chapter two precipitation -...

CHAPTER TWOPRECIPITATION

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Engineering Hydrology (ECIV 4323)

Instructor:

Dr. Yunes Mogheir

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The term precipitation denotes all forms of water that reach the earth from the atmosphere. The usual forms are rainfall, snowfall, hail, frost and dew

Precipitation

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(i) the atmosphere must have moisture,(ii) there must be sufficient nucleii present to aid

condensation, (iii) weather conditions must be good for condensation of

water vapour to take place, and (iv) the products of condensation must reach the earth

For precipitation to form

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The term rainfall is used to describe precipitations in the form of water drops of sizes larger than 0.5 mm. The maximum size of a raindrop is about 6 mm

FORMS OF PRECIPITATION

Rain

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Snow is another important form of precipitation. Snow consists of ice crystals which usually combine to form flakes. When new, snow has an initial density varying from 0.06 to 0.15 g/cm3 and it is usual to assume an average density of 0.1 g/cm3.


Snow

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A fine sprinkle of numerous water droplets of size less than 0.5 mm and intensity less than 1 mm/h is known as drizzle. In this the drops are so small that they appear to float in the air.


Drizzle

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When rain or drizzle comes in contact with cold ground at around 00 C, the water drops freeze to form an ice coating called glaze or freezing rain.


Glaze

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It is frozen raindrops of transparent grains which form when rain falls through air at subfreezing temperature. In Britain, sleet denotes precipitation of snow and rain simultaneously.


Sleet

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It is a showery precipitation in the form of irregular pellets or lumps of ice of size more than 8 mm. Hails occur in violent thunderstorms in which vertical currents are very strong.


Hail

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A front is the interface between two distinct air masses. Under certain favorable conditions when a warm air mass and cold air mass meet, the warmer air mass is lifted over the colder one with the formation of a front. The ascending warmer air cools adiabatically with the consequent formation of clouds and precipitation.

WEATHER SYSTEMS FOR PRECIPITATION

Front

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A cyclone is a large low pressure region with circular wind motion. Two types of cyclones are recognized: tropical cyclones and extratropical cyclones.


Cyclone

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In this type of precipitation a packet of air which is warmer than the surrounding air due to localized heating rises because of its lesser density. Air from cooler surroundings flows to take up its place thus setting up a convective cell. The warm air continues to rise, undergoes cooling and results in precipitation.


Convective Precipitation

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The moist air masses may get lifted-up to higher altitudes due to the presence of mountain barriers and consequently undergo cooling, condensation and precipitation. Such a precipitation is known as Orographic precipitation


Orographic Precipitation

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Precipitation is expressed in terms of the depth to which rainfall water would stand on an area if all the rain were collected on it. Thus 1 cm of rainfall over a catchment area of 1 km represents a volume of water equal to 104 m3

The precipitation is collected and measured in a raingauge

MEASUREMENT

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For setting a rain gauge the following considerations are important:

1.The ground must be level and in the open and the instrument must present a horizontal catch surface.

2. The gauge must be set as near the ground as possible to reduce wind effects.

3. The instrument must be surrounded by an open fenced area of at least 5.5 m x 5.5 m. No object should be nearer to the instrument than 30 m or twice the height of the obstruction.

Rain gauge Setting

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Non-recording Gauges

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ó Tipping—Bucket Typeó Weighing—Bucket Typeó Natural—Syphon Type

Recording Gauges

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ÒTelermetering Raingauges

ÒRadar Measurement of Rainfall

where Pr = average echopower, Z = radar-echo factor, r = distance to target volume and C = a constant Generally the factor Z is related to the intensity of rainfall as

Z=aIb

Recording Gauges

2rCZPr =

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1. In flat regions of temperate, Mediterranean and tropical zones:

ideal – 1 station for 600 – 900 km2

acceptable – 1 station for 900 – 3000 km2

2. in mountainous regions of temperate, Mediterranean and topical zones:

ideal - 1 station for 100—250 km2

acceptable - 1 station for 250—1000 km2

3. in arid and polar zones: I station for 1500—l0,000 km2

depending on the feasibility.

RAINGAUGE NETWORK

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where N = optimal number of stations, ε = allowable degree of error in the estimate of the mean rainfall and Cv = coefficient of variation of the rainfall values at the existing m stations (in per cent)

Adequacy of Rain gauge Stations

2

=

εvC

N

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Adequacy of Rain gauge Stations

PC m

V1100 −=

σ

ionderddeviatsm

PPm

i

m tan1

)(1

2

1 =

−

−=

∑−σ

Pi = precipitation magnitude in the i4th station

itationmeanprecipPm

Pm

i =

= ∑

1

1

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EXAMPLEA catchment has six rain gauge stations. In a year, the annual rainfall recorded by the gauges are as follows:-

Station A B C D E

Rainfall (cm) 82.6 102.9 180.3 98.8 136.7

For a 10% error in the estimation of the mean rainfall, calculate the optimum number of stations in the catchment

Solution:- from first data

1004.35

6.118

6

1

==

=

=

−

εσ m

P

m

9,7.810

54.29

54.296.118

04.35*100

2

sayN

Cv

=

=

==

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PREPARATION OF DATAEstimation of Missing DataGiven the annual precipitation values, P1, P2, P3, . Pm at neighbouring M stations 1,2,3 M respectively, it is required to find the missing annual precipitation P . at a station X not included in the above M stations

If the normal annual precipitations at various stations are within about 10% of the normal annual precipitation at station X:

[ ]PmPPM

Px +++= .......211

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PREPARATION OF DATAEstimation of Missing Data

If the normal precipitations vary considerably

+++=

NmPm

NP

NP

MNP x

x ......22

11

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PREPARATION OF DATATest for Consistency of Record Some of the common causes for inconsistency of record are:(i) shifting of a rain gauge station to a new location,(ii) the neighborhoods of the station undergoing a marked change, (iii) change in the ecosystem due to calamities, such as forest fires, land slides, and (iv) occurrence of observational error from a certain date

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PREPARATION OF DATATest for Consistency of Record

Accumulated Annual Rainfall of 10 station MeanΣP in units of l03 cm

Acc

umul

ated

Ann

ual R

ainf

all a

t x

ΣP

in u

nits

of l

03 c

m

a

cxcx M

MPP =

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PRESENTATION OF RAINFALL DATAMass Curve of Rainfall

Time (days)

Acc

umul

ated

pre

cipi

tatio

n (c

m)

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PRESENTATION OF RAINFALL DATAHyetograph

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MEAN PRECIPITATION OVER AN AREA

Arithmetical—Mean Method

∑=

=++++

=N

Ii

ni PNN

PPPPP1

21 1......

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Thiessen-Mean Method

)....(...

621

662211

AAAAPAPAP

P++++++

= AA

PA

APP i

M

ii

M

iii

∑∑

=

= ==1

1

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Isohyetal Method

A

PPaPPaPPaP

nnn

+++

++

+

=

−− 2

.....22

11

322

211

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DEPTH-AREA—DURATION RELATIONSHIPS

Depth-Area Relation

)(exp no kAPP −=

where P = average depth in cms over an area A km2, Po = highest amount of rainfall in cm at the storm centre and K and n are constants for a given region

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DEPTH-AREA—DURATION RELATIONSHIPS

Maximum Depth-Area-Duration Curves

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TP 1

=

FREQUENCY OF POINT RAINFALL

rnrrnrr

nnr qP

rrnnqPCP −−

−==

!)!(!

,

If the probability of an event occurring is P, the probability of the event not occurring in a given year is q= (1 -P)

where Pr,n = probability of a random hydrologic event (rainfall) of given magnitude and exceedence probability P occurring r times in nsuccessive years

22,2 !2)!2(

! −

−= n

n qPn

nP

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FREQUENCY OF POINT RAINFALLexample,

(a) The probability of an event of exceedence probability P occurring 2 times in n successive years is(b) The probability of the event not occurring at all in , successive years is

( )nnn PqP −== 1,0

(c) The probability of the event occurring at least once in n successive years

nn PqP )1(111 −−=−=

Method P

California m/NHazen (m-0.5)/N

Weibull m/(N+1)Chegodayev (m-0.3)/(N+0.4)

Blom (m-0.44)/(N+0.12)Gringorten (m-3/8)/(N+1/4)

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FREQUENCY OF POINT RAINFALLPlotting Position

+=

1NmP

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FREQUENCY OF POINT RAINFALL

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For a station A, the recorded annual 24 h maximum rain fall are given below. (a) Estimate the 24h maximum rainfall with return period of 13 and50 year. (b) What would be the probability of a ran fall of magnitude equal to or exceeding 10cm occurring in 24 h at station A.

Year 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961

Rain-Fall cm

13.0 12.0 7.6 14.3 16.0 9.6 8.0 12.5 11.2 8.9 8.9 7.8

Year1962 1963 1964 1965 1966 1967 1968 1969 1970 1971

Rain-Fall cm

9.0 10.2 8.5 7.5 6.0 8.4 10.8 10.6 8.3 9.5

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TABLE 2.3 ANNUAL MAXIMUM 24 h RAINFALL AT STATION A

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Probability

1+=

nmP

mRainfall (cm)

Return periodT=1/PYears

m Rainfall (cm)

Return periodT=1/PYears

1 16.0 0.043 23.00 12 9.0 0.522 1.92

2 14.3 0.087 11.50 13 8.9 - -

3 13.0 0.013 7.67 14 8.9 0.609 1.64

4 12.5 0.174 5.75 15 8.5 0.652 1.53

5 12.0 0.217 4.60 16 8.4 0.696 1.44

6 11.2 0.261 3.83 17 8.3 0.739 1.35

7 10.8 0.304 3.29 18 8.0 0.783 1.28

8 10.6 0.348 2.88 19 7.8 0.826 1.21

9 10.2 0.391 2.56 20 7.6 0.870 1.15

10 9.6 0.435 2.30 21 7.5 0.913 1.10

11 9.5 0.478 2.09 22 6.0 0.957 1.05

Probability

1+=

nmP

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INTENSITY-DURATION-FREQUENCY RELATIONSHIP

n

x

aDKTi

)( +=

where K, x, a and n are constants for a given catchment

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σKPPMP +=

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PROBABLE MAXIMUM PRECIPITATION (PMP)

where = mean of annual maximum rainfall series, σ = standard deviation it the series and K = a frequency factor

P

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HW2

ó2.1ó2.3ó2.7ó2.10ó2.17

chapter two precipitation -...

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