the flow duration curve for the station D02A161 below AGENCY STATION DATE (Month, Day, Year) STREAMFLOW (m3/s) DSI D02A161 8.8.2016 76 2.8.2016 72 3.8.2016 86 4.8.2016 80 5.8.2016 77 6.8.2016 105 7.8.2016 9.8.2016 75 14.8.2016 10.8.2016 73 11.8.2016 98 12.8.2016 1.8.2016 60 13.8.2016 48 15.8.2016 45

Percent Exceeded (m/n+1) Example: Please calculate the flow duration curve for the station D02A161 below Data should be sorted from largest to smallest n=total number of data, 15 in this example AGENCY STATION DATE (Month, Day, Year) STREAMFLOW (m3/s) Rank (m) Percent Exceeded (m/n+1) DSI D02A161 8.8.2016 105 1 6.25% 2.8.2016 98 2 12.50% 3.8.2016 86 3 18.75% 4.8.2016 80 4 25.00% 5.8.2016 77 5 31.25% 6.8.2016 76 6 37.50% 7.8.2016 7 43.75% 9.8.2016 75 8 50.00% 14.8.2016 9 56.25% 10.8.2016 73 10 62.50% 11.8.2016 72 11 68.75% 12.8.2016 12 75.00% 1.8.2016 60 13 81.25% 13.8.2016 48 14 87.50% 15.8.2016 45 15 93.75%

76 m3/s of discharge is exceeded in 40% of time

2. Flow Mass Curve Total flow volume can be computed as In practice, total flow volume Where Qi is the average discharge in the time interval (month, year)

Variation of total flow volume in time What is flow mass curve? Variation of total flow volume in time What is the slope of tangent at a certain point? Discharge The slope of the line OM is average discharge the required storage capacity providing continuosly average flow The vertical distance between AB and CD is

A reservoir should be designed for the constant reservoir release of 2000 ac-ft per month Points A1, A2, A3, and A4 define the beginning of low-flow periods whereas points B1, B2, B3, and B4 define the end of the low-flow periods.   10 months 20000 AF

Please design reservoir with a constant release of 1000 AF/month   Storage capacity 2 20000 AF Storage capacity 1

Q1: Design reservoir capacity by MASS CURVE ANALYSIS Dt St (Months) (106 m3) 1 40 35 2 50 3 60 4 5 25 6 30 7 20 8 13 9 27 10 55 11 76 12 14 15 16 17 18 19

Q1: Design reservoir capacity by MASS CURVE ANALYSIS Dt St ∑(Dt) ∑(St) (Months) (106 m3) 1 40 35 2 50 80 85 3 60 120 145 4 160 180 5 25 200 205 6 30 240 235 7 20 280 255 8 13 320 268 9 27 360 295 10 55 400 350 11 76 440 426 12 480 481 520 521 14 560 551 15 600 576 16 640 596 17 680 631 18 720 681 19 760 741