runoff calculations - lth · vvr111 – hydrology and aquatic ecology 60 min of 10mm/h = 10 mm of...
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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