Runoff Calculations

Cintia Bertacchi Uvo

VVR111 – Hydrology and Aquatic Ecology

Hydrograph theory

Losses

Time (h)

Time (h)

Ptot (mm/h)

Qtot (m3/s)

Base flow

Qdirect

Φindex

Peffective

Peffective = Qdirect

Ptot = Peffective + Φindex

Qtot = Qdirect + QBase flow

VVR111 – Hydrology and Aquatic Ecology

Unit Hydrograph

• The runoff hydrograph for Peffective = 1mm

Time (h)

Time (h)

Peff (mm/h)

Qtot (m3/s)

Qdirect

Peffective = Qdirect

1

VVR111 – Hydrology and Aquatic Ecology

Unit Hydrograph – Calculation

• Start from an observed hydrograph

• Extract Qbase flow from Qobs at each time step

• Divide Qobs-Qbase at each time step by the total Peffective.

q = (Qobs-Qbase)/ Peffective

VVR111 – Hydrology and Aquatic Ecology

• Find below the discharge values for a 30 min Unit Hydrograph. a) What is the size of the catchment area? b) Calculate and plot the hydrograph for a 60 minute rain with an effective intensity of 10 mm/h.

Time (min) Discharge (m3/s) 0 0 15 4.5 30 10 45 12.5 60 11 75 9 90 6.5 105 4 120 2.5 135 1 150 0

VVR111 – Hydrology and Aquatic Ecology

Vol Qdir = sum(q)[m3/s.mm]* ΔT[s]

ΔT = 15*60s

sum(q) = 61m3/s

Vol Qdir=61 * 15*60 = 54900 m3

Peff[mm] = vol Qdir/area =>

area = vol Qdir[m3]/Peff [m3/m2]

area = 54900000 m2 area =54.9 km2

Time (min) Discharge (m3/s)

0 0

15 4.5

30 10

45 12.5

60 11

75 9

90 6.5

105 4

120 2.5

135 1

150 0

a) What is the size of the catchment area?

VVR111 – Hydrology and Aquatic Ecology

60 min of 10mm/h = 10 mm of rain in one hour

We can the assume that we had 5 mm in the first 30 min and 5 mm in the next 30 min. (we need that as our unit hydrograph is per 30 min)

b) Calculate and plot the hydrograph for a 60 minute rain with an effective intensity of 10 mm/h.

Time (min) q (m3/s

.mm) q*5 q*5 Σ (m3/s)

0 0 0 0

15 4.5 22.5 22.5

30 10 50 0 50

45 12.5 62.5 22.5 85

60 11 55 50 105

75 9 45 62.5 107.5

90 6.5 32.5 55 87.5

105 4 20 45 65

120 2.5 12.5 32.5 45

135 1 5 20 25

150 0 0 12.5 12.5

165 5 5

180 0 0

VVR111 – Hydrology and Aquatic Ecology

0

20

40

60

80

100

120

0 15 30 45 60 75 90 105 120 135 150 165 180

Hydrograph m3/s

s

VVR111 – Hydrology and Aquatic Ecology

• This hydrograph (total runoff in m3/s every 10 min) from a 15 mm rainfall that fell during 10 min was observed on a 4.8 ha catchment.

• a) How large was the base flow?

• b) How much was the direct runoff in m3?

• c) What was the effective rainfall in mm?

• d) How large were the losses in mm?

• e) What will the hydrograph look like for the total runoff from a design rainfall of 50 mm during 10 min?

• f) If another 50-mm rain will fall during the next 10 min (100 mm under 20 min), what will the hydrograph look like for this total runoff?

VVR111 – Hydrology and Aquatic Ecology

time (min)

disch (m3/s)

0 0.01

10 0.11

20 0.11

30 0.21

40 0.01

50 0.01

60 0.01

VVR111 – Hydrology and Aquatic Ecology

• a) How large was the base flow?

Qbase = 0.01 m3/s?

time (min)

disch (m3/s)

0 0.01

10 0.11

20 0.11

30 0.21

40 0.01

50 0.01

60 0.01

VVR111 – Hydrology and Aquatic Ecology

• b) How much was the direct runoff in m3?

• Qdir = ΔT * Σ(Qobs –Qbase)

ΔT = 10*60 s

Σ(Qobs –Qbase) = 0.4 m3/s

Qdir = 240 m3

time (min)

disch (m3/s)

0 0.01

10 0.11

20 0.11

30 0.21

40 0.01

50 0.01

60 0.01

Qobs – Qbase (m3/s)

0

0.1

0.1

0.2

0

0

0

VVR111 – Hydrology and Aquatic Ecology

• c) What was the effective rainfall in mm?

• Qdir = 240 m3

• Area = 4.8 ha = 4.8 · 104 m2

• Peff = 240/ 4.8 · 104 * 1000 = 5 mm

VVR111 – Hydrology and Aquatic Ecology

• d) How large were the losses in mm?

• Ptot = Peff + Φindex (Φindex = losses)

• Ptot = 15 mm

• Peff = 5 mm

• Losses = Φindex = 10mm

VVR111 – Hydrology and Aquatic Ecology

• e) What will the hydrograph look like for the total runoff from a design rainfall of 50 mm during 10 min?

• First we need the unit hydrograph

• Then multiply it by a 50 mm /10 min rainfall

time (min)

Qobs (m3/s)

Qobs – Qbase (m3/s)

q (m3/s.mm)

q*50 (m3/s)

q*50+Qbase (m3/s)

0 0.01 0 0 0 0.01

10 0.11 0.1 0.02 1 1.01

20 0.11 0.1 0.02 1 1.01

30 0.21 0.2 0.04 2 2.01

40 0.01 0 0 0 0.01

50 0.01 0 0 0 0.01

60 0.01 0 0 0 0.01

VVR111 – Hydrology and Aquatic Ecology

• f) If another 50-mm rain will fall during the next 10 min (100 mm under 20 min), what will the hydrograph look like for this total runoff?

time (min)

Qobs (m3/s)

Qobs – Qbase

(m3/s) q (m3/s.mm)

q*50 (m3/s)

q*50 (m3/s)

ΣQ + Qbase

(m3/s) 0 0.01 0 0 0 0.01

10 0.11 0.1 0.02 1 0 1.01 20 0.11 0.1 0.02 1 1 2.01 30 0.21 0.2 0.04 2 1 3.01 40 0.01 0 0 0 2 2.01 50 0.01 0 0 0 0 0.01 60 0.01 0 0 0 0 0.01 70 0 0.01