hydrology - eng.uowasit.edu.iq · turbulent air current. measurement of precipitation. all forms of...

Asst. Lec. Ali Abdul-Hussein Abed

Fourth year

HYDROLOGY Precipitation

Ali Abdul-Hussein Abed

1

Precipitation and its measurement

Precipitation is measured in mm or inch.

Type of precipitation:-

Precipitation is often typed according to the factor mainly responsible for the lifting,

which causes it.

The types of precipitation can be classified as:-

1) Cyclonic precipitation: - resulting from the lifting of air converging into low-

pressure area.

2) Convective precipitation: - is caused by the raising of warmer, lighter air in

colder, density surroundings.

3) Orographic precipitation: - result from mechanical lifting over mountain

barriers.


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Forms of precipitation

1- Rain: its consists of water drops more than o.5 mm in diameter the upper limit of

water drop may be 6.4 mm . It can be classified into (light, moderate, heavy)

2- Drizzle: it consists of water drops less than 0.5 mm.

3- Glaze: it is ice coating formed when drizzle or rain freezes

4- Snow: it is precipitation in the form of ice crystals resulting from sub limitation of

water vapor directly to ice.

5- Snow flake: - It is made up of number of ice crystals fused together

6- Hail: it is precipitation in the forms of balls or lumps of ice over 5 mm in diameter

formed by alternate freezing and melting as they are carried up and down in highly

turbulent air current.

Measurement of precipitation.

All forms of precipitation are measured on the basis of the vertical depth of water that

would accumulate on a level surface

Types of rain gauges: -

- Non recording gauges

- Recording gauges

- Storage gauges

The number of observations stations may be decided by the following

considerations:-

1- For plains regions, one station for each (600-900) km2.

2- For mountain regions, one station for each (100-250) km2.

3- For dry and polar regions, one station for each (1500-10000) km2.


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Selection of site for rain gauge

- The rain gauge should be setup in open placed.

- The distance between the rain gauge and the nearest object should not be less than

twice the height of the object .in no case this distance should be less than 30m.

- If suitable level ground is available, rain gauge should never be installed on side or

top of hill.

- In hilly areas, the rain gauge should be located where it is best shielded from high

velocity winds.

Non-recording gauges

A. The standard 8" gage: -

Rain pass from the collector into a cylindrical measuring tube inside the

overflow can. The measuring tube has a cross-sectional area one-tenth that

of the collector so that 0.1-in rainfall will fill the tube to a depth of 1-in.

𝑉 = 𝐴 ∗ 𝐻

=𝜋

4𝐷2 ∗ 1 … … … … … 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟

=𝜋

4𝑑2 ∗ 10 … … 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑖𝑛𝑔 𝑡𝑢𝑏𝑒

To find the diameter of measuring tube this form can be used.

𝑑 =𝐷2

10


4

Recording gauges

A. Tipping-bucket Rain gages:

In the tipping-bucket gage water caught in the collector and guided into a two-

compartment bucket 0.1 mm or some other designed quantity of rain will fill one

compartment (partition) and overbalance the bucket so that it tips, emptying into a

reservoir and moving the second compartment into place below the funnel. As

bucket is tipped, it actuates an electric circuit.

B. The weighing-type gage: -

The weighing-type gage is weighs the rain which falls into a bucket set on the

platform of spring or level balance. The increasing weight of bucket and its

content is recording on a chart. The record thus shows the accumulation of

precipitation.

Estimating the missing precipitation data.

Many precipitation stations have short disruptions in their records because of

absences of the observer or because of instrumental failure.

A. Simple arithmetic: -

In this method the amounts at the index station are equal weighted with all

other stations. This method used when the normal annual precipitation at any


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index station differs from that at the station in question by less than 10

percent.

𝑃𝑥 =1

𝑁∗ (𝑃𝐴 + 𝑃𝐵 + 𝑃𝐶)

Where:-

𝑃𝑥= precipitation of station x,

𝑁= number of stations, and

𝑃𝐴, 𝑃𝐵, 𝑃𝐶= precipitations of stations A, B, and C

B. Normal-ratio method: -

In this method the amounts at the index station are weighted by the ratio

of the normal-annual-precipitation values. This method used when the normal

annual precipitation at any index station differs from that at the station in

question by more than 10 percent.

𝑃𝑥 =1

𝑁[𝑁𝑥

𝑃𝐴𝑃𝐴 +

𝑁𝑥

𝑁𝐵𝑃𝐵 +

𝑁𝑥

𝑁𝐶𝑃𝐶]

Example: - Find precipitation of station using data in Table (3-1).

Station name Precipitation (cm) Annual precipitation (cm)

A 4.2 44.1

B 3.5 36.8

C 4.8 47.2

D ? 38.5

Solution:

X

A

B

C


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C. Double-mass analysis.

Tests the consistency of the record at a station by comparing its accumulated

annual or seasonal precipitation with the simultaneous accumulated value of mean

precipitation for a group of surrounding stations.

Years Annual

precipitation (A)

Average annual

precipitation of 20

station

Accumulated annual

precipitation of 20 station

1918 𝐴1 𝐵1 𝐵1

1919 𝐴2 𝐵2 𝐵1 + 𝐵2

1920 𝐴3 𝐵3 𝐵1 + 𝐵2 + 𝐵3

. . .

. . .

. . .

2008 𝐴𝑛 𝐵𝑛 ∑ 𝐵𝑖

𝑛

𝑖=1

𝑆1 =𝐻1 − 𝐻𝑜

𝑋1 − 𝑋𝑜

𝑆2 =𝑌1 − 𝐻𝑜

𝑋1 − 𝑋𝑜

𝑆2

𝑆1

Acc

um

ula

ted p

reci

pit

atio

n o

f st

atio

n A

Accumulated precipitation of 20 stations

(𝑋𝑜, 𝐻𝑜)

(𝑋1, 𝑌1)

(𝑋1, 𝐻1)


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𝑆1

𝑆2=

𝐻1 − 𝐻𝑜

𝑌1 − 𝐻𝑜

𝑌1 =𝑆2

𝑆1

(𝐻1 − 𝐻𝑜) + 𝐻𝑜

𝑌1 = −𝑆1

𝑆2

(𝐻𝑜 − 𝐻1) + 𝐻𝑜

Example: The annual precipitation at station X and the average annual precipitation at

15 surrounding stations are as shown in the flowing table

a) Determine the uniformity of the record at the station X

b) In what year is a change in regime indicated?

c) Compute the mean annual precipitation for station X for the entire 30 years

period without adjustment.

d) Repeat part C for station X at its 1979 site with the data adjusted for the change

in regime.

Years Annual precipitation (cm)

Station X Average of 15 stations

1950. 47 29

1951. 24 21

1952. 42 36

1953. 27 26

1954. 25 23

1955. 35 30

1956. 29 26

1957. 36 26

1958. 37 26

1959. 35 28

1960. 58 40

1961. 41 26

1962. 34 24

1963. 20 22

1964. 26 25

1965. 36 34

1966. 35 28

1967. 28 23

1968. 29 33

1969. 32 33

1970. 39 35

1971. 25 26

1972. 30 29

1973. 23 28


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1974. 37 34

1975. 34 33

1976. 30 35

1977. 28 26

1978. 27 25

1979. 34 35

Solution:

Average precipitation over area.

There are three ways to estimate the average precipitation over area can be explained

below:

1) Arithmetic mean:

This method yields good estimates in flat country if the gages are uniformly

distributed and the individual gage catches do not vary widely from the

mean.

𝑃𝑎𝑣 =∑ 𝑃𝑖

𝑛𝑖=1

𝑁

2) Thiessen method:

The Thiessen method attempts to allow for non-uniform distribution of gages

by providing a weighting factor for each gage.

The method can be described as:

Perpendicular bisectors of these connecting from polygons around each station.

The sides of each polygon are the boundaries of the effective area assumed for

the station. The area of each polygon is determined by geometrical method;

where the area can be classified as geometrical shapes; or by using Planimetry.

Weighted average rainfall for the total area is computed by multiplying the

precipitation at each station by its assigned percentage of area and totaling.


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Example: By using Thiessen method, find the average precipitation of gages located as

shown at the whiteboard; where the table below found from the procedure mentioned

earlier.

Solve it within the table:

Observed

precipitation

(in)

Area

(𝑚𝑖𝑙𝑒2)

Percent of total

area

%

Weighted

precipitation

col 1*col3

(in)

0.65 7

1.46 120

1.92 109

2.69 120

1.54 20

2.98 92

5.00 82

4.50 76

Total area = Total = Total =


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3) Isohyetal method:

This method is the most accurate method of averaging precipitation over an

area. Station locations and amounts are plotted on a suitable map, and contours of

equal precipitation (isohyets) are drowning. The average precipitation for an area

is computed by weighted the average precipitation between successive isohyets

(usually taken as the average of two Isohyetal values) by the area between

isohyets, totaling these products and dividing by the total area.

Example:- By using Isohyetal method find the average precipitation of gages located as

shown at the whiteboard; where the table below found from the procedure mentioned

earlier.

Solve it within the table:

Isohyet

(in)

Area enclosed

(𝑚𝑖𝑙𝑒2)

Net area

(𝑚𝑖𝑙𝑒2)

Average

precipitation

(in)

Precipitation

volume

(col 3 * col 4)

5 13

4 90

3 206

2 402

1 595

<1 626


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Variation of precipitation:-

Geographical variation:

In general precipitation is heaviest near the equator and decreases with increasing

coordinate.

Time variation:-

With the allowance of daytime and seasonal variation, no persistent steady

cycles of any considerable magnitude have been conclusively demonstrated.

The time distribution of rain fall within storms is important for estimating

flood hydrographs. Distribution varies with storm type, intensity, and duration;

there is no typical distribution that is applicable to all situations.

Measurement of snow: Snow density(𝜌): The volume of water content of the sample per the initial of the

sample.

𝜌 =𝑎𝑟𝑒𝑎 ∗ 𝑑

𝑎𝑟𝑒𝑎 ∗ 𝐷=

𝑑

𝐷

𝑆𝑛𝑜𝑤 𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦 = 100% − 𝑤𝑎𝑡𝑒𝑟 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 %

𝐴𝑣. 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑓𝑜𝑟 𝑓𝑟𝑒𝑠ℎ 𝑠𝑛𝑜𝑤 = 0.1 𝑜𝑟 10%

Example: Depth of snow sample = 18", weight of sample tube = 15 #, weight of sample

tube + 15 #, diameter of tube = 1.5", find the depth of the sample.


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Graphical Representation of Rainfall

The variation of rainfall with respect to time (Intensity) may be shown graphically by (i)

a hyetograph, and (ii) a mass curve.

Intensity is a measure of quantity of rainfall in a given time; mm per hour.

A hyetograph is a bar graph showing the intensity of rainfall with respect to time and is

useful in determining the maximum intensities of rainfall during a particular storm as is

required in land drainage and design of culverts.

of rainfall (or precipitation) is a plot of cumulative depth of rainfall A mass curve

against time, from the mass curve, the total depth of rainfall and intensity of rainfall at

any instant of time can be found.

Optimum rain gauge network design

The aim of the optimum rain-gauge network design is to obtain all quantitative data

averages and extremes that define the statistical distribution of the hydro-meteorological

elements, with sufficient accuracy for practical purposes. This method all the more

important when the mean depth of rainfall is calculated by sample arithmetic mean

method

The number in the basin is given by… 𝑁 = (𝐶𝑣

𝑝)^2


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N= optimum number of rain gauge station.

Cv= Coefficient of variation.

P= the desired degree of percentage error.

CV=σ/x/……………..𝑥− = ∑ 𝑥

𝑛

𝜎 = √∑(𝑥−𝑥−)^2

𝑛−1

Example: - For the basin shown in Fig. 2.12, the normal annual rainfall depths recorded

and the isohyetals are given. Determine the optimum number of rain-gauge stations to be

established in the basin if it is desired to limit the error in the mean value of rainfall to

10%. Indicate how you are going to distribute the additional rain-gauge stations

required, if any. What is the percentage accuracy of the existing network in the

estimation of the average depth of rainfall over the basin?


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Note: - x = Arithmetic mean, σ = standard deviation.

The optimum number of rain-gauge stations to limit the error in the mean value of

rainfall to p = 10%.

Additional rain-gauge stations to be established = N – n = 11 – 5 = 6

The additional six rain gauge stations have to be distributed in proportion to the areas

between the isohyetals as shown below:

These additional rain gauges have to be spatially distributed between the different

isohyetals after considering the relative distances between rain-gauge stations, their

accessibility, personnel required for making observations, discharge sites, etc.

The percentage error p in the estimation of average depth of rainfall in the existing

network,

𝑃 = (𝑪𝒗

√𝑵) , putting N = n

P =33.1/ (5) ^0.5 = 14.8%

Or, the percentage accuracy = 85.2%

Analysis of Rainfall Data

Rainfall during a year or season (or a number of years) consists of several storms. The

characteristics of a rainstorm are (i) intensity (cm/hr.), (ii) duration (min, hr., or days),

(iii) frequency (once in 5 years or once in 10, 20, 40, 60 or 100 years), and (iv) areal

extent (i.e., area over which it is distributed).

Correlation of rainfall records

(i) The intensity and duration of storms,

If there are storms of different intensities and of various durations, then a relation may

be obtained by plotting the intensities (i, cm/hr.) against durations (t, min, or hr.) of the

respective storms either on the natural graph paper, or on a double log (log-log) paper,

Fig. 2.18(a) and relations of the form given below may be obtained:-


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Where t = duration of rainfall or its part, a, b, k, n and x are constants for a given region.

Since(x) is usually negative.

Correlation of intensity and duration of storms

On the other hand, if there are rainfall records for 30 to 40 years, the various storms

during the period of record may be arranged in the descending order of their magnitude

(of Maximum depth or intensity). When arranged like this in the descending order, if

there are a total number of n items and the order number or rank of any particular storm

(maximum depth or intensity) is m, then the recurrence interval T (also known as the

return period) of the storm magnitude is given by one of the following equations:

Frequency this is refers to the expectation that a given depth of rainfall will in a given

time. Such an amount may be equaled or exceeded in a given number of days or years.

Duration is the period of time during which rain falls.


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(ii) The intensity, duration and frequency of storms. (IDF)

If the intensity-duration curves are plotted for various storms, for different recurrence

intervals, then a relation may be obtained of the form

The lines obtained for different frequencies (i.e., T values) may be taken as roughly

parallel for a particular basin though there may be variation in the slope ‘e’. Suppose, if

a 1-year recurrence interval line is required, draw a line parallel to 10–year line, such

that the distance between them is the same as that between 5-year and 50-year line;

similarly a 100-year line can be drawn parallel to the 10-year line keeping the same

distance (i.e., distance per log cycle of T). The value of i where the 1-year line intersects

the unit time ordinate (i.e., t = 1min, say) gives the value of k. Thus all the constants of

Equation`s Sherman can be determined from the log-log plot of ‘i vs. t’ for different

values of T.


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18


19


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Probable maximum precipitation (PMP)

It is the maximum possible of quantity rainfall to certain duration above station or

certain basin and used the following equation for its calculation.

PMP = P\ + K*σ

σ = Standard deviation

P\ = Average of rainfall.

K = Frequency factor, it is function of independent probability distribution and return

period.

Example:-For ten years ago the max annual rainfalls are recorded as shown below and

it has the same duration (60 min). Find the return period and probability for each rainfall

for this duration.

Years 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

Max. Annual

Rainfall (mm) 32 21 8 5 14 29 26 35 40 30

Sol.

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