02 Precipitation Lecture 2

7/21/2019 02 Precipitation Lecture 2

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LECTURE-2

Precipitation





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Precipitation

• Lifting cools air massesso moisture condenses

• Condensation nuclei – Aerosols (suspension of particles in gas: a

suspension of solid or liquid particles in a gaseous

medium) (10-3 – 10 µm)

– water molecules attach

• Rising & growing – Critical size (~0.1 mm)

– Gravity overcomes anddrop falls

Terminal Velocity

• Three forces

– Buoyancy, Friction, Gravity

• Accelerate until terminal velocity, V t

– Where forces balance

• Stokes Law

32

23

6246

0

DgV

DC Dg

W F F F

wad a

D Bvert

πρ

πρ

πρ

332

2

6624 Dg Dg

V DC

W F F

wat

ad

B D

πρ

πρ

πρ

1

3

4

a

w

d t

C

gDV

ρ

ρ

Re

24d C

a

aVD

µ

ρRe

W

F B

F D

D

V



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Precipitation – various forms

• Rain (most important and devastating)

• Snow (significant in cold countries - Canada, northern Europe – and mountain areas)

• Hail ( pellets of ice: small balls of ice and hardened snow that fall like rain). (devastating but confined to shortperiods of time)

CVG 3120



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Precipitation Mechanisms• Convective

– Heating of air at ground level leads to expansion and rise of air

• Frontal (Cyclonic)

– Movement of large air mass systems (warm & cold fronts)

• Orographic

– Mechanical lifting of air masses over windward sides of mountain ranges



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Global Precipitation

http://geography.uoregon.edu/envchange/clim_animations/#Global%20Water%20Balance

Precipitation Variation

• Influenced by

– Distance from the sea: The sea affects the climateof a place. Coastal areas are cooler and wetterthan inland areas.

– Ocean currents:

– Direction of prevailing winds: Winds that blow

from the sea often bring rain to the coast and dryweather to inland areas.

– Relief: Mountains receive more rainfall than lowlying areas



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Measurement of rainfall – Required parameters

1. Depth of precipitation (in, cm or mm)

2. Duration (min, hrs)

3. Rainfall intensity (in/hr, cm/hr)

4. Space-time distribution of precipitation

Measurement of rainfall – Types of Recordings

Point measurements (Localized)

– Non-recording (standard) gages – measure only (1)

– Recording gages – tipping bucket, weighing-type, float recording-type

- measure (1) to (4)

Area measurements (over a certain area)

– Radar measurements (LIDAR, NEXRAD)

– Gauge network

Tipping Bucket Rain Gage

1. Recording gage

2. Collector and Funnel

3. Bucket and Recorder

4. Accurate to .01 ft

5. Telemetry- computer



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(Source: NationaL Wweather Service - US, 2000)

Rainfall measurement - Radar

1. Recent Innovation

2. Digital data is measured every 5

min over each grid cell as storm

advances (4 km x 4 km cells)

3. The radar data can be summed

over a storm to provide total

rainfall depths by sub-area

4. Accurate to 150-250 km

5. Provides spatial detail better

than gages

Rainfall measurement - Radar



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Raingauge network

• Since the catching area of raingauge is very small

compared to areal extent of a storm, it is obvious

that to get a representative picture of a storm

over a catchment the number of raingauges

should be as large as possible

• On the other hand, economic considerations to a

large extent and other considerations, such as

topography, accessibility, etc restrict the number

of gauges to be maintained.

Raingauge network

• Hence one aims at the optimum density of

gauges from which reasonably accurate

information about the storms can be obtained

• WMO recommends the following densities:

– In flat regions of temperature, Mediterranean and tropical

zones: ideal -1 station for 600-900km2; acceptable: 1

station for 900 – 3000km2.

– In mountainous regions of temperate, Mediterranean and

tropical zones: Ideal – 1 station for 100-250km2;

acceptable: - 1 station for 25-1000km2



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Raingauge network

• WMO recommends the following densities:

– In arid and polar zones: 1 station for 1500 –

10,000km2 depending on the feasibility

• Adequacy of raingauge stations:

– If there are already some raingauge stations in a

catchment, the optimal number of stations should

exist to have an assigned percentage of error in

the estimation of mean rainfall.

2

ε

vC N N = optimal number of stations, ε = allowabledegree of error in the estimate of mean rainfall

and C v = coefficient of variation of the rainfall values

Analysis of Temporal Distribution of Rainstorm Event

- Only feasible for data obtained from recording gauges.

- Rainfall Mass Curve : A plot showing the cumulative rainfall

depth over the storm duration

- Rainfall Hyetogragh : A plot of rainfall depth or

intensity with respect to time

Time

Time



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Graphical Representation of Rainfall Data

- Mass curves & rainfall hyetographs -

Example of Rainfall Analysis



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Double Mass Curve Analysis

Shifting of a rain-gauge station to a new

location, exposure, instrumentation, or observational

error from a certain date may cause relative change

in the precipitation catch. This information is not

usually included in the published records.

Double – mass curve analysis tests the consistency of

the record at a gage by comparing its accumulated

annual or seasonal precipitation with the concurrent

cumulated values of mean precipitation for a group of

surrounding stations. This technique is based on the

principle that when each recorded data comes from

the same parent population, they are consistent .

Double Mass Curve Analysis

Abrupt changes or discontinuities in the resulting

mass curve reflect some changes at the target gage.

Gradual changes in the slope of the mass curve

reflect progressive changes in the vicinity of the

target gage, such as the growth of trees around a rain

gage.

The slopes of different portions of the mass curvecan be used as a basis for correcting the record of the

target gage.



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Operation of Double Mass Analysis

Pi,t or Pi,t / n

Px,t

Adjustment factor for data

after 1916 = S1 / S2 , i.e.,

Px, t = Px, t S1 /S2 , t > 1916

S2

S1

1916

A change of slope should not be considered significant unless it persists for

at least 5 years.

Due to the fact that the data may have some scatter, an indicated change in

slope should be confirmed by other evidence unless the change in slope is

substantial (say, greater than 10%).

Example –Double Mass

Analysis



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Areal Precipitation Estimates:

Arithmetic Mean

• When the area is physically and climatically

homogenous and the required accuracy is

small, the average rainfall ( ) for a basin

can be obtained as the arithmetic mean of

the Pi values recorded at various stations.

P

N

i

ini P

N N PPPPP

1

21 1..........

Areal Precipitation Estimates:Arithmetic Mean

J

j jP

J P

1

1

Station Observed Rainfall

mm

P2 20

P3 30

P4 40

P5 50

140

Ave. Rainfall = 140/4 = 35 mm



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Thiessen Polygon Method

Thiessen polygons ……….



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A 1 A 2

A 3 A 4

A 5

A 6

A 7

A 8P1

P2

P3

P4

P5

P6

P7

P8

m

mm

A A A

AP AP APP

.....

.....

21

2211

M

i

ii

total

i

M

i

i

A

AP

A

AP

P1

1


Generally for M station

The ratio is called the weightage factor of station i A

Ai



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Thiessen Polygon Method

J

j j jP A

AP

1

1

Station Observed

Rainfall

Area Weighted

Rainfall

mm km2 mm

P1 10 0.22 2.2

P2 20 4.02 80.4

P3 30 1.35 40.5

P4 40 1.60 64.0

P5 50 1.95 97.5

9.14 284.6

Ave. Rainfall = 284.6/9.14 = 31.1 mm

Areal Precipitation Estimates:Thiessen Polygon Method



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Isohyetal Method

• An isohyet is a line joining points of equal rainfallmagnitude.

Isohyetal Method

F

B

E

A

C

D

12

9.2

4.0

7.0

7.2

9.110.0

10.0

12

8

8

6

6

4

4

a1a1

a2

a3

a4

a5





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Distance-Weighted Mean Areal Precipitation

Distance-Weighted Mean Areal Precipitation



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Mean areal precipitation1. Arithmetic Method

2. Thiessen Polygon

3. Isohyetal Method

N

P

P

N

i

i 1

N

i T

ii A

APP

1

HIGHER ACCURACY

N

i w

ii A APP

1

Areal Precipitation Estimates

Three Methods

• Arithmetic Average

– Gages must be uniformly distributed

– Individual variations must not be far from mean rainfall

– Not accurate for large area where rainfall distribution is variable

• Thiessen Polygon

– Areal weighting of rainfall from each gage

– Does not capture orographic effects

– Most widely used method

• Isoheytal – Most accurate method

– Extensive gage network required

– Can include orographic effects and storm morphology



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Filling-in missing rainfall records

1. Often, rainfall data are missing over various periods of time

2. One has to estimate the missing data based on information provided by surrounding gages

1e wher11

N

i

i

N

i

ii x aaPP

1. Arithmetic Average method

N

iai

When normal precipitation of the surrounding gages is within 10 % of

the missing gage

2. Normal Ratio method

When normal precipitation of the surrounding gages is more than 10 %

of the missing gage

n

i i

xii

i

x x x x

nN

N PP

N

N P

N

N P

N

N

nP

1

2

2

1

1

...1

3. Inverse Distance (Quadrant) method

N

i

i

ii

D

Da

1

2

2

1

1

Calculate the weights of the surrounding gages based on the distances

from the gage missing the rainfall data

Ni is the normal precipitation (average value of a particular date, month or year over a specified long period



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Example

Station Annual precipitation

(cm)

Monthly precipitation

(cm)

A 114 11.5

B 95 9.0

C 122 12.4

D 102 ??

Use: (1) Arithmetic Average Method and (2) Normal Ratio Method

http://geography.uoregon.edu/envchange/clim_animations/#Global%20Water%20Balance



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Intensity-Duration-Frequency

• IDF curves

• Various return periods &

durations

• Used for drainage design

• Used for floodplain designs

Characteristics of IDF Curves

•IDF curves do not represent time

histories of real storms, intensities are

averages over indicated durations

• A single curve represents data from

several storm events, likely from different

years

•Duration is not the duration of an actual

storm (typically represents a shorter

period within a longer storm)

•It is theoretically incorrect to obtain a

storm event volume because the duration

is arbitrarily assigned (or selected).



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Development of IDF Curves

•Using a long-term rainfall record ( 20 – 25 years), for each specified

duration (common values 15 min., 30, 60, 120, up to 24 hours) the following

steps are used;

• The annual maximum (or exceedences) rainfall depths are extracted from

the period of record. This results in one depth value for each year of record.

• A frequency analysis is conducted on the annual series (or partial duration

series): The precipitation values are arranged in descending order and the

return period for each value is obtained using the formula: T=(n+1)/m

• The intensity and duration points are plotted and smoothed for selected

frequencies

•IDF curves provide the average intensity (depth) for a specified duration

and frequency and serve as the most common source for synthetic design

storms.

• IDF curves are developed based on statistical analysis of rainfall records

• The intensities are ranked in descending order and assigned a rank m

• The return period (T) are calculated according to a plotting-position formula

such Weibull

where:

m = rank of data

n = number of observationsm

n yearsT

1)(

• For each duration, series of intensities and return periods are plotted



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Example –Dar Airport Data

YEAR 15MIN 30MIN 1 HR 2 HRS 3 HRS 6 HRS 12 HRS 24 HRS

1955 21.59 30.48 33.78 34.04 34.04 46.99 73.91 93.73

1956 20.32 30.48 43.94 50.29 53.34 58.17 58.17 58.17

1957 21.84 30.48 36.83 51.05 57.15 74.93 85.09 92.20

1958 10.10 16.26 21.08 22.61 27.69 43.18 50.54 50.55

1959 15.24 28.70 32.00 36.83 37.59 38.35 38.35 40.641960 25.40 46.74 52.07 52.07 52.07 53.34 53.34 53.34

1961 24.13 36.07 44.20 56.64 62.74 87.63 88.14 88.14

1962 21.59 22.35 28.70 33.53 34.29 48.26 49.78 51.05

1963 30.48 40.64 53.34 76.45 77.72 84.84 84.84 84.84

1964 21.84 28.19 37.85 38.35 39.62 49.02 50.55 55.55

1965 26.67 37.34 49.78 51.31 52.58 52.83 62.74 66.55

1966 19.05 27.94 28.96 28.96 30.48 33.02 33.02 33.02

1967 22.86 36.10 47.24 48.26 50.29 50.29 50.29 50.29

1968 24.13 40.64 58.42 81.28 81.53 94.23 96.77 96.77

1969 24.38 32.00 48.51 49.53 52.32 66.80 67.82 71.88

1970 24.13 34.29 36.32 38.35 45.21 48.26 48.26 48.26

1971 20.83 22.35 22.64 22.61 27.18 27.69 27.94 34.29

1972 22.86 31.50 41.91 53.34 60.96 71.63 76.20 77.22

1973 17.78 35.56 40.64 40.64 42.26 53.34 54.10 69.85

1974 22.50 36.00 52.50 52.50 55.50 57.50 58.50 58.50

1975 25.00 50.00 103.00 111.00 113.00 113.00 113.00 113.00

1976 19.00 25.00 50.00 59.00 59.00 60.00 60.00 60.00

1977 15.00 19.00 30.00 37.00 39.00 52.00 52.70 52.70

1978 24.50 33.50 51.00 52.00 52.10 52.50 52.50 71.00

1979 41.00 53.00 64.00 66.00 66.00 66.00 66.00 66.001980 29.00 41.00 52.00 57.50 65.00 80.00 80.00 80.00

1981 33.00 43.50 44.00 44.30 44.30 44.50 45.00 55.50

1982 20.00 31.00 35.00 43.00 46.00 54.50 74.90 77.00

1983 20.20 24.00 30.20 39.00 42.00 51.50 59.00 67.20

1984 25.50 32.70 50.00 51.90 53.00 53.00 53.00 53.00

1985 15.00 16.80 27.00 38.50 45.90 46.50 47.00 58.00

1986 25.20 26.00 40.00 48.00 55.00 57.00 57.00 61.00

Data Dar Airport

15 MIN 30 MIN 1 HR 2 HRS 3 HRS 6 HRS 12 HRS 24 HRS

2 YRS 92.08 65.04 42.78 23.66 16.62 9.50 4.99 3.90

5 YRS 117.48 84.18 57.02 31.61 21.92 12.77 7.49

10 YRS 134.32 96.84 66.44 36.87 25.42 14.93 7.91 4.08

25 YRS 155.60 112.84 78.35 43.52 29.85 17.67 9.37 4.80

50 YRS 171.40 124.72 87.19 48.45 33.13 19.70 10.46 5.33

100 YRS 187.08 136.50 95.96 53.34 36.39 21.71 11.54 5.86



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IDF CURVE

0

20

40

60

80

100

120

140

160

180

200

0 100 200 300 400 500 600 700 800

R a i n f a l l i n t e n s i t y ( m m / h r )

Time (min)

T=2years

T=5 years

T=10years

T=25 years

T=50 years

T=100years

APPLICATIONS

IDF Curves



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RATIONAL METHOD

• Empirical method for small watersheds (less then 2000

acres)

• For small ungaged watersheds

Q = C I A where:Q = peak runoff rate, cfs

C = runoff coefficient, non-dimensionalI = rainfall intensity, in/hr

A = area, acres

Q = 0.278 C I A

Imperial system

Metric system

where:

Q = peak runoff rate, m3/sC = runoff coefficient, non-dimensional

I = rainfall intensity, mm/hr

A = area, km2



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The "rationale" of this method is: (1) Units agree: 1 cfs = 1 in/hr x 1 acre, and

(2) C (a dimensionless quantity) varies from 0 to 1 and can be thought of as the

percent of rainfall that becomes runoff .

Assumptions for the rational formula are related to the intensity term and toquantifying C (the runoff coefficient):

•Rainfall occurs uniformly over the entire watershed.

•Rainfall occurs with a uniform intensity for a duration equal to the time of concentration

for the watershed.

•The runoff coefficient, C, is dependent upon physical characteristics of the watershed, e.g. soil type.

•It is assumed that, when the duration of a storm equals the time of concentration, allparts of watershed are contributing simultaneously to the discharge at the outlet..

Weaknesses of the Rational Method: Estimation of tc. Especially critical on small watershed where tc is short and

changes in design intensities can occur quickly.

Reflects only the peak and gives no indication of the volume or the timedistribution of the runoff.

Lumps many watershed variables into one runoff coefficient.

Lends little insight into our understanding of runoff processes - Beware of cases where watershed conditions vary greatly across the watershed.

This method is a great oversimplification of a complicated process; however, the

method is considered sufficiently accurate for runoff estimation in the design of relatively inexpensive structures where the consequences of failure are limited.

Application of rational method is normally limited to watersheds of less than 2000acres.



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Runoff Coefficient "C": Because most watersheds contain more than one soil type with multiple land usesand slopes, it is necessary to determine the runoff coefficient that represents this

total variability.

Average coefficients for composite areas may be calculated on an area weightedbasis using:

where C i is the coefficient applicable to the area Ai . In areas where large parts arelaid out in typical, repeating patterns such as sub-divisions, the weighting factors

and weighted C can be determined by considering a single, typical layout.

i

ii

A

AC C

Typical values for C:

•Downtown areas : 0.70-0.95

•Neighborhood areas : 0.50 – 0.70•Lawns : 2 % slopes – 0.05 – 0.10

•Lawns : 7 % slopes – 0.15 – 0.20

CVG 3120

Concentration time “tc":

The time needed for a water particle to travel from the most hydraulically distantpart of the watershed to the outlet.For the rational method, it is the time at which the entire watershed will contribute

to the runoff at the outlet The storm duration is assumed equal to tc

385.077.00195.0

S Lt c

where:L = maximum length of flow (m)

S = Watershed gradient (m/m)

tc = concentration time (min)

Kirpich method – for small drainage basins

Morgali – Linsley method – for small urban drainage areas

3.04.0

6.094.0

S I

nLt c

where:L = length of flow, (ft)

I = rainfall intensity (in/hr)

n = Manning coefficient (dimensionless)

S = slo e of flow (dimensionless)



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Rainfall intensity “I":Chosen based on the concentration time, tc and the return period, Tr

Assume steady intensity for the entire duration of the rain – overdesign!

Return period, Tr (pg. 758, Singh)

Can be calculated also based on the IDF curves drawn for the region for which

the calculation is made:

ec d t

b I

where:

I = design rainfall intensity, (in/hr)

tc = time of concentration (min)b, d, e = parameters(varying with location and return period)

Procedure for use:

i) Select design return period. (Ex.,Tr = 10 years)ii) Determine time of concentration for the watershed.

iii) Determine design intensity for T r [return period] = selection fordesign and duration = t c .

iv) Determine weighted runoff coefficient. v) Determine watershed area. vi) Calculate peak flow.



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Hydraulic Shapes

Manning’s Equation used to

estimate flow rates

Q = k/n A R 2/3 S 1/2

Where Q = flow rate

n = roughness

A = cross sect A

R = A / P

S = Slope

k = 1.49 imperial

k = 1 metric

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02 Precipitation Lecture 2