POLYTECHNIC UNIVERSITY OF THE PHILIPPINES

College of Engineering

Department of Civil Engineering NDC Compound, Anonas St., Sta. Mesa, Manila

DAM ENGINEERING

GROUP 1

Written Report

HYDROLOGIC STUDIES

GROUP MEMBERS:

Alcaraz, Aprilito

Allones, Harold John

Bacho, Edison

Benliro, Jezreel

Bernal, Divina

Estrabo, Jonas

Nadala, Jermaine Benjch

Sevial, Nico

Rosales, Angelica May

Yuzon, Jaycee

BSCE 5-4

HYDROLOGY STUDIES

Hydrology studies are performed by environmental consultants or hydrologic engineers.

The studies are based on the review of existing maps and records, as well as the

collection of site- specific hydrologic measurements.

Hydrologic Studies involves learning about the properties of water and its maintenance.

Hydrologic technicians are vital to the health and sustainability of water resources,

providing maintenance and management skills necessary for environmental protection.

Characteristics of a hydrologic technician include having a love of nature and passion for

the environment. Many technicians spend a majority of their time working outdoors.

EVALUATION AND REVISION OF EXISTING RECORDS

Before beginning any hydrologic analysis it is important to be sure that the data are

homogeneous. This requires checking history and / or double mass analysis. Stream flow data

can be further evaluated by checking the changes which have occurred in the basin during the

period of record. In each case, the data should be appropriately adjusted to either current

conditions or natural conditions. The errors resulting from lack of homogeneity in data are

especially serious because they lead to bias in the final answers.

Double Mass Analysis

Changes in gage location, exposure, instrumentation, or observational procedure may

cause a relative change in the precipitation catch. Frequently, these changes are not disclosed in

the public records. To test the consistency of the record double-mass analysis can be used.

Double-mass analysis-tests record consistency at a station by comparing its accumulated

annual or seasonal precipitation with the concurrent accumulated values of mean

precipitation for a group of surrounding stations.

For example, a change in slope about 1961 indicates a change in the precipitation regime

of Dillon, Colorado. A change due to meteorological causes would not cause a change in slope,

as all base stations would be similarly affected. The station history of Dillon discloses a change

in gage location in June 1961. To make the record prior to 1961 comparable with that for the

more recent location, it should be adjusted by the ratio of the slopes of the two segments of the

double-mass curve (0.74/1.19). The consistency of the record for each of the base stations should

be tested, and those showing inconsistent records should be dropped before other stations are

tested or adjusted.

ESTIMATING DISCHARGE OF PAST FLOODS

Flood stage record in conjunction with a stage-discharge relation is the preferred method

for estimating the magnitudes of past floods.

Factors affecting the above procedure:

1. The greatest known flood may have occurred prior to the establishment of a

gaging station or after its discontinuance.

2. The greatest flood may have destroyed the gaging station.

3. Records of past floods are only available at other points in the river basin.

In populated river basins the heights reached by great floods of the past have often been

noted on buildings and bridges, and estimates have been made of the corresponding

discharges.

In sparsely developed areas it is necessary to make a search for floodmarks noted by local

inhabitants.

The inflow-outflow storage relations at existing dams and reservoirs can also be used to

estimate flood flows.

If past floods have been determined elsewhere on a river, the corresponding discharge at

the dam site may be estimated by assuming that flood magnitudes are proportional to

some exponential power of the drainage area, usually 0.53

EXTENDING THE PERIOD OF RECORDS

Correlation of Runoff Records

There is often a need to estimate the additional periods in runoff records to increase

the length of a short record or to fill the periods, where the record was interrupted for

various reasons.

THE PROCEDURE IS TO CORRELATE FLOWS with those at another gaging

station in the same or in an adjacent basin which has a longer record.

The relation established between the stations can then be used to extend the stream

flow record at the dam site.

For example, if X and Y are to variables, one with data for the period of N time units, and

the other for K time units respectively with N>K.

The area to be compared should be:

AREA- about the same size

Having similar hydrologic

Topographic

Geologic characteristics

Average flows for a month are generally adequate for reservoir capacity studies and reservoir

operation studies.Estimates of daily flows are not generally reliable unless based on records

collected at points on the same stream and where differences in drainage area are small.

The correlation was used to extend the dam site record, 1964-71, to the additional period

available at Montague, 1936-63.

If the number of values to be estimated is not to great, a graphical comparison of the hydrographs

at two stations can be made. The discharge values are plotted on a logarithmic scale as this

permits equivalent accuracy for a wide range of magnitudes.

Correlation Of Runoff And Precipitation Records

If a drainage basin has a sufficient number of precipitation records to provide an index of

the average basin precipitation, a RUNOFF- PRECIPITATION RELATION may be

developed and used to extend monthly runoff records.

Multiple correlation may be required in which runoff is related to various percentages of

precipitation in previous.

Use of an electronic computer for this type of analysis can save considerable time.

Generation of synthetic records by statistical methods

In recent years, several statistical procedures have been proposed for the sequential

generation of synthetic records.

The generated record exhibits the same characteristics and statistical parameters (mean

and standard deviation) as the basic record, but may indicate possible sequences of high

and low flows which are more critical than those in the record.

The time unit in such studies is usually a month.

ANALYSIS OF RUNOFF RECORDS

(a) HOMOGENITY OF RECORDS

Before a record of river runoff can be analyzed for the use in the design of water resources development

project it must be determined that the hydrologic character of the river basin particularly in regard to man-

made developments, has not change significantly through out the record. In other words, the record must

be statistically homogeneous.

Changes that may take place in a river basin include the following:

*diversions of flow into or out of the basin

*changes in artificial storage by construction of reservoirs

*changes in natural storage by drainage of swamps and lakes

*progressive changes in cover and land use caused by deforestation, afforestation, agricultural practices,

or construction of impervious areas.

(b) HYDROGRAPH

The chronological record of flow is termed the hydrograph. It is basic data for all statistical analyses of

the runoff of a drainage basin. The hydrograph reveals many aspects of the runoff characteristics of the

basin including:

*the seasonal distribution of high and low flows.

*the character of flood flows, whether occurring isolated flood rises or in a succession of floods rising

above a high seasonal base and lasting several months.

*the influence of snowmelt.

*the effect of valley storage.

*the contribution of ground-water flow.

Example of hydrograph

The time unit used in compiling and analyzing the hydrograph will vary with its intended use. Annual

discharges are usually of interest only in comparing sequences of high and low years. Monthly flows are

the most useful unit in reservoir design for municipal water supply, irrigation development, and

hydroelectric power. Hydrographs in units of a day or less are needed to develop design floods.

(c) MASS CURVE

A useful device in the analysis of runoff records is the mass curve which is a plot of the cumulative runoff

from the hydrograph against time. The time scale is the same for the hydrograph and may be in days or

months. The volume ordinate may be in cfs-days, cfs-months, acrefeet, million gals per day, etc. The

slope of the mass curve is the derivative of the volume with respect to time or the rate of discharge.

Example of Mass Curve

(d) STORAGE –DRAFT CURVE

The results of a mass curve analysis can be plotted as a storage-draft curve. This curve gives the storage

needed to sustain various draft rates.

If the storage is unlimited, the storage-draft curve will approach the available mean flow as an asymptote.

It is rarely possible to develop the mean annual flow of a river basin. For most projects, some spillage will

occur in years of high runoff. To impound all flood flows will require an excessively large reservoir.

Such a reservoir may not fill in many years, and probably could not be justified economically. The

selected rate of regulated flow to be developed will depend on:

*the demands of the water users,

*the available runoff,

*the physical limits of the storage capacity,

*and the overall economic project

The storage draft curve indicates only the specific storage needed to achieve different rates of regulated

flow.

Example of Storage-Draft Curve

(e) Selection of Design Flow

The hydrologic analyses, combined with economic analyses of costs and benefits for different heights of

dam and reservoir capacities will lead to the selection of the reservoir capacity and the corresponding

dependable flow that can be justified. The selected design flow may not necessarily be available 100

percent of the time. The proposed water use may permit deficiencies at intervals, for example, a 15

percent storage once in 10 years. Irrigation water supplies permit greater deficiencies than those for urban

and industrial use. Hydroelectric power plants, connected to a large systems, may tolerate substantial

water supply deficiencies.

OPERATION AND ROUTING STUDIES

A plan devised to achieve the greatest value of benefit from the storage capacity.

Based on:

1. Knowledge of the flow characteristics of the stream ( how it perform in the past years)

2. Purposes of the reservoir ( must be analyzed to determine how the hydrograph of flow should

be altered to produce the greatest benefits).

a. Single-Purpose Operation

b. Multi-Purpose Operation

3. Effect of sudden releases on stream banks and long sustained flows from the reservoir on

agricultural development in the valley below the reservoir.

ROUTING TECHNIQUES

The Calculus Method

(Applicable only for preliminary studies of reservoir behavior to save time and labor involved in making

the exact analysis)

Assumptions:

1. The area –depth curve for a reservoir is a semi- cubical parabola with area denoted by A and depth by

H, while B and C are constants

A= CH 3/2

2. The outflow depth curve for the outlet is an ordinary parabola

A = BH 1/2

3. The inflow hydrograph of the flood maybe replace d by a rectangle representing a uniform inflow rate

I, lasting for a length of time T.

The above assumptions lead to simple mathematically derived conclusions as below:

1. The average rate of outflow during a uniform flood is approximately 5/6 of the maximum

rate of outflow during this period.

2. During the emptying period, the average outflow is 4/5 the maximum rate of outflow

during this period.

The two conclusions are known as the 5/6 and 4/5 rules.

Example 1.

The average intensity of the flood to be controlled in 20hrs is 3.0 Mm3/hr, and the

maximum possible outflow is 0.84 Mm3 /hr. Find the storage capacity needed for the proposed

reservoir.

Sol’n:

Ave. outflow during filling period = 5/6 x 0.84 Mm3/hr = 0.70 Mm

3/hr

Total outflow during this period = ave. outflow x duration

= 0.70 x 20 =14.0 Mm3

Storage Capacity required = total inflow – total outflow

= (20 x 3.0) – 14.0

= 46.0 Mm3

DESIGN FLOODS

Flood

A flood is commonly considered to be an unusually high stage of a river. For a river in its natural state,

occurrence of a flood usually fills up the stream up to its banks and often spills over to the adjoining

flood plains.

Design Flood

• The maximum flood that any structure can safely pass.

• The flood considered for the design of a structure corresponding to a maximum tolerable risk.

• The flood which a project (involving a hydraulic structure) can sustain without any substantial

damage, either to the objects which it protects or to its own structures.

• The largest flood that may be selected for design as safety evaluation of a structure.

Design Flood is also known as the Inflow Design Flood (IDF). It is the flood adopted for design purpose,

and could be:

o The entire flood hydrograph, that is, the possible values of discharge as a function of time.

o The peak discharge of the flood hydrograph.

Factors for Selecting the Method of Peak Flow and Frequency Determination

1. Desired Objective- A distinction can be made between the method to determine the magnitude

of the peak flow and the method to determine the maximum volume of flow during a flood period. The

peak may be important in one design problem, while volume in another.

2. Available Data- Long term records of hydrologic data permit the rational application of

statistical procedures, but success in the use of these techniques is inhibited by short term records.

3. The area and characteristics of the watershed – these factors affect the runoff process and

consequently govern the way in which the runoff and hence the peak flow occurs.

4. The importance of the project and time available for analysis- The time available for analysis

governs mainly the sophistication attempted in the analysis.

PEAK FLOW DETERMINATION

1. Unit Hydrograph Method

-Is the most popular and widely used method for predicting flood hydrograph resulting from a known

storm

-First suggested by Sherman in 1932

-A unit hydrograph is defined as the hydrograph of direct runoff resulting from one unit depth (1cm) of

rainfall excess occurring uniformly over the basin and at a uniform rate for a specified duration (D

hours)

Standard Project Flood (SPF)

Standard project flood (SPF) is the flood that would result from a severe combination of meteorological

and hydrological factors that are reasonably applicable to the region. Extreme rare combinations of

factors are excluded. SPF is often used where the failure of a structure would cause less severe damages.

Typically the SPF is about 40 to 60% of the PMF for the same catchment.

Probable Maximum Flood (PMF)

Probable maximum flood (PMF) is the extreme flood that is physically possible in a region as a result of

severe most combinations, including rare combinations of meteorological and hydrological factors. The

PMF is used in situations where the failure of the structure would result in loss of life and catastrophic

damage and as such complete security from potential floods is sought.

To estimate the design flood for a project by the use of a unit hydrograph, one needs the design

storm. This can be the storm producing PMF or SPF as per the design case.

2. Flood Routing

-is the technique of determining the flood hydrograph at a section of a river by utilizing the data of

flood flow at one or more upstream sections. Flood routing is used in

flood forecasting

flood protection

reservoir design

design of spillway and outlet structures

Flood routing types

reservoir routing

channel routing

Routing methods

hydrologic routing (I − O = dS/dt)

hydraulic routing

3. Flood Frequency Analysis

This is the calculation of the statistical probability that a flood of a certain magnitude for a given river

will occur in a certain period of time. Each flood of the river is recorded and ranked in order of

magnitude with the highest rank being assigned to the largest flood. The return period here is the likely

time interval between floods of a given magnitude and can be calculated as:

number of years of river records + 1rank of a given flood

FLOOD ESTIMATION by Rational Method

Rational Method is based on the principle that if a rainfall of uniform intensity and unlimited duration

falls on a basin, the runoff rate will be maximum at the time of concentration tc , as it is only at this

time when the first drop of rainfall, which fell at the remotest part of the basin, reaches the outlet point.

The method is suitable for peak flow prediction in small size (< 50 km2) catchments.

Qp = CIA

Qp = peak runoff rate (m3/s)

C = runoff coefficient / ratio of total volume of runoff to rainfall

-integrated effect of the catchment losses and hence depends upon the nature of the surface, surface

slope and rainfall intensity

I = rainfall intensity (cm/h) of a storm whose duration is equal to the time of concentration of the basin

A = area of watershed (km2)

For a rainfall of uniform intensity and very long duration over a catchment the runoff increases

as more and more flow from remote areas of the catchment reach the outlet. If the rainfall

continues beyond the time of concentration (t > tc), the runoff will be constant and at the peak

value (Qp) equal to Qp = CiA.

FLOOD ESTIMATION by Empirical Formula

The formula is based on statistical correlation of the observed peak and important catchment and storm

properties.

Most of the formulae use the catchment area as a single parameter affecting the flood peak and other

factors are clubbed in a region specific constant parameter.

Dickens Formula

Qp = CD A3/4

in which Qp is in m3/s and A is in km2

CD = Dicken’s constant with value between 6 to 30 depending upon the region (catchment type and

average rainfall)

Ryves Formula

Qp = CR A3/2

in which CR = Ryves’s constant with value between 6.8 to 12 depending upon the region (catchment

type and average rainfall)

Inglis Formula

Q p= 124A/ √(A +10.4)

SAMPLE PROBLEM

Determine the 10-year peak flow over a downtown drainage area of 3 ha with the length of water course

as 1.0 km and slope 0.5%. The IDF curve may be used.

A= 3 ha = 0.03 sq km

L = 1.0 km =1000 m

S = 0.5% = 0.5/100 = 0.005

tc= 0.50 h or 3o min

I = 3.3 cm/h for a tc = 3o min

C = 0.80

10- year peak flow rate, Qp = CIA

Qp = 0.80 x 3.3 x (3.0/100) m3/s

Qp = 0.0792 m3/s

ANALYSIS OF STORMS AND FLOOD OF RECORDS

Analysis of Storms of Records

The major storms over a project basin and its surrounding area are analyzed with regard

to its orientation, isohyetal patterns, areal coverage, total depth, duration and short-term

intensities. First step in the analysis is to plot the isohyetal map of total storm rainfall. Such maps

are used to determine depth-area relations for the total storm or for selected time periods. In

mountainous topography, it may be advisable to draw isohyetal lines considering the topographic

and orographic effects where affects. Another method of determining the depth-area relations is

called the Thiessen method. Second step in the analysis of storm rainfall over a particular basin

is the determination of the depth-time distribution. The time distribution is determined by

analysis of observations registered by continuous recording gages. For a given storm, the

cumulative rainfalls from various recording gages may be plotted as mass curves for a visual

appraisal of consistency and a check for obvious errors. And by comparing cumulative rainfalls,

it may be concluded that the entire basin rainfall could be represented by the direct or weighted

average time distribution shown by the recording gages. Once the representative time

distribution pattern and the desirable time increment have been selected, the difference between

rainfall depths at successive time intervals can be plotted to form a hyetograph , which is a bar

graph pictorially representing basin average rainfall intensities.

Analysis of Flood of Records

Flood frequency method is a method dealing with the runoff directly. This method does

not provide a hydrograph shape but gives only a peak discharge known frequency.

Frequency studies interpret a past record of events to predict the future possibilities of

occurrence. In analyzing by statistical method, it is assumed that the occurrences are:

Individual events

Factors influencing character of each event remain unaltered.

Measurement technique and size of observation are identical.

It may be difficult to find data conforming to all requirements. Thus a preliminary step

the basic data should first be screened and adjusted to remove.

The following are the most important conditions:

Effect of man-made changes in the regime of flow should be investigated and

adjustment made as required.

For small watersheds, a distinction should be made between daily maxima and

instantaneous or momentary flood peaks.

Changes in the stage-discharge relationship make stage records nonhomogeneous

and unsuitable for frequency analysis. It is therefore preferable to work with the

discharges. In case stage frequencies are required, refer the results to the moist

recent rating.

Any useful information contained in data publications and manuscripts should be

made use of after proper scrutiny.

Determination of Frequency

The first problem that a hydrologist faces in practice is to decide on the frequency

of the flood to be adopted in the design of hydraulic structure. This obviously depends

upon the degree of risk he is prepared to take.. The degree of risk that we run in designing

a structure during an anticipated service of life of n years for a flood of a particular

frequency can be theoretically evaluated from the binomial distribution is reproduced as:

P(X = x) = [n!/x!(n-x)!](1-ρ) n-x

Where:

x= number of times a given flood magnitude is to be equalled or exceeded

ρ = the probability of occurrence of a flood equal to or greater than the given

flood magnitude.

n = number of trials, or in other words, the life of the project.

Method of Frequency Analysis

Frequencies can be evaluated graphically by plotting magnitudes of a hydrologic

variable against the frequencies with which they have been equalled or exceeded and

fitting a smooth curve through the plotted points and assuming the same as representative

of future possibilities. To standardize the basis for fitting a curve , the concept of

theoretical distribution is employed. Once a distribution is employed, it is a simple and

straightforward process to calculate the required probabilities.

Two Distributions Commonly Used

Logarithmic normal

Curve fitting methods, graphical or mathematical

Extreme value

Gumbel Method

Log-normal Method

Foster Method

Hazen Method

The methods based on frequency factors use the equation:

x = X + Ks eq. (13.25)

Where:

x = flood magnitude of given return period T

X = mean of recorded flood

s = standard deviation of recorded floods

K = frequency factor

Gumbel’s method

- This form of distribution law with a bearing on the nature of the data is accepted

as the best suited for the frequency analysis.

The magnitude of the flood x for the desired return period T years can be

estimated from eq. (13.25) provided the value of K is known as X and s can be estimated

from the observed flood data. The value K for Gumbel’s distribution has been has been

derived and its values based on the sample size and given return period.

Log- Normal Method

- This is based on the log-normal probability law and assumes that the flood is

such that their natural logarithms are normally distributed.

Foster’s Method

- Foster suggested the use of Pearson’s skew functions for fitting observed flood

data. Pearson adopted the general differential equation,

Where:

x = deviation of the variable X from its mean

J = frequency corresponding to x

a = a constant

f(x) = function of x

Hazen’s Method

- adopted the same values of ô x and C s as calculated in foster’s method.

However, instead of the table of skew factors based on the Pearson’s curve, he

developed a series of factors on the assumption that the logarithms of the variable are

normally distributed. He recognized that the resulting curve might not fit the actual data

in all cases and suggested that several values of C s may be tried and one giving the best

fit selected. Reducing the coefficient of skew tends to reduce extreme values and increase

those near the centre of the distribution.

Design Storms

Reported by: Aprilito D. Alcaraz

A design storm is a precipitation pattern defined for use in the design of a hydrologic system.

Usually the design storm serves as the system input, and the resulting rates of flow through the system

are calculated using rainfall-runoff and flow routing procedures. A design storm can be defined by a

value for precipitation depth at a point, by a design hyetograph specifying the time distribution of

precipitation during a storm, or by an isohyetal map specifying the spatial pattern of the precipitation.

Design storm can be based upon historical precipitation data at a site or can be constructed

using the general characteristics of the precipitation in the surrounding region. Their application ranges

from the use of point precipitation values in the rational method for determining peak flow rates in

storm sewers and highway culverts, to the use of storm hyetographs as inputs for rainfall-runoff analysis

of urban detention basins or for spillway design in large reservoir projects. This chapter covers the

development of point precipitation data, intensity-duration-frequency relationships, design

hyetographs, and estimated limiting storm based on probable maximum precipitation.

DESIGN PRECIPITATION DEPTH

POINT PRECIPITATION

A point precipitation is precipitation occurring at a single point in space as opposed to areal

precipitation which is precipitation over a region. For point precipitation frequency analysis, the annual

maximum precipitation over a region for a given duration is selected by applying the method outlined in

Sec. 3.4. to all storms in a year, for each year of historical record. This process is repeated for each series

of duration. For each duration, frequency analysis is performed on the data, to derived the design

precipitation depths for various return periods; then the design depths are converted to intensities by

dividing by the precipitation duration.

By analyzing data in this way, Hershfield (1961) develop isohyetal maps of design rainfall depth

for the entire United States; these were published in U.S. Weather Bureau technical paper no. 40,

commonly called TP 40. The maps presented in TP 40 are for durations from 30 mins. To 24 hours and

return periods from 1 to 100 years. Hershfield also furnished interpolation diagrams for making

precipitation estimates for duration and return periods not shown on the maps. Fig. 14.1.1 shows the TP

40 map for 100-year 24-hour rainfall. The U.S. Weather Bureau (1964) later published maps for

durations of 2 to 10 days.

In many design situations, such as storm sewer design, duration of 30 minutes or less must be

considered. In publication commonly known as HYDRO 35 (Frederick, Meyers, and Auciello, 1977), the

US National Weather Service presented isohyetal maps for events having durations from 5 to 60

minutes, partially superseding TP 40. The maps of precipitation depths for 5-, to 15-, and 60-minute

durations and return periods of 2 and 100 years for the 37 eastern states are shown in fig 14.1.2. Depths

for 10- and 30-minute durations for a given return period are obtained by interpolation from the 5-, 15-,

and 60-minute data for the same return period.

P10min =0.41P5min + 0.59P15min (14.1.1a)

P30min =0.51P15min + 0.49P60min (14.1.1b)

For return periods other than 2 or 100 years, the following interpolation equation is used, with the

appropriate coefficients a and b from table 14.1.1.

PT yr. =aP2 yr. + bP100 yr. (14.1.2)

Miller, Frederick, and Tracey (1973) present isohyetal maps for 6- and 24-hour durations for the 11

mountainous states in the Western United States, these supersede the corresponding maps in TP 40.

Table 14.1.1. Coefficients for interpolating design precipitation depths using Eq. (14.1.2)

Return period T years a B

5 0.674 0.278

10 0.496 0.449

25 0.293 0.669

50 0.146 0.835

EXAMPLE: Determine the design rainfall depth for a 25-year 30-minute storm in Oklahoma City.

Solution: Oklahoma City is located near the center of the state of Oklahoma and the values of 15- and

60-minute precipitation for 2- and 100-year return periods are read from Fig. 14.1.2 as P2,15= 1.02in,

P100,15= 1.86in, P2,60= 1.85in and P100,60= 3.80in, respectively. Using (14.1.1b) the values for 30-minute

precipitation depth are calculated:

P30min =0.51P15min + 0.49P60min

For T= 2 years, P2,30= 0.51 x 1.02 + 0.49 x 1.85= 1.43 in.

For T= 100 years, P100,30= 0.51 x 1.86 + 0.49 x 3.80= 2.81 in.

Then (14.1.2) is used with coefficients a=0.293 and b=0.669 from table 14.1.1 to give the 25-year

30minute precipitation depth:

P25,30 = aP2,30 + bP100,30

P25,30 = 0.293 x 1.43 + 0.669 x 2.81

P25,30 = 2.30 in.

INTENSITY-DURATION-FREQUENCY RELATIONSHIPS

One of the first steps in many hydrologic design projects, such as in urban drainage design, is the

determination of the rainfall event or events to be used. The most common approach is to use a design

storm or event that involves a relationship between rainfall intensity (or depth), duration, and the

frequency or return period appropriate for the facility and site location. In many cases, the hydrologist

has standard intensity-duration-frequency (IDF) curves available for the site and does not have to

perform this analysis. However, it is worthwhile to understand the procedure used to develop the

relationships. Usually the information is presented as a graph, with duration plotted on the horizontal

axis, intensity on the vertical axis, and a series of curves, one for each design return period, as illustrated

for Chicago in Fig. 14.2.1.

The intensity is the time rate of precipitation, that is, depth per unit time (mm/h or in/h). it can

be either the instantaneous intensity or the average intensity over the duration of the rainfall. The

average intensity is commonly used and can be expressed as

𝑖 =𝑃

𝑇𝑑

Where P is the rainfall depth (mm or in) and 𝑇𝑑 is the duration, usually in hours. The frequency is usually

expressed in terms of return period, T, which is the average length of time between precipitation events

that equal or exceed the design magnitude.

Table 14.2.1. Design precipitation depths (in) at Oklahoma City for various durations and return periods

Return period T (yr)

Duration Td (min)

5 10 15 30 60

2 0.48 0.80 1.02 1.43 1.85

5 0.57 0.94 1.20 1.74 2.30

10 0.63 1.05 1.34 1.97 2.62

25 0.72 1.21 1.54 2.30 3.08

50 0.80 1.33 1.70 2.56 3.44

100 0.87 1.45 1.86 2.81 3.80

EXAMPLE:

Determine the design precipitation intensity and depth for a 20-minute duration storm with a 5-year

return period in Chicago.

Solution: From the IDF curves for Chicago (Fig. 14.2.1), the design intensity for a 5-year, 20-minute storm

is 𝑖 = 3.50 in/h. the corresponding precipitation depth is given by Eq. (14.2.1) with 𝑇𝑑= 20 min= 0.333h.

𝑃 = 𝑖𝑇𝑑

𝑃 = 3.50 𝑥 0.33

𝑃 = 1.17 𝑖𝑛

DESIGN PRECIPITATION HYETOGRAPHS

Most often hydrologists are interested in precipitation hyetographs and not just the peak estimates.

Techniques for developing design precipitation hyetographs

1. SCS method

2. Triangular hyetograph method

3. Using IDF relationships (Alternating block method)

SCS METHOD

SCS (1973) adopted method similar to DDF to develop dimensionless rainfall temporal patterns

called type curves for four different regions in the US. SCS type curves are in the form of percentage

mass (cumulative) curves based on 24-hr rainfall of the desired frequency. If a single precipitation depth

of desired frequency is known, the SCS type curve is rescaled (multiplied by the known number) to get

the time distribution. For durations less than 24 hr, the steepest part of the type curve for required

duration is used

SCS Method Steps

Given Td and frequency/T, find the design hyetograph

1. Compute P/i (from DDF/IDF curves or equations)

2. Pick a SCS type curve based on the location

3. If Td = 24 hour, multiply (rescale) the type curve with P to get the design mass curve. If Td

is less than 24 hr, pick the steepest part of the type curve for rescaling

4. Get the incremental precipitation from the rescaled mass curve to develop the design

hyetograph

Example – SCS Method

Find - rainfall hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a

one-hour time increment a = 81, b = 7.7, c = 0.724 (from Tx-DOT hydraulic manual).Find

◦ Cumulative fraction - interpolate SCS table

◦ Cumulative rainfall = product of cumulative fraction * total 24-hour rainfall (10.01 in)

◦ Incremental rainfall = difference between current and preceding cumulative rainfall

hrin

bt

ai

c/417.0

7.760*24

81724.0

inhrhrinTiP d 01.1024*/417.0*

TRIANGULAR HYETOGRAPH METHOD

Td: hyetograph base length = precipitation duration

ta: time before the peak

r: storm advancement coefficient = ta/Td

tb: recession time = Td – ta = (1-r)Td

Given Td and frequency/T, find the design hyetograph

1. Compute P/i (from DDF/IDF curves or equations)

2. Use above equations to get ta, tb, Td and h (r is available for various locations)

ALTERNATING BLOCK METHOD

Given Td and T/frequency, develop a hyetograph in Dt increments

1. Using T, find i for Dt, 2Dt, 3Dt,…nDt using the IDF curve for the specified location

2. Using i compute P for Dt, 2Dt, 3Dt,…nDt. This gives cumulative P.

3. Compute incremental precipitation from cumulative P.

4. Pick the highest incremental precipitation (maximum block) and place it in the middle of

the hyetograph. Pick the second highest block and place it to the right of the maximum

block, pick the third highest block and place it to the left of the maximum block, pick the

fourth highest block and place it to the right of the maximum block (after second block),

and so on until the last block.

DESIGN AERIAL PRECIPITATION

Point precipitation estimates are extended to develop an average precipitation depth over an

area.Depth-area-duration analysis

d

d

T

Ph

hTP

2

2

1

Time

Rainfall intensity, i

h

t t

d

a

T

tr

Td

◦ Prepare isohyetal maps from point precipitation for different durations

◦ Determine area contained within each isohyet

◦ Plot average precipitation depth vs. area for each duration

ROUTING OF SPILLWAY DESIGN FLOOD

A spillway for a dam may serve one or more of three principal functions, defined by Cochran as follows:

1. Provides protection against overtopping of non-overflow sections of the dam, acting in

conjunction with other outflow facilities, such as regulating outlets or turbines.

2. Limits water surface elevations in the reservoir above the normal full pool elevation to avoid

damages upstream from the dam.

3. Supplements regulating outlet for flood control operation when reservoir levels are above the

spillway crest.

The spillway design flood is the most important flood to be provided for in the design of a dam. The

selected magnitude and probable recurrence interval of this flood is related to the importance of a dam,

its functional use, the economic value of the investment , and the potential damages to property and

even loss of life that would result total or partial failure of the structure.

Cochran has proposed the following general standards for the hydrologic design of spillways:

Standard 1: Design the dam and spillway large enough to assure that the dam will not be

overtopped by floods up to the probable maximum categories.

Standard 2: Design the dam and appurtenances so that the structure can be overtopped without

failing and, insofar as practicable, without suffering serious damage.

Standard 3: Design the dam and appurtenances in such a manner as to assure that breaching of the

structure from overtopping would occur at a relatively gradual rate, such that the rate and magnitude of

increases in flood stages downstream would be within acceptable limits.

Standard 4: Keep the dam low enough and storage impoundments small enough that no serious

hazard would exist downstream in the event of breaching.

ROUTING OF SPILLWAY DESIGN FLOOD

(a) General Principles

This section is concerned with the routing of the spillway design flood through the reservoir, including a

discussion of possible modifications to the total inflow hydrograph resulting from the creation of the

reservoir, and the assumptions to be made regarding reservoir elevation and outlet conditions. The

routing is carried out for a number of assumed spillway designs and corresponding hydraulic capacities

to determine, along with structural and cost analyses, the most economic design. The important factor

in the routing procedure is the evaluation of the effect of storage in the upper levels of the reservoir,

termed “surcharge storage,” on the required outflow capacity. In computing the available storage, the

water surface is generally considered to be level. There will be sloping water surface at the head of the

reservoir due to backwater effect and this condition will create an additional “wedge storage.” However,

in most large and deep reservoirs this incremental storage can be neglected.

(b) Total Inflow Hydrograph

The hydrograph of the spillway design flood, developed as outlined in Section 11, is derived initially for

the drainage area at the head of the reservoir. Additional adjustments are necessary to make it

applicable to the total drainage area at the dam site. Such adjustments are necessary to make it

applicable to the total drainage area at the dam site. Such adjustments are necessary, because large

reservoirs, many miles in length and covering many square miles, may significantly change the runoff

characteristics of the lower reaches of the river, resulting in modifications to the shape and timing of the

natural flood hydrograph.

The spillway design flood hydrograph may be made up of three or more components as follows:

1. The hydrograph of the main river at the point where the channel intersects the reservoir

surface. There may be two or more principal tributaries for which hydrographs must be

developed.

2. The hydrograph of the tributary area surrounding the reservoir. This may be composed of

several small streams. Usually a hydrograph is developed for one typical stream and then its

characteristics are considered applicable to the total contributing area. The resulting

hydrograph will peak sooner than the hydrograph from the main channel.

3. The hydrograph resulting from the design storm rainfall falling directly on the reservoir area.

This hydrograph will also peak sooner than the contributions from the main channels, and is

generally significant only as a contribution to the total volume of runoff.

The total inflow hydrograph is the sum of the ordinates of the component hydrographs. In

combining the hydrographs, no allowance is usually necessary for the time of travel through the

reservoir, as the effect of the inflow will be transmitted to the spillway as a pressure wave. With very

large reservoirs, the contribution from the peripheral areas and/or the rainfall on the water area may

cause an initial peak which is higher than that contributed by the main channel at the head of the

reservoir.

(c) Initial Reservoir Elevation

If a reservoir is drawn down at the time of occurrence of the spillway design flood, the initial increments

of inflow will be stored, with the corresponding reduction in ultimate peak outflow. Therefore, for

maximum safety in design it is generally assumed that a reservoir will be full to the spillway crest in the

case of an uncontrolled spillway and to the normal operating pool elevation when a gated spillway is

used.

There may be exceptions to the above criteria in the case of reservoirs with large reservoirs with

large reservations for flood control storage. However, even in such cases a substantial part (50 percent

or more) of the flood control storage should be considered as filled by runoff from antecedent floods.

The effect on the economics and safety of the project should be analyzed before adopting such

assumptions.

When the storage is to be used for power, irrigation, or water supply, the reservoir should be

assumed to be full to the normal operating pool at the beginning of the spillway design flood.

Any assumption that a reservoir can be significantly drawn down in advance of the spillway

design flood (other than one with definite flood control storage reservation) as the result of a short-

term flood warning system, is generally not acceptable for several reasons. The volume that can be

withdrawn is the product of the total rate of discharge at the dam times the warning time. Since the

warning time is usually short, except on great rivers, the released rate must be the greatest possible

without flood damage downstream. Even under the most favorable conditions, it will be found that the

volume that can be released will not be significant relative to the volume of the spillway design flood.

(d) Outflow Conditions

The facilities available for discharge of the inflow from the spillway design flood will depend on the type

and design of the dam and its proposed use. A single dam installation may have two or more of the

following discharge facilities:

Uncontrolled overflow spillway

Gated overflow spillway

Regulating outlet

Power plant

Uncontrolled and gated spillways may take several forms such as conventional gravity (ogee)

section, side-channel overflow, chutes, or shaft (morning glory) spillways.

Uncontrolled Overflow Spillway. With a reservoir full to the spillway crest at the beginning of the design

flood, discharge will begin at once and continue at a rate proportional to the three-halves power of the

head on the spillway. Surcharge storage is created as the head increases and thus storage will also be

proportional to some function of the head, depending on the characteristics of the elevation-capacity

curve. The peak outflow will always be less, to some degree, than the inflow.

Gated Overflow Spillway. With a gated spillway, the normal operating level is usually near the top of

the gates, although at times it may be drawn below this level by other outlets. The usual purpose in

selecting a gated spillway is to make maximum use of available storage and head and at the same time

to limit backwater damages by providing a high initial discharge capacity. In routing the spillway design

flood, an initial reservoir elevation at the normal full pool operating level is assumed. Operating rules for

spillway gates must be based on careful study to avoid releasing discharges that would be greater than

would occur under natural conditions before construction of the reservoir. The effect of a large reservoir

on the inflow hydrograph has been discussed in Section 12(b). In general, releases should be less than

the inflow during the progress of a flood, thereby causing limited surcharge to build up. Furthermore, it

is generally the practice in the design of gated spillways for the peak discharge from the spillway design

flood to exceed the capacity of the gates at full opening with the results that the maximum water

surface will rise above the normal pool operation.

Regulating Outlet. Most dams are designed with low-level outlets, either through the dam or the

abutments for normal downstream releases in carrying out their single or multipurpose functions. The

discharge capacity of these outlets is usually small relative to the potential flood flows. These outlets

may be assumed to be operating, at least in the initial stages of the design flood, and with due

consideration for needs for flood control downstream. As spillways flow increases, it is conservative to

assume that these outlets are closed.

Power plants. When a hydroelectric plant is located at a dam and reservoir, it may be assumed that the

turbines are discharging initially, thereby delaying use of the spillway. As in the case of the regulating

outlets, the discharge should be limited to non-damaging channel capacity downstream, considering

inflow from contributing areas below the dam. As the spillway discharges increase, the elevations of the

tailwater below the dam may limit turbine discharge capacity. It is common practice to assume that the

turbines are discharging at 75 percent of capacity, unless special conditions may prevent it. An

assumption that the plant discharge is completely stopped, as in the case of the regulating outlets, may

be unrealistic, as the power production may be required in the region regardless of flood conditions.

(e) Selection of Maximum Water Surface Elevation

Determination of the maximum reservoir level by routing of the spillway design flood hydrograph under

various assumed lengths, heads, and possible types of spillway is a basic step in the selection of the

elevation of the crest of the dam. The spillway length and corresponding capacity may have an

important effect on the overall cost of the project, and the selection of the ultimate spillway

characteristics is based on an economic analysis. Among the many economic factors that may be

considered are damage due to backwater in the reservoir, cost-height relations for gates, and utilization

in the dam of material excavated from the spillway channel.

After the economic water surface elevation is selected, an additional vertical distance to the

crest of the dam must be provided for wave action as described in Section 13. Actually this computation

may be done concurrently with the reservoir routing in order to have a correct estimate of the total

volume in the dam, for use in the economic studies.

Freeboard Against Wave Action

FREEBOARD – vertical distance between the crest of a dam or embankment and some specified pool

level.

It is provided to protect dams and embankments from overflow caused by wind induced tides and wave.

Riprap or other types of slope protection are provided within the freeboard to control erosion that may

occur even without overtopping.

The reference elevation for setting freeboard is generally the normal operating level, or the maximum

flood level.

There are generally three basic considerations in establishing freeboard allowance:

1. Wind tide

2. Wave characteristics

3. Wave runup

Wind Tide

Wind Tide is the tilting of the reservoir surface above the horizontal water surface level on the

leeward side and below it on the windward side.

Wind blowing over an enclosed body of water exerts a horizontal force that causes a buildup in

level along the leeward shore. There is a similar reduction in the opposite direction. This phenomenon is

called wind tide or setup.

𝑆 = 𝑉𝐴2𝐹

1400𝐷

Where:

S = setup in feet above the reference level

V = wind velocity in miles per hour

F = fetch or water distance in miles over which the wind blows

D = mean reservoir depth in feet along the fetch

Wave Characteristics

The characteristics of wind generated waves measured in several large inland reservoirs have

been analyzed using the dimensionless parameters, gT/V, gHs/V2 and gF/V

2 where:

g = gravity constant of 32.2

T = time between wave crests in seconds

F = effective fetch in miles

Hs = average of the highest one third of the waves occurring in a particular series

The wind velocity used in the equations was that measured over water and is greater than velocities

measured at land stations, which are the data usually available in reservoir studies. Wind speeds recorded

over land should be adjusted as follows:

Fetch

in Miles

Percentage

Increase

>4 30

2 20

<1 10

To evaluate the effect of differences in reservoir shapes and to obtain a better correlation between

fetch and wave height, a weighted or effective fetch has been devised. The steps in a typical computation

for estimating the effective fetch in a reservoir are summarized as follows.

1. The maximum fetch line in the reservoir in the direction of the wind is located.

2. Seven secondary fetch lines radiating from the dam and on each side of the maximum fetch

are drawn at 6° intervals.

3. The length of each fetch line is multiplied by the cosine of the angle between the line and the

maximum fetch line.

4. The sum of the products in step 3 divided by the sum of the cosines to obtain the effective

fetch distance.

Wave Runup

- is the maximum vertical extent of wave uprush on a beach or structure above the still water

level.

The vertical height that a deep-water wave will run up a slope are functions of the wave

characteristics as measured by the ratio between wave height and wave length, the slope of the

embankment, the permeability and the relative surface rougness.

Freeboard Allowance

Design freeboard for wave action or the vertical distance between the selected still-water level

and the crest of the dam is the computed runup from a selected wave height plus the wind tide. For major

embankments a minimum freeboard of 5.0 ft is customary. For other embankments a lesser minimum

may be used.

Sedimentation of Reservoir

Sediments

Sediment, a naturally occurring material that is broken down by processes of weathering and

erosion, and is subsequently transported by the action of wind, water, or ice, and/or by the force of

gravity acting on the particle itself.

The matter that settles to the bottom of a liquid.

Geology: mineral or organic matter deposited by water, air, or ice.

Importance and reasons of reservoir sedimentation

• Morphological and hydrological characteristics of reservoirs

• Reasons of reservoirs sedimentation

– Transport of bed load and suspended sediments into the reservoir – Creation of sediments by biological processes – Vegetation growth (creation of swamps and marshy land)

• Mean volume loss of reservoirs due to sedimentation in worldwide

Measures against reservoir sedimentation

Measures in the catchment area

1. Erosion protection (soil conservation)

– Plantations (forestation) – Stabilization of slopes – Erosion protection at rivers (against bank and bed erosion)

2. Bed load retention basins:

– Built on torrents and mountain rivers – Regular emptying is required – Insignificant retention of suspended load – Small effect on reservoir sedimentation

3. Measures in the catchment area

4. Sediment retention dams upstream of reservoir:

– Bed load and suspended load is captured – Degree of retention for fine sediments is 90% for – example if the capacity of the retention basin is in – minimum 10 % of the yearly inflow – Mechanical cleaning or flushing is required

Measures in the reservoir

1. Mechanical removal

1. Dredging – at full or empty reservoir

2. Hydrosuction (Airlift) – at full lake (limited depth)

3. SPSS - Slotted Pipe Sediment Sluicer – at full lake (limited depth)

2. Hydraulic removal = flushing

a. Negative impacts downstream of the dam:

– damaging or destruction of aquatic organisms, especially fishes – covering of benthos by sediments – local depositions in the river bed and increase of bed elevation – blockage of diversion and intake structures – reduction of flood safety – increased abrasion at turbines and gates – decrease of water quality especially at diversion structures – hindering of leisure activities – sedimentation of downstream reservoirs – damaging or destruction of aquatic organisms, especially fishes

– covering of benthos by sediments

Measures at the dam

1. Heightening of the dam

2. Heightening of water release structures (bottom outlet, power intake)

3. Cone flushing in front of water release structures under pressure

4. Venting of turbidity currents (high capacity release structures required)

a. Drawdown of reservoir during yearly floods

b. Release of highly sediment charged water trough

c. turbines under controlled concentration

REFERENCES:

Mutreja, K.N. Applied Hydrology, Tata McGraw- Hill Publishing Company limited, 1986.

Alfred R. Golze. Handbook of Dam Engineering. Manila : National Book Store, 1980.

Ven TE Chow, “Applied Hydrology”, Mc Graw-Hill Book,Co.,1998.

Web resources for TP 40 and rainfall frequency maps

http://www.tucson.ars.ag.gov/agwa/rainfall_frequency.html

http://www.erh.noaa.gov/er/hq/Tp40s.htm

http://hdsc.nws.noaa.gov/hdsc/pfds/