Runoff (2:61-79; Ex )

Transcription

1 Runoff (2:61-79; Ex ) Learning goals: - environmental effects of runoff - measuring methods - hydrograph analysis - unit hydrograph effective rainfall (P effective ) direct runoff (Q direct ) base flow phi-index (Φ index ) - calculation and use of unit hydrograph

2 Draining effects....! Typical runoff hydrograph for a rainfall Avrinning Q (m 3 /s) Före Tid t (s) Avrinning Q (m 3 /s) Efter Tid t (s)

3 Hydrograph theory Losses Time (h) P tot (mm/h) Φ index P effective P effective = Q direct Q tot (m 3 /s) P tot = P effective + Φ index Q tot = Q direct + Base flow Q direct Base flow Time (h) Figure 4.14, Exemple of observed rainfall and runoff and relationship between P tot, P effective, Φ index, Q base flow, and Q direct (note the different units for P and Q, respectively.

4 Total runoff = direct runoff + base flow

5 Measuring total runoff by current meter v Q = v A A Q = total runoff (m 3 /s) A = area of water flow (m 2 ) v = mean velocity water (m/s)

6 Unit hydrograph = direct runoff from 1mm effective rainfall P effective Time Effective rain 1 mm (eg 1 mm /3 min) Q direct Direct runoff from 1 mm effective rain (eg m 3 /s) Time Assumptions unit hydrograph: 1) The rainfall is evenly distributed over the entire catchment. 2) For each individual time interval, e.g., 1 minute, the rainfall intensity is constant. 3) The runoff is directly linear proportional to the rainfall, e.g., if 2 mm effective rain falls, the runoff will become double as compared to 1 mm rainfall. 4) The runoff from the rainfall does not depend on seasonal variation, i.e., variations in evaporation, infiltration, and other losses are disregarded. ) The duration of runoff depends only on the duration of rainfall and not on the rainfall intensity.

7 Ex Unit hydrograph application Runoff from a.2 km 2 catchment was observed after a mm/h rainfall according to: t (h) Q (m 3 /s) a) Estimate base flow. b) What was the direct runoff in mm? c) What was the effective rainfall? d) Calculate Φ index. e) Calculate the unit hydrograph. f) What is the total runoff after an effective rain of 2 mm/h directly followed by a rain of 3 mm/h from the catchment?

8 Steps in calculation of unit hydrograph Set up a table with columns. Put time step in first column and total runoff in the second column Subtract base flow and put direct runoff in the third column In the fourth column calculate average runoff during each time interval; [Q(t=)+Q(t=t+Δt)]/2, etc Calculate direct runoff volume in m 3 by adding up all rows in column 4 and multiplying with Δt. Divide direct runoff volume with catchment area to get effective rainfall in mm. Divide direct runoff in column 3 with effective rainfall to get the unit hydrograph. Put results in column.

9 Use of unit hydrograph for rainfall during same time step P Q 1 h 1 mm/h q h 2 mm/h 2q h q mm/h P Q

10 Always do calculations in table Table 4.1, The use of unit hydrograph q to calculate runoff from a 2 and mm/h rainfall, respectively. Time (h) q (m 3 /s mm) 2 q (m 3 /s) q (m 3 /s)

11 Use of unit hydrograph for rainfall during two consecutive time steps P Q 1 h q 1 mm/h h 2q 2 mm/h h 2 h q mm/h h 2 h 2q + q 2 mm/h mm/h h 2 h 2 mm/h Φ index mm/h 2q + q + 2 m3/s Figure 4.13, Use of the unit hydrograph q to calculate runoff from two effective rainfalls of first 2 and then mm/h (total 7 mm/h; units according to Table 4.2).

12 Calculation in table Table 4.2, Use of the unit hydrograph q to calculate runoff from two effective rainfalls of first 2 and then mm/h (total 7 mm/h). Rrrt Time (h) q (m 3 /(s mm)) 2 q (m 3 /s) q (m 3 /s) 2 q + q (m 3 /s) Total runoff (+ base flow 2 m 3 /s)

13 Ex. 4.1, During two days + mm rain fall over a catchment (A = km2). The runoff in the water course draining the area was Q = at the start of rainfall and then during six days Qmean = m3/s and after this again Q =. The following questions arise: How large were the losses (mm)? How large was the effective rainfall (mm)? What does this give as Φindex (mm/dygn)?

14 Ex. 4.2, A catchment has a one-hour unit hydrograph according to Time (h) Q (m 3 /(s mm) What is the direct runoff from an effective rainfall of mm/h? What is the direct runoff from an effective rainfall of two rains during two hours according to first and then mm? What is the total runoff from the rains in b) if the base flow is a constant 1 m3/s?

15 4.3 Runoff (l/s) has been observed from a ha large catchment after a total rainfall of mm during 3 min. What is the unit hydrograph for the area? Time (min) Q (l/s)