presentación de powerpoint · determine runoff hydrograph for a 20 min excess rainfall of 8.5 cm...

8.- Runoff

Dr. Luis E. Lesser

All Tables and Figures (except where noted) were kindly provided by Pearson, from the

textbook by David A. Chin, 2013. Water –Resources Engineering, 3rd edition.

Runoff Methods

There are different empirical methods to determine runoff, some of these area:

• Kirpich• Izzard• Herby• NRCS

These methods use parameters such as:• Basin length• Precipitation• Vegetation cover• Time of concentration• Slope

In Mexico, the preferred method is the one outlined in the regulation: NOM-011-CNA-2000

Runoff – Method NOM-011-CNA-2000

From: Norma Oficial Mexicana NOM-011-CNA-2000 “Conservación del recurso agua-Que establece las especificaciones y el método para determinar la disponibilidad media anual de las aguas nacionales”. Publicado en el DOF el 17 de abril de 2002.

Runoff = Precip x Area x Runoff Coefficient (Ce)Dimensions: [L3/T] = [L/T] x [L2] x [-]

CeUse of soil

Precipitation

Type of Soil

C – Almost Impermeable

B – Medium permeability

A – Permeable

Type of crop

Constant K

(Not hydraulic conductivity!)



What happens if in a basin there are different types of soils and/or different uses of soil?

The basin must be subdivided into homogeneous sub-basins, and a weighted K must be obtained

GIS

If K ≤ 0.15 → 𝐶𝑒 =𝐾 (𝑃−250)

2000

If K > 0.15 → 𝐶𝑒 =𝐾 (𝑃−250)

2000+

(𝐾−0.15)

1.5

Empirical relationship

P must be in mm/yr

This equation is valid for: 350 mm/yr < P < 2150 mm/yr

Unit Hydrograph

Continuous Runoff Models:

Runoff Hydrograph – Measured at the outflow of the basin

From: Viessman, Lewis and Knapp, 1989, Introduction to Hydrology, 3rd edition.

Runoff Hydrographs – Unit hydrograph Method

• The unit hydrograph is the most common method to estimate runoff hydrographs

• A unit hydrograph is a resultant from a runoff corresponding to a unit of precipitation depth (let it be 1 cm, 1 inch, etc.)


We will see:

a) How to create a unit hydrograph from:• Precipitation data, AND• River discharge data

b) Once we have a unit hydrograph, how do we use it to get the river discharge data for any precipitation event

i. If the length of precipitation is the same as the length of the unit-hydrographii. If the length of precipitation is different from the length of the unit-

hydrograph, but it is a multiple of the unit hydrograph you are usingiii. Precipitation is a multiple of the unit hydrograph, but flow measurements are

not iv. precipitation time is not a multiple of the unit-hydrograph (just conceptual)


To obtain a unit hydrograph:

1) Remove baseflow

2) Divide the flow (Q) by the total excess precipitation (h) → (in cm or inches)

Example:

Assume no baseflow and an excess precipitation of 3 cm

Time (min) 2 8 20 30 35 40 45 50 55

Runoff (Q) (m3/s)

0 0 110 460 550 320 200 120 100

0/3 0/3 110/3 460/3 550/3 320/3 200/3 120/3 100/3

Unithydrograph(m3/s/cm)

0 0 36.7 153.3 183.3 106.7 66.7 40 33.3

We have our unit hydrograph! – but not done yet…

These units are not correct, they should only be m3/s. I write them like this in an attempt to be clear on the calculations.


• The precipitation time is different form this one, and MUST be specified, in this way we will have unit hydrographs with different durations, e.g.:

10-min unit hydrograph 6-hr unit hydrograph

This time refers to the excess precipitation only

• A NOTE ON TIME: We are talking in here about the time we are seeing the water moving through the outflow of the basin, but what about the time it took to precipitate the water?


• Now, how do we apply the unit hydrograph to obtain a run off hydrograph?

Steps to obtain a runoff hydrograph from a unit hydrograph:

CASE 1: If the length of precipitation is the same as the length of the unit-hydrograph, multiply the unit hydrograph by the precipitation depth

Runoff – Unit Hydrograph

Example 10.7

A 10 min-unit hydrograph for a 2.25 km2 basin is given by:

a) Calculate the runoff hydrograph for a 10 min excess rainfall of 3.5 cm

Time (min)

0 30 60 90 120 150 180 210 240 270 300 330 360 390

Runoff (unithydrograph) (m3/s/cm)

0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.50 0.28 0.17 0

Time (min)

0 30 60 90 120 150 180 210 240 270 300 330 360 390


0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.50 0.28 0.17 0

Runoffhydrograph

(m3/s)0 4.2 9.8 6.0 4.9 4.2 3.9 3.2 2.6 2.1 1.8 0.98 0.60 0


FIGURE 10.4 Applications of the unit hydrograph.


CASE 2: If the length of precipitation is different from the length of the unit-hydrograph, but it is a multiple of the unit hydrograph you are using

1) Divide the excess precipitation for the number individual simulated storms2) Multiply the unit hydrograph by the precipitation depth of the individual

simulated storms3) Add another unit-hydrograph in the next row, sliding in time as necessary4) Add the events and get the total runoff

Hydrology -Unit hydrograph Method

With the following 10-min unit hydrograph, determine runoff hydrograph for a 30 min excess rainfall of 6 cm:

6 cm total precip. / 3 events = 2 cm/event

Time (min) 0 10 20 30 40 50 60 70 80


0 1.2 2.8 1.7 2.8 1.1 0.3

Runoff - 1 (m3/s)

0 2.4 5.6 3.4 5.6 2.2 0.6

Runoff - 2 (m3/s)

0 2.4 5.6 3.4 5.6 2.2 0.6

Total Runoff(m3/s)

0 2.4 8 11.4 14.6 11.2 8.4 2.8 0.6

Runoff - 3 (m3/s)

0 2.4 5.6 3.4 5.6 2.2 0.6

Hydrology -Unit hydrograph Method

CASE 3: Precipitation is a multiple of the unit hydrograph, but flow measurements are not

Example:A 10 min-unit hydrograph for a basin is given by:

Determine runoff hydrograph for a 20 min excess rainfall of 8.5 cm

In this case the 20 minutes precipitation is a multiple of the 10-min unit hydrograph (the 10-min refers to the precipitation time when the unit hydrograph was prepared)

But the flow measurements of the unit hydrograph were taken every 30 minutes

Time (min)

0 30 60 90 120 150 180 210 240 270 300 330 360 390

Runoff (unithydrograph)

(m3/s)0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.50 0.28 0.17 0


b) Determine runoff hydrograph for a 20 min excess rainfall of 8.5 cm

𝑌 = 𝑌𝑎 + 𝑌𝑏 − 𝑌𝑎𝑋 − 𝑋𝑎𝑋𝑏 − 𝑋𝑎

Time

(min)

0 0 0 0 0 0.00

10 1.7 0.00 1.70

20 3.4 1.70 5.10

30 1.2 5.1 5.10 3.40 8.50

40 7.37 5.10 12.47

50 9.63 7.37 17.00

60 2.8 11.9 11.90 9.63 21.53

Unit

hydrograph

*4.25 cm

Slided

Runoff 2

(m3/s)

Unit

hydrograph

(m3/s/cm)

Interpolated

Runoff 1

(m3/s)

Total

Runoff

(m3/s)


Time

(min)

0 0 0 0 0 0.00

10 1.7 0.00 1.70

20 3.4 1.70 5.10

30 1.2 5.1 5.10 3.40 8.50

40 7.37 5.10 12.47

50 9.63 7.37 17.00

60 2.8 11.9 11.90 9.63 21.53

70 10.34 11.90 22.24

80 8.78 10.34 19.13

90 1.7 7.225 7.23 8.78 16.01

100 6.80 7.23 14.03

110 6.38 6.80 13.18

120 1.4 5.95 5.95 6.38 12.33

130 5.67 5.95 11.62

140 5.38 5.67 11.05

150 1.2 5.1 5.10 5.38 10.48

160 4.96 5.10 10.06

170 4.82 4.96 9.78

180 1.1 4.675 4.68 4.82 9.49

190 4.41 4.68 9.08

200 4.14 4.41 8.54

210 0.91 3.8675 3.87 4.14 8.00

220 3.63 3.87 7.49

Unit

hydrograph

*4.25 cm

Slided

Runoff 2

(m3/s)

Unit

hydrograph

(m3/s/cm)

Interpolated

Runoff 1

(m3/s)

Total

Runoff

(m3/s) Time

(min)

230 3.39 3.63 7.01

240 0.74 3.145 3.15 3.39 6.53

250 2.96 3.15 6.11

260 2.78 2.96 5.74

270 0.61 2.5925 2.59 2.78 5.37

280 2.44 2.59 5.03

290 2.28 2.44 4.72

300 0.50 2.125 2.13 2.28 4.41

310 1.81 2.13 3.94

320 1.50 1.81 3.32

330 0.28 1.19 1.19 1.50 2.69

340 1.03 1.19 2.22

350 0.88 1.03 1.91

360 0.17 0.7225 0.72 0.88 1.60

370 0.48 0.72 1.20

380 0.24 0.48 0.72

390 0 0 0 0.24 0.24

Unit

hydrograph

*4.25 cm

Slided

Runoff 2

(m3/s)

Unit

hydrograph

(m3/s/cm)

Interpolated

Runoff 1

(m3/s)

Total

Runoff

(m3/s)

Runoff – S-Hydrograph

FIGURE 10.5 Estimation of unit hydrograph from S-hydrograph.

• CASE 4: Storms in which the precipitation time is not a multiple of the unit-hydrograph (S-Hydrographs → cumulative graph)

• An S hydrograph is defined as the response to a storm of infinite duration

Runoff – S-Hydrograph

FIGURE 10.5 Estimation of unit hydrograph from S-hydrograph.

S-Hydrographs are used for storms in which the precipitation time is not a multiple of the unit-hydrograph

Espey Altman Synthetic Unit

Hydrograph

Continuous Runoff Models:

Synthetic Unit Hydrographs –Espey Altman Method

• Creates synthetic 10-min unit hydrographs• It is specific for urban areas• It was created in 1978, in a study of 41 basins ranging from 0.036 to 39 km2

• Soil cover ranged from 2 to 100% impermeable

A = basin area (mi2)L = Length of main channel (ft)S = SlopeI = % of impermeable cover (assume 5% if not urbanized)𝜙 = 𝑓(𝐼, 𝑚𝑎𝑛𝑛𝑖𝑛𝑔)


From: Chin, 2006, Water-Resources Engineering, 2nd edition.

(min)

(min)

(min)

(min)

(cfs=ft3/s)

1) Do: “Flash Processes"

MetEd Online - 5

Hydrologic Routing

Hydrologic Routing

• Routing: Is the process of determining the spatial and temporal distribution of flowrate and flow depth along a water course

• Also called “flow routing” or “flood routing”

• The basic equation is the continuity equation:

S = StorageI = Inflow rateO = Outflow ratet= Time

𝑑𝑆

𝑑𝑡= 𝐼 𝑡 − 𝑂(𝑡)

Hydrologic Routing

• There are different methods to solve for routing, such as:o Puls Methodo Modified Puls Methodo Muskingum Methodo Muskingum-Cunge Method

• Here we will use the Modified Puls Method:

S1 = Storage at time tS2 = Storage at time t+Δt

I1 = Inflow rate at time tI2 = Inflow rate at time t+Δt

O1 = Outflow rate at time tO2 = Outflow rate at time t+Δt

t= Time

𝐼1 + 𝐼2 +2𝑆1∆𝑡

− 𝑂1 =2𝑆2∆𝑡

− 𝑂2

Hydrologic Routing

A stormwater-detention basin is estimated to have the following storage characteristics:

𝑄 = 1.83𝐻 3 2

Stage Storage(m) (m3)5.0 05.5 6946.0 15256.5 25077.0 36527.5 49738.0 6484

The discharge weir from the detention basin has a crest elevation of 5.5 m, where:

Q = weir flowrate or discharge (m3/s)H = height of water above the crest of the weir (m)

Hydrologic Routing

The runoff hydrograph for the catchment is:

Time Runoff

(min) (m3/s)

0 0

30 2.4

60 5.6

90 3.4

120 2.8

150 2.4

180 2.2

210 1.8

240 1.5

270 1.2

300 1.0

330 0.56

360 0.34

390 0

If the prestorm stage in the detention basin is 5.0 m, estimate the discharge hydrograph from the detention basin

Hydrologic Routing

Solution:

0

1

2

3

4

5

6

0 100 200 300 400 500 600

Flo

wra

te (

m3/s

)

Time (min)

Inflow (m3/s) Outflow (m3/s)

Time lag

presentación de powerpoint · determine runoff hydrograph for a 20 min excess rainfall of 8.5 cm...

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