Unit Hydrograph Runoff Hydrograph – Measured at the Outflow of the Basin

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

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

A – Permeable Type of Soil B – Medium permeability C – Almost Impermeable Constant K Ce Use of soil Type of crop (Not hydraulic conductivity!) Precipitation

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 – Method NOM-011-CNA-2000

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 GIS sub-basins, and a weighted K must be obtained

퐾 (푃−250) If K ≤ 0.15 → 퐶 = 푒 2000 퐾 (푃−250) (퐾−0.15) If K > 0.15 → 퐶 = + 푒 2000 1.5

Empirical relationship

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

Unit Hydrograph 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.) Runoff Hydrographs – Unit hydrograph Method

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-hydrograph ii. 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 iii. 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) Runoff Hydrographs – Unit hydrograph Method

To obtain a unit hydrograph:

1) Remove baseflow

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

Example: Time (min) 2 8 20 30 35 40 45 50 55 Runoff (Q) 0 0 110 460 550 320 200 120 100 Assume no (m3/s) baseflow and an excess 0/3 0/3 110/3 460/3 550/3 320/3 200/3 120/3 100/3 precipitation Unit of 3 cm hydrograph 0 0 36.7 153.3 183.3 106.7 66.7 40 33.3 (m3/s/cm)

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.

We have our unit hydrograph! – but not done yet… Runoff Hydrographs – Unit hydrograph Method

• 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?

• 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 Runoff Hydrographs – Unit hydrograph Method

• 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:

Time 0 30 60 90 120 150 180 210 240 270 300 330 360 390 (min) Runoff (unit hydrograph) 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 (m3/s/cm) a) Calculate the runoff hydrograph for a 10 min excess rainfall of 3.5 cm

Time 0 30 60 90 120 150 180 210 240 270 300 330 360 390 (min) Runoff (unit hydrograph) 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 (m3/s/cm) Runoff hydrograph 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 (m3/s) Runoff – Unit Hydrograph

FIGURE 10.4 Applications of the unit hydrograph. Runoff Hydrographs – Unit hydrograph Method

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 storms 2) Multiply the unit hydrograph by the precipitation depth of the individual simulated storms 3) Add another unit-hydrograph in the next row, sliding in time as necessary 4) 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:

Time (min) 0 10 20 30 40 50 60 70 80 Runoff (unit hydrograph) 0 1.2 2.8 1.7 2.8 1.1 0.3 (m3/s/cm)

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

Runoff - 1 0 2.4 5.6 3.4 5.6 2.2 0.6 (m3/s)

Runoff - 2 0 2.4 5.6 3.4 5.6 2.2 0.6 (m3/s)

Runoff - 3 0 2.4 5.6 3.4 5.6 2.2 0.6 (m3/s)

Total Runoff 0 2.4 8 11.4 14.6 11.2 8.4 2.8 0.6 (m3/s) 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:

Time 0 30 60 90 120 150 180 210 240 270 300 330 360 390 (min) Runoff (unit hydrograph) 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 (m3/s)

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 Runoff – Unit Hydrograph

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

푋 − 푋푎 푌 = 푌푎 + 푌푏 − 푌푎 푋푏 − 푋푎

Unit Unit Interpolated Slided Total Time hydrograph hydrograph Runoff 1 Runoff 2 Runoff (min) (m3/s/cm) *4.25 cm (m3/s) (m3/s) (m3/s) 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 Runoff – Unit Hydrograph

Unit Unit Interpolated Slided Total Unit Unit Interpolated Slided Total Time hydrograph hydrograph Runoff 1 Runoff 2 Runoff hydrograph hydrograph Runoff 1 Runoff 2 Runoff (m3/s/cm) *4.25 cm (m3/s) (m3/s) (m3/s) Time (min) (min) (m3/s/cm) *4.25 cm (m3/s) (m3/s) (m3/s) 0 0 0 0 0 0.00 230 3.39 3.63 7.01 10 1.7 0.00 1.70 240 0.74 3.145 3.15 3.39 6.53 20 3.4 1.70 5.10 250 2.96 3.15 6.11 30 1.2 5.1 5.10 3.40 8.50 260 2.78 2.96 5.74 40 7.37 5.10 12.47 270 0.61 2.5925 2.59 2.78 5.37 50 9.63 7.37 17.00 280 2.44 2.59 5.03 60 2.8 11.9 11.90 9.63 21.53 290 2.28 2.44 4.72 70 10.34 11.90 22.24 300 0.50 2.125 2.13 2.28 4.41 80 8.78 10.34 19.13 310 1.81 2.13 3.94 90 1.7 7.225 7.23 8.78 16.01 320 1.50 1.81 3.32 100 6.80 7.23 14.03 330 0.28 1.19 1.19 1.50 2.69 110 6.38 6.80 13.18 340 1.03 1.19 2.22 120 1.4 5.95 5.95 6.38 12.33 350 0.88 1.03 1.91 130 5.67 5.95 11.62 360 0.17 0.7225 0.72 0.88 1.60 140 5.38 5.67 11.05 370 0.48 0.72 1.20 150 1.2 5.1 5.10 5.38 10.48 380 0.24 0.48 0.72 160 4.96 5.10 10.06 390 0 0 0 0.24 0.24 170 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 Runoff – 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

FIGURE 10.5 Estimation of unit hydrograph from S-hydrograph. Runoff – S-Hydrograph

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

FIGURE 10.5 Estimation of unit hydrograph from S-hydrograph. Continuous Runoff Models:

Espey Altman Synthetic Unit Hydrograph 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 = Slope I = % of impermeable cover (assume 5% if not urbanized) 휙 = 푓(퐼, 푚푎푛푛푖푛푔) Synthetic Unit Hydrographs –Espey Altman Method Synthetic Unit Hydrographs –Espey Altman Method Synthetic Unit Hydrographs –Espey Altman Method

(min) (min)

(cfs=ft3/s) (min) (min)

From: Chin, 2006, Water-Resources Engineering, 2nd edition. MetEd Online - 5

1) Do: “Flash Processes" 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:

푑푆 = 퐼 푡 − 푂(푡) 푑푡

S = Storage I = Inflow rate O = Outflow rate t= Time Hydrologic Routing • There are different methods to solve for routing, such as: o Puls Method o Modified Puls Method o Muskingum Method o Muskingum-Cunge Method • Here we will use the Modified Puls Method:

2푆 2푆 퐼 + 퐼 + 1 − 푂 = 2 − 푂 1 2 ∆푡 1 ∆푡 2

S1 = Storage at time t S2 = Storage at time t+Δt I1 = Inflow rate at time t I2 = Inflow rate at time t+Δt O1 = Outflow rate at time t O2 = Outflow rate at time t+Δt t= Time Hydrologic Routing

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

Stage Storage (m) (m3) 5.0 0 5.5 694 The discharge weir from the detention basin has a 6.0 1525 crest elevation of 5.5 m, where: 6.5 2507 3 7.0 3652 푄 = 1.83퐻 2 7.5 4973 3 8.0 6484 Q = weir flowrate or discharge (m /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 If the prestorm stage in the detention 60 5.6 basin is 5.0 m, estimate the discharge 90 3.4 hydrograph from the detention basin 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 Hydrologic Routing

Solution:

6 Time lag

/s) 3

Flowrate (m Flowrate 2

0 0 100 200 300 400 500 600 Time (min) Inflow (m3/s) Outflow (m3/s)