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1 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University

Hydrology

[5]Rainfall

Mohammad N. Almasri


Precipitation

Precipitation replenishes surface water bodies,renews soil moisture for plants, and rechargesaquifers

Its principal forms are rain and snow

Some of precipitated water may be intercepted,

evaporated, infiltrated and/or become surface flow

Precipitation is the primary input of the hydrologiccycle


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Hyetograph

A hyetograph isa graph thatshows thetemporaldistribution ofrainfall at a givenlocation

So it shows the

relationshipbetween rainfalldepth and time


Rainfall Measurements and Hydrologic Design

Rainfall measurements are seldom used directly indesign applications

Rather, the statistics of the rainfall measurementsare typically used

Rainfall statistics are most commonly presented inthe form ofintensity-duration-frequency (IDF) curves

IDF curves express the relationship between rainfallmaximum intensity and the time (duration) with agiven probability ofoccurrence


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Time Series of Nablus Daily Rainfall

If we wouldlike toconsider thedaily rainfallfor a drainagesystem design,then whichvalue to pick?


Important Definitions Related to Rainfall

Intensity: time rate of precipitation or depth ofprecipitation per unit time (mm/h)

Duration: period of time (h) during which rainfalloccurs

Depth: the total amount of rainfall (mm) for a givenperiod of time

Frequency: the average length of time needed for atleast one precipitation event to return with anintensity equals or exceeds a specific (maximum)value


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FrequencyReturn Period and Exceedance Probability

Frequency can be represented as exceedanceprobability and return period

Exceedance Probability: the probability that rainfallintensity is being exceeded during a given timeperiod

Return Period: the event with a return period ofNyears is the event that is expected to be equaled or

exceeded every N years


Return Period

If a 100-year storm occurs this year then it is totallywrong to assume that this storm will return in 100years

Instead, the storm can have the chance forreturning two successive years in the near future ormay not return for another 150 years

It should be noted that the relationship betweenreturn period (T) and exceedance probability (P) isgiven as follows:

T

1P =


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Intensity Duration Frequency Relationships

One of the first steps in many hydrologic designprojects is the determination of the rainfall event orevents to be used in the design

The most common approach is to use a designstorm or event that involves a relationship betweenrainfall intensity (or depth), duration, and thefrequency appropriate for the facility and sitelocation

As such, the IDF curves can be used by hydrologists


Intensity Duration Frequency Relationships

IDF curves enables the hydrologists to develop hydrologicsystems that consider worst-case scenarios of rainfallintensity and duration during a given interval of time

The idea here is that high intensity rainfall in short periodsmay cause catastrophic consequences

For instance, in urban watersheds, flooding may occursuch that large volumes of water may not be handled bythe storm water system

Thus, appropriate values of precipitation intensities andfrequencies should be considered in the design of thehydrologic systems


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Intensity versus Depth of Rainfall

Intensity is expressed as:

where P is the rainfall depth (mm) and Td is theduration (hr)

dT

Pi =


Rainfall Intensity and Corresponding Depth

In general, wemay havedifferent rainfallintensities butwith the samedepth

Apparently,

rainfall durationplays animportant role indeterminingrainfall depth


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Rainfall Intensity versus Duration

Apparently,withincreasingthe duration,Maximumrainfallintensitybecomes less

This is

somehow ageneral trendbut not alinear one


Running Totals

Finding Intensities and Corresponding Durations


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Recorded Total depth

0.46

0.48

0.33

0.7115-minduration




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A Typical IDF Curve

The interpretationof any point valueobtained from theIDF curve is thaton the average,for any given timeduration, stormshaving an intensity

(i) for that durationwould have a

recurrence intervalequal to thecorrespondingcurve value


Interpretation of IDF Curves

For example, in anytime duration of 90minutes, a locationcould experience apeak2 in/hr stormonce every 20 years

The 20-yr 90-mindesign storm for thelocation would havea depth ofP = 3 in


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A20-yr 30-min designstorm would have anintensity of4.6 in/hr butwith a depth of only 2.3in

Although the latter stormproduces less depth, itshigh intensity could bethe governing factor indetermining the size of

drainage works. Theprobability of occurrenceof both storms would bethe same




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Development of IDF Curves

Select a specific rainfall duration

For each year and for the selected duration find themaximum rainfall

Arrange the annual maximum precipitation in descendingorder

The return period equals T = (n + 1) / m where m is therank and n is the total number of years

Repeat the above procedure but for different rainfalldurations



This tableprovides themaximum totalrainfall depth forthe years from1949 to 1972 fordifferent rainfalldurations

You need tocompute the IDFcurves


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Rankfor each duration

Compute the returnperiod (frequency)

The highlighted linesrepresent frequenciesof interest

Ep is the exceedanceprobability



Compute intensitiesthat correspond tothe differentdurations then selectfor specificfrequencies


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Depth-Duration-Frequency Curve


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Intensity Versus Return Period for DifferentDurations

Apparently, asthe return periodincreases, theintensityincreases

Also, low rainfalldurations tend tohave higher

intensitiescompared to highrainfall durations


Depth Versus Return Period for Different

Durations

Apparently, asthe returnperiodincreases, thedepthincreases

Also, lowrainfalldurations tendto have lowdepths valuescompared tohigh rainfalldurations


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Probable Maximum Precipitation

The Probable maximum precipitation (PMP) istheoretically the greatest depth of precipitation for agiven duration that is physically possible at aspecific location at a certain time of the year


Gross and Net Precipitation

The net (excess) precipitation that contributesdirectly to surface runoff is equivalent to the grossprecipitation minus losses to interception,evaporation, depression storage, and infiltration

The relation between excess precipitation Pe andgross precipitation P is:

Pe = P losses


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Areal Precipitation

It is important to know the areal distribution ofprecipitation

In general, an average depth for the watershed isdetermined and used

For this, point precipitation readings are utilized todevelop average precipitation depth over an area

There are different methods for finding the arealaverage rainfall for an area of interest


Areal Rainfall

The Arithmetic-Mean Method

This is the simplest method of determining the arealaverage rainfall

The average rainfall depth for an area is found bycomputing the average of the depth values for allthe gages using the following formula:

where n is the number of gages and Pi is the rainfallrecorded at gage i

=

=

n

1i

iPn

1

P


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Areal RainfallThe Isohyetal Method

The isohyetal method is basedon interpolation betweengauges

Plot the rain gauge locationsand record the rainfall amounts

Interpolation between gauges isperformed

Rainfall amounts at selectedincrements are plotted

Identical depths from eachinterpolation are then connectedto form isohyets (lines of equalrainfall depth)


Areal Rainfall

Thiessen Method The area is subdivided into subareas using rain gauges as

centers

The subareas are used as weights in estimating thewatershed average depth

The Thiessennetwork is fixed fora given gaugeconfiguration, andpolygons must be

reconstructed ifany gauges arerelocated


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Areal RainfallThiessen Method


Areal Rainfall

Thiessen Method Faria Catchment


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Areal RainfallThiessen Method Gaza City and Jabalia Camp



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Estimation of Missing Rainfall Data

Rainfall data are generally collected at pointlocations (mainly at meteorological stations)

However, rainfall data might be incomplete. Missingdata therefore could be attributed to:

Malfunctioning

Mismanagement

Inability to take the measurement

Vandalism

Therefore, when part of rainfall data is missing, thenestimation of missing data should be made


Station Average Method

Consider n rain gages present in a region withmeasured data for a given storm event

The data at station X are missing for a storm event

Then

Use this method when the annual rainfall of anystation is within the 10% of the average annualrainfall from the gages

=

=n

1i

ixP

n

1P


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Station Average Method

Find the missing rainfalldata at station D for thefollowing storm eventsgiven the average annualrainfall data

The average annual rainfallat the four gages is 40.7 inand thus all the annual

readings are within 10% ofthe average

( ) in67.23.21.36.23

1PD

=++=

44.7740.736.63


Normal Ratio Method

In regions where the annual average rainfall differsconsiderably between locations, the normal ratiomethod is preferred

Px: missing rainfall data at x

Ax: annual rainfall at x

Ai: annual rainfall at i

n: number of gages

i

n

1i i

x

xP

nA

AP

=

=


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Normal Ratio Method

Find the missing rainfalldata at station D for thefollowing storm eventsgiven the average annualrainfall data

in51.21.3463

403.2

373

404.2

413

40PD =++=

i

n

1i i

x

xP

nA

AP

=

=


Checking Consistency of Point Measurements

Changes in type, location, and/or environment of thegage are common

Trees may grow up or buildings may be constructedaround a gage

So it is important for a hydrologist to determine if theprecipitation record is affected by such artificialalterations of measurement conditions and to correctthem if they are present

The most common technique for detecting andcorrecting the inconsistent precipitation data is thedouble-mass curve


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The double-mass curve is a plot of the successivecumulative annual precipitation collected at a gagewhere measurement conditions may have changedsignificantly versus the successive cumulative ofaverage annual precipitation for the same period ofyears collected at several gages in the same region

A change in the proportionality between themeasurements at the suspect station and those of

the region is reflected in a change in the slope ofthe trend of the plotted points




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The problemis in station E

Find theaverage forstations A to Dand then thecumulative

Find thecumulative forstation E



Slope=0.77

Slope=1.05


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Apparently, there is a slope difference

The slope before the change is 0.77while after the change it is 1.05

To reflect the conditions that existbefore the break then multiply by0.77/1.05 all the records after change

To reflect the conditions that exist afterthe break then multiply by 1.05/0.77 allthe records before the change


Rainfall Classification

Very light < 0.25 mm/hr

Light 0.25 mm/hr - 1.0 mm/hr

Moderate 1.0 mm/hr - 4.0 mm/hr

Heavy 4.0 mm/hr - 16.0 mm/hr

Very heavy 16.0 mm/hr 50 mm/hr

Extreme > 50.0 mm/hr

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