HYDROLOGY Lecture 10 Unit Hydrograph Assoc.Prof. dr.tarkan erdik

What’s hydrograph? (just a reminder) A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point

Why Construct & Analyse Hydrographs ? 1-To find out discharge patterns of a particular drainage basin 2-To help predict flooding events.

What is the main source of Direct flow? 0 12 24 36 48 30 72 t(hrs) Hours from start of rain storm ___ Components of Streamflow ___ Elements of Hydrograph 3 2 1 Discharge (m3/s) Base flow Direct flow Rising limb Recession limb Basin lag time mm 4 Peak flow (crest) Flood Hydrograph Direct runoff (Surface flow + undelayed subsurface flow) Base flow (Groundwater flow + delayed subsurface flow) What is the main source of Direct flow? Runoff What is the main source of Base flow? Groundwater

3 2 1 Discharge (m3/s) 0 12 24 36 48 30 72 Hours from start of rain storm

Rainfall shown in mm, as a bar graph 3 2 mm Discharge (m3/s) 4 1 3 2 0 12 24 36 48 30 72 Hours from start of rain storm

Discharge in m3/s, as a line graph 2 mm Discharge (m3/s) 4 1 3 2 0 12 24 36 48 30 72 Hours from start of rain storm

The rising flood water in the river Rising limb The rising flood water in the river 3 Rising limb 2 mm Discharge (m3/s) 4 1 3 2 0 12 24 36 48 30 72 Hours from start of rain storm

Maximum discharge in the river Peak flow Peak flow Maximum discharge in the river 3 Rising limb 2 mm Discharge (m3/s) 4 1 3 2 0 12 24 36 48 30 72 Hours from start of rain storm

Falling flood water in the river Recession limb Peak flow Falling flood water in the river 3 Rising limb Recession limb 2 mm Discharge (m3/s) 4 1 3 2 0 12 24 36 48 30 72 Hours from start of rain storm

Hours from start of rain storm Basin lag time Basin lag time Peak flow Time difference between the peak of the rain storm and the peak flow of the river 3 Rising limb Recession limb 2 mm Discharge (m3/s) 4 1 3 2 0 12 24 36 48 30 72 Hours from start of rain storm

Normal discharge of the river Base flow Basin lag time Peak flow Normal discharge of the river 3 Rising limb Recession limb 2 Direct flow mm Discharge (m3/s) 4 1 3 2 Base flow 0 12 24 36 48 30 72 Hours from start of rain storm

Direct Flow: Volume of water reaching the river from surface run off (Source: rainfall Baseflow: Volume of water reaching the river from surface run off (Source: Groundwater flow)

Unit hydrograph assumptions Excess rainfall has constant intensity during duration Excess rainfall is uniformly distributed on watershed Base time of runoff is constant Ordinates of unit hydrograph are proportional to total runoff (linearity) Unit hydrograph represents all characteristics of watershed and is time invariant (stationarity)

Area Area Drainage Density Shape Soil Precipitation / Temp Large basins receive more precipitation than small therefore have larger runoff Larger size means longer lagtime as water has a longer distance to travel to reach the outlet Area Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Shape Area Drainage Density Shape Soil Precipitation / Temp Elongated basin will produce a lower peak flow and longer lag time than a circular one of the same size Area Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Slope Area Drainage Density Shape Soil Precipitation / Temp Channel flow can be faster down a steep slope therefore steeper rising limb and shorter lag time Area Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Soil Area Drainage Density Shape Soil Precipitation / Temp The more infiltration occurs the longer the lag time and shallower the rising limb Area Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Land Use Area Drainage Density Shape Soil Precipitation / Temp Urbanisation - concrete and tarmac form impermeable surfaces, creating a steep rising limb and shortening the time lag Afforestation - intercepts the precipitation, creating a shallow rising limb and lengthening the time lag Area Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Drainage Density Area Drainage Density Shape Soil Precipitation / Temp A higher density will allow rapid overland flow Area Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Precipitation & Temperature Short intense rainstorms can produce rapid overland flow and steep rising limb If the ground is frozen rapid surface run off occurs Snow on the ground can act as a store producing a long lag time and shallow rising limb. Once a thaw sets in the rising limb will become steep Area Rock Type Drainage Density Shape Soil Precipitation / Temp Slope Land Use

Unit Hydrograph Theory (Transforming the Runoff from Rainfall) A mathematical concept (based on linearity) A unit hydrograph is defined as the hydrograph of direct runoff resulting from one unit depth (1cm) of rainfall excess occurring uniformly over the basin and at a uniform rate for a specified duration (D hours) total amount of rainfall minus all abstractions including interception, depression storage, and infiltration.

Unit Hydrograph Components Duration of excess precip. Duration Lag Time Time of Concentration Rising Limb Recession Limb (falling limb) Peak Flow Time to Peak (rise time) Recession Curve Separation Base flow Lag time Time of concentration Base flow Time Base

Derived Unit Hydrograph

Derived Unit Hydrograph

Area under hydrograph / area of the catchment A unit hydrograph is defined as the hydrograph of direct runoff resulting from one unit depth (1cm) of rainfall excess occurring uniformly over the basin and at a uniform rate for a specified duration (D hours). Area under hydrograph / area of the catchment

EXAMPLE Given below are the ordinates of a 6-h unit hydrograph for a catchment. Calculate the ordinates of the DRH due to a rainfall excess of 3.5 cm occurring in 6 hr.

EXAMPLE Given below are the ordinates of a 6-h unit hydrograph for a catchment. Calculate the ordinates of the DRH due to a rainfall excess of 3.5 cm occurring in 6 hr.

Exercise2:Two storms each of 6-h duration and having rainfall excess values of 3.0 and 2.0 cm, respectively occur successively. The 6-h unit hydrograph for the catchment is the same as given in tha table below. Please calculate the resulting DRH

Ordinate of 3-cm DRH (col.2) 1 2 3 4 5 Time (h) Ordinate of 6-h UH (m3/s) Ordinate of 3-cm DRH (col.2) Ordinate of 2-cm DRH (col.2 lagged by 6 h) Ordinate of 5-cm DRH (col. 3 + col.4) (m3/s) 25 6 50 9 85 12 125 15 160 18 185 21 172.5 24 30 110 36 60 42 48 54 16 8 66 2.7 69 75

No lag 6-hr lag 1 2 3 4 5 Time (h) Ordinate of 6-h UH (m3/s) Ordinate of 3-cm DRH (col.2) x 3 Ordinate of 2-cm DRH (col.2 lagged by 6 h) x 2 Ordinate of 5-cm DRH (col. 3 + col.4) (m3/s) 25 75 6 50 150 9 85 255 305 12 125 375 100 475 15 160 480 170 650 18 185 555 250 805 21 172.5 517.5 320 837.5 24 370 850 30 110 330 36 60 180 220 400 42 108 120 228 48 72 147 54 16 98 8 32 56 66 2.7 8.1 24.1 69 10.6 No lag 6-hr lag

Exercise 3: The ordinates of a 6-hour unit hydrograph of a catchment is given below. The variation of accumulated rainfall is given. The baseflow can be assumed to be 15m3/s at the begining and increasing by 2m3/s for every 12 hours. The storm loss rate is estimated as 0.25cm/h. Calculate DRH. Interval 1st 6 hours 2nd 6 hours 3rd 6 hours Rainfall depth (cm) 3.5 7.5 5.5

Effective rainfall (cm) Interval 1st 6 hours 2nd 6 hours 3rd 6 hours Rainfall depth (cm) 3.5 7.5 5.5 Total loss (cm) 1.5 (0.25×6) Effective rainfall (cm) 2 6 4

DRH due to 6 cm ER x 6.0 (Advanced by 6 h) Time Ordinaters of U.H. DRH due to 2 cm ER DRH due to 6 cm ER x 6.0 (Advanced by 6 h) DRH due to 4 cm ER (Advanced by 12 h) Ordinates of final DRH (Col 3+ 4+5) Base flow (m3/s) Ordinates of flood hydrograph (m'Vs) (Col. 6 + 7) 3 25 6 50 9 85 12 125 15 160 18 185 21 172.5 24 27 135 30 110 33 60 36 39 42 16 45 8 48 2.7 51 54 57 63 66

DRH due to 6 cm ER x 6.0 (Advanced by 6 h) Time Ordinaters of U.H. DRH due to 2 cm ER DRH due to 6 cm ER x 6.0 (Advanced by 6 h) DRH due to 4 cm ER (Advanced by 12 h) Ordinates of final DRH (Col 3+ 4+5) Base flow (m3/s) Ordinates of flood hydrograph (m'Vs) (Col. 6 + 7) 15 3 25 50 65 6 100 115 9 85 170 150 320 335 12 125 250 300 550 17 567 160 510 930 947 18 185 370 750 200 1320 1337 21 172.5 345 960 340 1645 1662 24 1110 500 1930 19 1949 27 135 270 1035 640 1945 1964 30 110 220 740 1920 1939 33 60 120 810 690 1620 1639 36 72 660 1372 1393 39 360 540 950 971 42 16 32 216 440 688 709 45 8 240 406 427 48 2.7 5.4 96 144 245.4 23 268.4 51 148 171 54 16.2 64 80.2 103.2 57 55 10.8 35.8 63 66

Exercise 4: Given the ordinates of a 4-h unit hydrograph as below derive the ordinates of a 12-h unit hydrograph for the same catchment. Time (h) 4 8 12 16 20 24 28 32 36 40 44 Ordinate of 4-h UH (m3/s) 80 130 150 90 52 27 15 5 Pay attention: desired duration (12-h unit hydrograph) is multiple of given unit hydrograph (4-h unit hydrograph).

Ordinates of 4-h UH (m3/s) Ordinates of 4-h UH (m3/s) lagged by 4 h Time (h) Ordinates of 4-h UH (m3/s) Ordinates of 4-h UH (m3/s) lagged by 4 h Ordinates of 4-h UH (m3/s) lagged by 8 h DRH of 3 cm in 12 hours DRH of 1 cm in 12 hours 4 20 8 80 12 130 16 150 24 90 28 52 32 27 36 15 40 5 44 48

Ordinates of 4-h UH (m3/s) Ordinates of 4-h UH (m3/s) lagged by 4 h Time (h) Ordinates of 4-h UH (m3/s) Ordinates of 4-h UH (m3/s) lagged by 4 h Ordinates of 4-h UH (m3/s) lagged by 8 h DRH of 3 cm in 12 hours DRH of 1 cm in 12 hours 0.00 4 20 6.67 8 80 100 33.33 12 130 230 76.67 16 150 360 120.00 410 136.67 24 90 370 123.33 28 52 272 90.67 32 27 169 56.33 36 15 94 31.33 40 5 47 15.67 44 48 1.67

S hydrograph An S-hydrograph (summation) is the hydrograph that results from continuous rainfall excess at a constant rate for an indefinite (long) time An S-hydrograph (summation) is the hydrograph that results from continuous rainfall excess at a constant rate for an indefinite (long) time

S hydrograph is obtained by translating UH of duration tr by many times

S-hydrograph Example:Please compute the 3-hr unit hydrograph from the given 2-hour unit hydrograph by using S-hydrograph method. Time (hr) 2hr UH 2nd 2 hr UH 3rd 2 hr UH 4th 2 hr UH 5th 2 hr UH 6th 2 hr UH 7th 2 hr UH S hydrograph UH 1 20 2 45 3 60 4 46 5 34 6 21 7 14 8 9 10 11 12 13

Time (hr) 1st 2 hr 2nd 2 hr 3rd 2 hr 4th 2 hr 5th 2 hr 6th 2 hr 7th 2 hr S hydrograph 1 20 2 45 3 60 80 4 46 91 5 34 114 6 21 112 7 14 128 8 9 121 132 10 11 12 13 S hydrograph becomes horizontal after a while

Time (hr) S hydrograph Lagged S hydrograph Difference 3hr UH 0.00 1 20 13.33 2 45 30.00 3 80 53.33 4 91 71 47.33 5 114 69 46.00 6 112 32 21.33 7 128 37 24.67 8 121 4.67 9 132 20 *2 /3 where 2 is UH duration given and 3 is UH duration asked

Exercise: Please derive UH. intensity=50mm/hr, theta=10mm/hr, A=162km2

900*120*60/2=3.24×106 m3   RD=3.24×106 m3/162×106 m2=0.02m=2cm

UH Ordinates should be divided by 2cm RD =20mm The duration of unit hydrograph is 20𝑚𝑚 40𝑚𝑚/ℎ𝑟 =0.5 hr (50mm/hr-10mm/hr)