Rainfall Runoff Relationships - 2

# Rainfall Runoff Relationships - 2 | Engineering Hydrology - Civil Engineering (CE) PDF Download

Direct runoff calculations using unit hydrograph

Assume that a 6-hour unit hydrograph (UH) of a catchment has been derived, whose ordinates are given in the following table and a corresponding graphical representation is shown in Figure 8.

 Time (hours) Discharge (m3/s) 0 0 6 5 12 15 18 50 24 120 30 201 36 173 42 130 48 97 54 66 60 40 66 21 72 9 78 3.5 84 2

FIGURE 8. A 6-hour unit hydrograph

Assume further that the effective rainfall hyetograph (ERH) for a given storm on the region has been given as in the following table:

 Time (hours) Effective Rainfall (cm) 0 0 6 2 12 4 18 3

This means that in the first 6 hours, 2cm excess rainfall has been recorded, 4cm in the next 6 hours, and 3cm in the next.

The direct runoff hydrograph can then be calculated by the three separate hyetographs for the three excess rainfalls by multiplying the ordinates of the hydrograph by the corresponding rainfall amounts. Since the rainfalls of 2cm, 4cm and 3cm occur in successive 6-hour intervals, the derived DRH corresponding to each rainfall is delayed by 6 hours appropriately.

These have been shown in the figures indicated.

The final hydrograph is found out by adding the three individual hydrographs, as shown in Figure 12.

FIGURE 12. Final direct runoff hydrograph derived from summation of individual DRHs

The calculations to generate the direct runoff hydrograph (DRH) from a given UH and ERH can be conveniently done using a spreadsheet program, like the Microsoft XL.

A sample calculation for the example solved graphically is given in the following table. Note the 6 hour shift of the DRHs in the second and subsequent hours.

 Time(hours) UnitHydrograp h ordinates (m3/s) Direct runoff due to 2 cm excess rainfall in first 6 hours (m3/s)(I) Direct runoff due to 4 cm excess rainfall in second 6 hours (m3/s)(II) Direct runoff due to 3 cm excess rainfall in third 6 hours (m3/s)(III) DirectrunoffHydrograph(m3/s)(I)+(II)+(III) 0 0 0 0 0 0 6 5 10 0 0 10 12 15 30 20 0 50 18 50 100 60 15 175 24 120 240 200 45 485 30 201 402 480 150 1032 36 173 346 804 360 1510 42 130 260 692 603 1555 48 97 194 520 519 1233 54 66 132 388 390 910 60 40 80 264 291 635 66 21 42 160 198 400 72 9 18 84 120 222 78 3.5 7 36 63 106 84 2 4 14 27 45 90 0 8 10.5 18.5 96 0 0 6 6

The last column in the above table gives the ordinates of the DRH produced by the ERH.  If the base flow is known or estimated (Lesson 2.2), then this should be added to the DRH to obtain the 6-houly ordinates of the flood hydrograph.

The S – curve

This is a concept of the application of a hypothetical storm of 1 cm ERH of infinite duration spread over the entire catchment uniformly.  This may be done by shifting the UH by the T-duration for a large number of periods. The resulting hydrograph (a typical one is shown in Figure 13) is called the S – hydrograph, or the S – curve due to the summation of an infinite series of Thour unit hydrographs spaced T – hour apart. For the example of the UH given in the earlier section, the table below provides the necessary calculations.

FIGURE 13. S - Curve, or Summed up Unit Hydrographs

 Time(hr)06121824303642485460667278849096 UHOrdi-Nates0515501202011731309766402193.5200 UH Ordinates shifted by 6 hr00515501202011731309766402193.520 UHOrdi-nates shifted  by12 hr '000515501202011731309766402193.52 UHOrdi-natesshiftedby18 hr0000515501202011731309766402193.5 UHOrdi-natesshiftedby24 hr0000051550120201173130976640219 0000005155012020117313097664021 000000051550120201173130976640 00000000515501202011731309766 0000000005155012020117313097 000000000051550120201173130 0000000000051550120201173 00000000000051550120201 000000000000051550120 0000000000000051550 000000000000000515 00000000000000005 Sumofall the UH ordinates052070190391564694791857897918927930.5932.5932.5932.5

The average intensity of the effective rainfall producing the S – curve is 1/T (mm/h) and the equilibrium discharge is given as A/TX104m/ h where, A is the area of the catchment in Km2 and T is the unit hydrograph duration in hours.

Application of the S – curve

Though the S – curve is a theoretical concept, it is an effective tool to derive a t – hour UH from a T – hour UH, when t is smaller that T or t is lager than T but not an exact multiple of T. In case t is a multiple of T, the corresponding UH can be obtained without the aid of a S – hydrograph by summing up the required number of UH, lagged behind by consecutive T – hours.

For all other cases shift the original S – hydrograph as derived for the T – hour UH by t hours to obtain a lagged S- hydrograph. Subtract the ordinates of the second curve from the first to obtain the t – hour graph. Next, scale the ordinates of the discharge hydrograph by a factor t/T, to obtain the actual t – hour UH which would result due to a total 1 cm of rainfall over the catchment. This is illustrated by the S-curve derived in the previous section.

Recall that the S-curve was obtained from a 6-hour UH. Let us derive the UH for a 3-hour duration. Since we do not know the ordinates of the S-curve at every 3-hour interval, we interpolate and write them in a tabular form as given in the table below:

 Time S-curve ordinates as derived from 6-hr UH (I) S-curve ordinates as derived from 6-hr UH but with interpolated values (II) S-curve ordinates as derived from 6-hr UH lagged by 3 hrs. (III) Difference of the two S- curves (II) - (III) (IV) 3-hr UH ordinates Col. (IV) divided by (3hr/6hr) (IV)*2 (hours) (m3/s) (m3/s) (m3/s) (m3/s) (m3/s) 0 0 0 0 3 2.5 0 2.5 6 5 5 2.5 2.5 9 12.5 5 7.5 12 20 20 12.5 7.5 15 45 20 25 18 70 70 45 25 21 130 70 60 24 190 190 130 60 27 290.5 190 100.5 30 391 391 290.5 100.5 33 477.5 391 86.5 36 564 564 477.5 86.5 39 629 564 65 42 694 694 629 65 45 742.5 694 48.5 48 791 791 742.5 48.5 51 824 791 33 54 857 857 824 33 57 877 857 20 60 897 897 877 20 63 907.5 897 10.5 66 918 918 907.5 10.5 69 922.5 918 4.5 72 927 927 922.5 4.5 75 928.75 927 1.75 78 930.5 930.5 928.75 1.75 81 931.35 930.5 0.85 84 932.5 932.5 931.35 1.15 87 932.5 932.5 0 90 932.5 932.5 932.5 0 93 932.5 932.5 0 96 932.5 932.5 932.5 0

Derivation of unit hydrograph

An observed flood hydrograph at a streamflow gauging station could be a hydrograph resulting from an isolated intense short – duration storm of nearly uniform distribution in time and space, or it could be due to a complex rainfall event of varying intensities.  In the former case, the observed hydrograph would mostly be single peaked whereas for the latter, the hydrograph could be multi peaked depending on the variation in the rainfall intensities.  For the purpose of this course, we shall only consider rainfall to be more or less uniformly distributed in time and space for the purpose of demonstrating the derivation of unit hydrograph.  The procedure may be broadly divided into the following steps:

1. Obtain as many rainfall records as possible for the study area to ensure that the amount and distribution of rainfall over the watershed is accurately known.  Only those storms which are isolated events and with uniform spatial and temporal distribution are selected along with the observed hydrograph at the watershed outlet point.
2. Storms meeting the following criteria are generally preferred and selected out of the uniform storms data collected in Step 1.
3. Storms with rainfall duration of around 20 to 30 % of basin lag,
4. Storms having rainfall excess between 1 cm and 4.5 cm.
5. From the observed total flood hydrograph for each storm separate the base flow (discussed in lecture 2.2) and plot the direct runoff hydrograph.
6. Measure the total volume of water that has passed the flow measuring point by finding the area under the DRH curve.  Since area of the watershed under consideration is known, calculate the average uniform rainfall depth that produced the DRH by dividing the volume of flow (step 3) by the catchment area.  This gives the effective rainfall (ER) corresponding to the storm.  This procedure has to be repeated for each selected storm to obtain the respective ERs.
7. Express the hydrograph ordinate for each storm at T – hour is the duration of rainfall even.  Divide each ordinate of the hydrograph by the respective storm ER to obtain the UH corresponding to each storm.
8. All UHs obtained from different storm events should be brought to the same duration by the S – curve method.
9. The final UH of specific duration is obtained by averaging the ordinates of he different UH obtained from step 6.

Unit hydrograph for ungauged catchments

For catchments with insufficient rainfall or corresponding concurrent runoff data, it is necessary to develop synthetic unit hydrograph.  These are unit hydrographs constructed form basin characteristics.  A number of methods like that of Snyder’s had been used for the derivation of the Synthetic hydrographs.  However, the present recommendations of the Central Water Commission discourage the use of the Snyder’s method.

Instead, the Commission recommends the use of the Flood Estimation Reports brought out for the various sub–zones in deriving the unit hydrograph for the region.  These sub–zones have been demarcated on the basis of similar hydro – meteorological conditions and a list of the basins may be found.  The design flood is estimated by application of the design storm rainfall to the synthetic hydrograph developed by the methods outlined in the reports.

Catchment modelling

With the availability of personal computer high processing speed within easy reach of all, it is natural that efforts have been directed towards numerical modeling the catchment dynamics and its simulation.  It is not possible to outline each model in detail, but the general concept followed is to represent each physical process by a conceptual mathematical model which can be represented by an equivalent differential or ordinary equation.  These equations are solved by changing the equations to solvable form and writing algorithms in suitable computer language.  However, the user of the programs generally input data through a Graphical User Interface (GUI) since there is a lot of spatial information to be included like land-use, land-cover, soil property, etc.  Now a day, this information interaction between the user and the computer is through Geographic Information System (GIS) software.  Once the information is processed, the output results are also displayed graphically.

Examples of catchment models

Though many of these models are sold commercially, there are quite a few developed by academic institutions and government agencies worldwide which are free and can be downloaded for non – commercial purposes through the internet.  A few examples are given below.

• US Army corps of Engineers’ HEC-HMS and HEC-GeoHMS
• US Army corps of Engineers’ GRASS
• US Army corps of Engineers’ TOPMODEL

Water resources section of the Department of Civil Engineering, IIT Kharagpur has developed a watershed simulation model based on deterministic theory.  A copy of the same may be made available on request for educational purposes.

Important terms

1. Linearity: A linear relation between rainfall and runoff form a catchment suggests that variations in rainfall over a catchment is related to the variations in runoff from the outlet of the catchment by a linear function.
2. Basin lag: Basin lag is the time between the peak flow and the centroid of rainfall.
3. Graphical User Interface (GUI): An interface that represents programs, files, and options with graphical images is called GUI. These images can include icons, menus, and dialog boxes. The user selects and activates these options by pointing and clicking with a mouse or with the keyboard. A particular GUI item (for example, a scroll bar) works the same way in all applications.
4. Geographic Information System (GIS):  A system, usually computer based, for the input, storage, retrieval, analysis and display of interpreted geographic data.  The database is typically composed of map-like spatial representations, often called coverages or layers.  These layers may involve a three dimensional matrix of time, location, and attribute or activity.  A GIS may include digital line graph (DLG) data, Digital Elevation Models (DEM), geographic names, land-use characterizations, land ownership, land cover, registered satellite and/or areal photography along with any other associated or derived geographic data.
5. HEC-HMS: The Hydrologic Modeling System (HEC-HMS) is designed to simulate the precipitation-runoff processes of dendritic watershed systems. It is designed to be applicable in a wide range of geographic areas for solving the widest possible range of problems. This includes large river basin water supply and flood hydrology, and small urban or natural watershed runoff. Hydrographs produced by the program are used directly or in conjunction with other software for studies of water availability, urban drainage, flow forecasting, future urbanization impact, reservoir spillway design, flood damage reduction, floodplain regulation, and systems operation.
6. HEC-GeoHMS: The Geospatial Hydrologic Modeling Extension (HECGeoHMS) is a public-domain software package for use with the ArcView Geographic Information System. GeoHMS uses ArcView and Spatial Analyst to develop a number of hydrologic modeling inputs. Analyzing the digital terrain information, HEC-GeoHMS transforms the drainage paths and watershed boundaries into a hydrologic data structure that represents the watershed response to precipitation. In addition to the hydrologic data structure, capabilities include the development of grid-based data for linear quasi-distributed runoff transformation (ModClark), HEC-HMS basin model, physical watershed and stream characteristics, and background map file.
7. GRASS: GRASS is an integrated set of programs designed to provide digitizing, image processing, map production, and geographic information system capabilities to its users.  GRASS is open software with freely available source code written in C.
8. Topmodel: TOPMODEL predicts catchment water discharge and spatial soil water saturation pattern based on precipitation and evapotranspiration time series and topographic information.
The document Rainfall Runoff Relationships - 2 | Engineering Hydrology - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Engineering Hydrology.
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## FAQs on Rainfall Runoff Relationships - 2 - Engineering Hydrology - Civil Engineering (CE)

 1. What is the concept of rainfall-runoff relationship in civil engineering?
Ans. The concept of rainfall-runoff relationship in civil engineering refers to the understanding of how rainfall events on the land surface contribute to the flow of water in rivers, streams, and other water bodies. It involves studying the relationship between the amount and intensity of rainfall and the resulting runoff or flow of water.
 2. How is the rainfall-runoff relationship important in civil engineering?
Ans. The rainfall-runoff relationship is crucial in civil engineering as it helps in designing and managing drainage systems, flood control measures, and water resource management. By understanding how rainfall events translate into runoff, engineers can design infrastructure that can effectively handle and mitigate the impacts of rainfall on the built environment.
 3. What factors influence the rainfall-runoff relationship?
Ans. Several factors influence the rainfall-runoff relationship, including the characteristics of the watershed or catchment area, such as its size, shape, slope, and land use. The soil type and condition, as well as the antecedent moisture content, also play a significant role. Additionally, the intensity, duration, and distribution of rainfall events affect the runoff response.
 4. How can the rainfall-runoff relationship be quantified?
Ans. The rainfall-runoff relationship can be quantified through various methods and mathematical models. One commonly used approach is the use of hydrological models, which simulate the rainfall-runoff process based on input data such as rainfall records and watershed characteristics. These models can provide insights into the runoff volume, peak flow rates, and timing of runoff events.
 5. What are the challenges in predicting rainfall-runoff relationships?
Ans. Predicting rainfall-runoff relationships can be challenging due to the complex nature of hydrological processes. Factors such as uncertainty in rainfall data, variability in watershed characteristics, and the presence of non-linear processes can make accurate predictions difficult. Additionally, the impacts of land use changes, climate change, and extreme rainfall events further complicate the prediction of rainfall-runoff relationships.

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