5 rainfall
TRANSCRIPT
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1 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Hydrology
[5]Rainfall
Mohammad N. Almasri
2 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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3 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Hyetograph
A hyetograph isa graph thatshows thetemporaldistribution ofrainfall at a givenlocation
So it shows the
relationshipbetween rainfalldepth and time
4 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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5 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Time Series of Nablus Daily Rainfall
If we wouldlike toconsider thedaily rainfallfor a drainagesystem design,then whichvalue to pick?
6 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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7 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
8 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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9 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
10 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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11 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Intensity versus Depth of Rainfall
Intensity is expressed as:
where P is the rainfall depth (mm) and Td is theduration (hr)
dT
Pi =
12 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Rainfall Intensity and Corresponding Depth
In general, wemay havedifferent rainfallintensities butwith the samedepth
Apparently,
rainfall durationplays animportant role indeterminingrainfall depth
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13 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Rainfall Intensity versus Duration
Apparently,withincreasingthe duration,Maximumrainfallintensitybecomes less
This is
somehow ageneral trendbut not alinear one
14 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Running Totals
Finding Intensities and Corresponding Durations
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15 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Rainfall Intensity versus Duration
Recorded Total depth
0.46
0.48
0.33
0.7115-minduration
16 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Rainfall Intensity versus Duration
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17 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
18 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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19 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Interpretation of IDF Curves
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
20 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Interpretation of IDF Curves
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21 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
22 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Development of IDF Curves
This tableprovides themaximum totalrainfall depth forthe years from1949 to 1972 fordifferent rainfalldurations
You need tocompute the IDFcurves
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23 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Development of IDF Curves
Rankfor each duration
Compute the returnperiod (frequency)
The highlighted linesrepresent frequenciesof interest
Ep is the exceedanceprobability
24 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Development of IDF Curves
Compute intensitiesthat correspond tothe differentdurations then selectfor specificfrequencies
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25 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Development of IDF Curves
26 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Depth-Duration-Frequency Curve
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27 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Intensity Versus Return Period for DifferentDurations
Apparently, asthe return periodincreases, theintensityincreases
Also, low rainfalldurations tend tohave higher
intensitiescompared to highrainfall durations
28 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Depth Versus Return Period for Different
Durations
Apparently, asthe returnperiodincreases, thedepthincreases
Also, lowrainfalldurations tendto have lowdepths valuescompared tohigh rainfalldurations
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29 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
30 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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31 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
32 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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33 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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)
34 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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35 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Areal RainfallThiessen Method
36 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Areal Rainfall
Thiessen Method Faria Catchment
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37 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Areal RainfallThiessen Method Gaza City and Jabalia Camp
38 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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39 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
40 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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41 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
42 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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43 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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
=
=
44 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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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45 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Checking Consistency of Point Measurements
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
46 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Checking Consistency of Point Measurements
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47 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Checking Consistency of Point Measurements
The problemis in station E
Find theaverage forstations A to Dand then thecumulative
Find thecumulative forstation E
48 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Checking Consistency of Point Measurements
Slope=0.77
Slope=1.05
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49 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
Checking Consistency of Point Measurements
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
50 Hydrology Fall 2007 [5] Rainfall Mohammad N. Almasri, PhD An-Najah National University
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