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

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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 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 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. Continuous Runoff Models: 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.
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