Chapter 2
PRECIPITATION
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2.1
Introduction
Precipitation is the deposition of water from the atmosphere on the surface. Precipitation
is primarily responsible for replenishing surface water bodies, recharging aquifers,
renewal of soil moisture for plants with its principal forms being rain and snow. The
climate of a given area has a significant influence on the form in which precipitation
occurs, i.e. rain or snow or both. The hydrological cycle amply demonstrates the paths
that are followed by precipitated water. Precipitation is subjected to such processes as
evaporation, interception, infiltration and depression storage before its occurrence as
surface flow. A particular area's weather conditions in conjunction with topography
significantly influence the incidence of precipitation types while geology, vegetal cover,
antecedent soil moisture conditions and the actual amount of precipitation have a bearing
on the runoff rates and volumes.
2.2
The Atmosphere
The atmosphere is the gaseous layer that envelops the earth to an approximate height of
11km and is known as the troposphere. With respect to the study of hydrology, the
atmosphere can be divided into three parts that are a) dry air; b) water vapor(less than
4%) and; c) impurities.
2.2.1 Dry air
Dry air consists of a mixture of gases which if they were separated and brought to the
same temperature and pressure, the respective volumes occupied by the four principal
gases are as shown in Table 2.1.
Table 2.1:
1
2
3
4
Relative volumes of the four principal atmospheric gases
Gas Type
Nitrogen
Oxygen
Argon
Carbon Dioxide
N2
O2
Ar
CO2
Mass (%)
75.5
23.1
1.3
0.1
Volume (%)
78.09
20.95
0.93
0.03
2-1
Other trace gases include helium, ozone, hydrogen, radon, neon and krypton. Of
importance are ozone which shields the earth from the sun's ultraviolet radiation while
water vapor and carbon dioxide absorb the earth's radiation thus increasing the
temperatures.
2.2.2 Water vapor
The weight of the atmosphere is 5.6 x 1015 metric tons of which the weight of water
vapor is approximately 1.5 x 1013 metric tons. Petterssen (1964) reported that water vapor
occurs in the first (18 000 feet) of the atmosphere and it is important to the formation of
clouds and precipitation in conjunction with impurities. Water vapor essentially obeys the
gas laws under modest ranges of pressure and temperature. Within the atmosphere,
temperatures decrease as distance increases from the earth. Likewise, water vapor content
decreases as distance from the earth increases. The pressure that water vapor exerts in the
absence of other gases is known as vapor pressure. Thus the pressure of water vapor
saturating the air at 30oC is about 40 millibars (mbar)and at 0oC the vapor pressure is
about 7 millibars.
Since the atmosphere is infrequently saturated, the degree of saturation is expressed as
the ratio of actual vapor pressure to that at saturation for a particular temperature. This
ratio is expressed as a percentage and is known as the relative humidity which is
expressed as follows:
f  100
e
es
(2.1)
Where:
f = relative humidity (%)
e = actual vapor pressure (mbar)
es = saturation vapor pressure (mbar)
As the relative humidity increases towards 100% the greater the chances of precipitation
occurring.
2.3
Formation of precipitation
For precipitation to occur. Some mechanism is required to cool the air sufficiently to
bring it to near saturation. When unsaturated air is carried to high levels, expansion will
occur due to the reduction of pressure with altitude. At the higher levels the expansion is
adiabatic, meaning that no heat is added or subtracted from outside sources. However the
temperature is lowered because of the heat energy that is transformed into work in the
process of expansion. This adiabatic cooling is the principle cause of condensation and
directly responsible for practically all types of rainfall. Not all clouds yield precipitation.
Only when droplets, ice pellets or crystals become large enough to overcome the
buoyancy and upward drafts in the atmosphere does precipitation occur.
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2.3.1 Precipitation forms
Precipitation is differentiated depending on the form of water being deposited on the
surface, i.e., liquid or solid. The general forms of precipitation are described below:
i)
ii)
iii)
iv)
Rain is precipitation of liquid water drops that from 0.5mm to about 7mm
in diameter. Drizzle consists of water droplets that are less than 0.5mm in
diameter. Drizzle has a slow settling velocity and an intensity of less than
1 mm/hour.
Hailstones is precipitation of ice balls whose diameter is between 5mm
and 125mm in diameter with a specific gravity of about 0.7 to 0.9.
Hailstones are of significance as they cause damege to crops and property.
Snow is precipitation of complex ice crystals. Snowflakes are made up of
ice crystals. The average water content of snow is taken to be about 10%
of an equal volume of water.
Sleet is precipitation of freezing raindrops and usually in combination with
snow.
2.3.2 Types of precipitation
Precipitation is classified according to the factor responsible for the lifting mechanism
which induces condensation. The four main types of precipitation are described below:
i)
Cyclonic storms
Cyclonic precipitation results from the lifting of air converging into a low –pressure area
or cyclone. Pressure differences are created by the unequal heating of the earth’s surface.
The mechanism of uplifting air in a cyclone is demonstrated in Figure 2.1.
Divergence
ASCENT
Ground
Convergence
Figure 2.1
Illustration of air uplifting in a cyclone.
2-3
ii)
Convective precipitation
Convective precipitation is caused by the upward and downward transfer of air masses of
different temperatures. On hot summer days, the warm earth's surface in turn heats the air
directly above it which then rises into cooler overlying layers. If the rising air mass has
moisture content that equals the condensation level, then the moisture condenses and the
result is a thunderstorm
iii)
Orographic precipitation
Orographic precipitation occurs when a warm air mass rises over a high geographic
feature such as a mountain range. Moisture in the air mass condenses with precipitation
resulting. Normally mountain slopes facing prevailing winds get more rain than leeward
slopes.
ii)
Frontal precipitation
Air masses of widely differing properties exist together on the earth’s surface and move
under forces initiated by uneven heating. The boundary between dissimilar air masses is
known as a frontal surface. Frontal precipitation results from the lifting of warm air on
one side of a frontal surface over colder, denser air on the other side. Figure 2.2 (a)
illustrates the lifting of warm air by an approaching cold front, while Figure 2.2(b)
illustrates the approaching warm air uplifted by a cold dense air mass to form frontal
precipitation.
(source: Wisler & Brater, 1967)
Figure 2.2
Formation of frontal precipitation (a) Cold front (b) warm front.
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2.4
Measurement of precipitation
Precipitation is measure as the vertical depth of water that would accumulate over a flat
surface area and is reported in millimeters. A raingauge is an instrument which is used to
record rainfall. It is based on the simple idea of exposing in the open a hollow cylindrical
vessel with a bottom but no top. Raingauges are classified into two types namely nonrecording and recording.
2.4.1 Non-recording gauges
There are a number of non-recording gauges in use world-wide. An example of a
standard U.S. Weather Bureau raingauge is shown in Figure 2.3.The ordinary standard
rain gauge has a sampling orifice of 5 in diameter. The half-inch rim is made of brass and
the edges are sharp. The rain passes from the funnel receiver to a glass bottle with a
narrow neck to limit evaporation losses. The glass bottle is placed inside the overflow
can. The overflow can is used to collect water that may overflow from the glass bottle.
Any water collected in the bottle and overflow can is poured into a glass measure and the
reading taken at the lowest point of the meniscus. The glass measure is graduated in
relation to the orifice area of the rain gauge and so gives a direct reading of the depth of
rain that fell on the area contained by the brass rim. The gauge is set into the ground with
its rim level 12 inches above the ground level. The non-recording raingauges are read
daily while accumulation raingauges have a large storage reservoir and are read every 3
or 6 months.
Figure 2.3
Standard rain gauge
2-5
2.4.2 Recording gauges
To know the intensity of rainfall or the amounts for short duration, recording gauges
which give a continuos pen tracing on a clock driven drum are used. Types of recording
gauges commonly in use are described below:
i)
Tipping bucket gauge
The tipping-bucket gauge operates on the principle that the rain that falls into the receiver
is funneled into a two-compartment bucket whereby each bucket has a capacity of 0.1
mm, 0.25 mm or some other designed quantity of rain falling on the area contained by the
funnel. The principal of the tipping bucket is shown in Figure 2.4. The buckets alternately
fill up and empty their contents with each bucket tip of a given quantity being recorded
through an electrical signal that is sent to the recording unit. A tipping-bucket gage is
most ideal for rainfall and snow on melting it by heating.
(Source: Shaw, 1983)
Figure 2.4
ii)
Tipping bucket gauge (A,B: buckets; C: magnet; D: switch)
Weighing type gauge
The weighing-type gauge measures the weight of accumulated rain or snow or both in the
bucket. The bucket sits on a scale that is calibrated to read an equivalent depth of water
for a given weight of precipitation. Weighing-type gages are most ideal for installation in
remote areas where they are known to provide continuous records of up to three months.
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iii)
Float type gauge
A float type gauge (Figure 2.5) comprises of a collecting chamber, which contains a float
that rises with increasing catch of rainfall recorded.
(Source: Shaw, 1983)
Figure 2.5
Float type gauge (A: inlet funnel; B: collecting chamber; C: float; D:
pen arm; E: knife edge; F: trip release; G: siphon; H: counter weight)
The rising movement is transmitted through a suitable mechanism to the pen, which
moves on a revolving chart fixed on a drum to give a mass curve of rainfall. A clock
drives the drum. As soon as the chamber gets filled, thereby causing the float to touch the
top, the water is drained off through a siphon arrangement connected to the bottom of the
chamber.
iv)
Other methods
As technology has progressed over the decades, radars are also being used to measure
rainfall. A radar transmits a pulse of electro-magnetic energy as a beam in a direction
determined by a moveable antenna. The radiated wave, which travels at the speed of
light, is partially reflected by cloud or precipitation particles and return to the radar. The
energy returned to the radar can be interpreted to give a measure of the radar reflectivity
of the hydrometeors. The degree of reflectivity can give the measure of precipitation
intensity. Distance between the radar and the precipitation area can be measured with
respect to the time it takes to receive an echo after a pulse emission. The spatial
coordinates of precipitation can be determined from direction and distance
measurements.
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2.5
Problems in measuring rainfall
Errors in measuring precipitation normally arise from human error in taking a reading,
faulty instruments, damage to the collectors or covering part of the collector area. Other
errors are related to incorrect calibration of instruments and electrical current failures.
Thus it is necessary to correctly calibrate precipitation measuring devices and carry our
regular maintenance services.
To avoid more errors, precipitation gauges must be located well away from obstacles that
are likely to disturb or block precipitation from a collector. Greater wind velocity at a
collector is a source of error in precipitation measurement as diversion occurs. Larson
and Peck (1974) reported that wind velocities of greater than 20mph (32.21 km/hour) can
reduce the volume of rainfall collected by 20%. Errors are greater with lighter or less
dense precipitation types like mist and light drizzle. The height of a gauge should be set
at no more than twice the distance from a gauge to a windbreak. Wind breaks should be
provided where deemed necessary.
2.6
Determination of areal precipitation
Precipitation levels differ or vary quite significantly over large geographic regions as
influenced by air mass movements, topography and water-land locations. All these
factors combine to complicate the design and operation of processes of water resources
systems. Variations also occur on a significant scale in small geographic areas such as
cities and towns. The most commonly used methods for estimating average precipitation
over a specified area such as a drainage basin are described below:
2.6.1 The Arithmetic mean method
This is the simplest method of calculating the average rainfall over an area. It involves
taking the arithmetic mean of the rainfall stations within the catchment (Figure 2.6 (a)).
The rainfall stations used in the calculations are usually those inside the catchment area,
but neighboring gauges outside the boundary may be included if it is considered that the
measurements are representative of the nearby parts of the catchment.

1 N
P   Pi
N i 1
(2.2)
Where:
P = average precipitation depth in mm
Pi = precipitation depth at gauge i within the topographic basin in mm
N = total number of gauging stations within the topographic basin
The arithmetic mean method gives a satisfactory measure of the areal rainfall under the
following conditions:
2-8
i) The catchment area is sampled by many uniformly spaced rain gauges.
ii) The area has no marked diversity in surface characteristics, so that the range in altitude
is small and hence variations in rainfall amounts is minimum.
Figure 2.6
(Source: Linsley et al, 1988)
areal averaging of precipitation by (a) arithmetic mean (b) Thiessen
method (c) Isihyetal method.
2-9
2.6.2 The Thiessen method
The rainfall measurements at individual gauges are first weighted by the fractions of the
catchment area represented by the gauges, and then summed. The application of the
methods involves plotting the gauging stations on a map and then adjacent stations are
joined by straight lines thus dividing the entire area into a series of triangles.
Perpendicular bisectors are erected on each of the connecteing lines to form polygons
around each station. The sides of the polygon are the boundaries of the effective area
assumed for the station. The area of the polygon is determined by the plannimeter. The
procedure is well illustrated in Figure 2.6 (b).
Once the areas of the polygons are determined the average precipitation using the
Thiessen polygonal method is determined as follows:
P
n
 Wi Pi
(2.3)
in
Where:
P = average precipitation in mm
Pi = gauge precipitation for polygon i
Wi = weighted area (Ap/A)
Ap = area of the polygon within the topographic basin in km2
A = total area in km2
n = total number of polygons
2.6.3 The Isohyetal method
This is the most accurate method of determining areal precipitation. Station locations and
amounts are plotted on a suitable map and contours of equal precipitation (isohyets) are
then drawn. The average precipitation for an area is computed by weighting the average
precipitation between successive isohyets, summing these products and dividing by the
total area. The procedure is illustrated in Figure 2.6 (c).
The average isohyetal average is determined as follows:
P
n
Wi Pi
in
(2.4)
Where:
P = isohyetal average precipitation in mm
Pi = average precipitation between contours in mm
2-10
Wi = weighted area (Ai / A)
Ai = sub-area between contours in km2
A = total area in km2
n = total number of sub-areas
2.7 Intensity-duration-frequency curves
Precipitation is the basic input in the design of structures that are used for controlling
storm water volumes and flows. Volumes and flow rates of water to be stored or
conveyed by a system are mathematically related to precipitation. Predictive measures of
precipitation are therefore required in the design of storm water systems. Intensity and
duration of rainfall storms are the two important storm water parameters that can be
statistically related to a frequency of occurrence.
Intensity-duration-frequency (IDF) curve is a graphical presentation of this relationship.
It gives a plot of average rainfall intensity versus rainfall duration for various frequencies
of occurrence or return periods. This information can be presented as an isohytel map of
intensity over an area for a given return period and duration. Such information is used in
the design and operation of closed or open conduits, reservoirs, groundwater pumps,
pollution control structures and assimilative capacity studies.
The intensity-duration-frequency relationship is generally expressed in the general form
as follows:
i
aT m
(b  D)
(2.5)
n
Where:
i = average rainfall in cm/hr for a fixed duration
T = frequency of occurrence or return period in years
D = duration of storm in minutes or hours
a,b,m,n = coefficients and exponents varying from one region to another
2.8 Probable Maximum Precipitation
Probable maximum precipitation (PMP) is defined as that depth of precipitation which,
for a given area and duration, can be reached, but not exceeded under known
meteorological conditions. The PMP is a value of precipitation that have a very low risk
of exceedance, which is used to design the high-hazard structures such as spillways on
large dams. In the first place, the structure of the large dams is often very expensive, so
that its loss would involve a large economic expense. Also, the construction creates a risk
of great loss of life and property down-stream that otherwise would not exist in an event
of a failure of such a structure. For these reasons, design engineers usually have to
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consult with the meteorologists for the estimates of the probable maximum precipitation
as the basis for design of such spillways.
The estimates represent the best judgment of the meteorologists of the realistic upper
limit of precipitation that can occur. The estimation of probable maximum precipitation
was developed and has involved in the United states as a hydrometeorological procedure
(Myers, 1967). Three meteorological components determine maximum possible
precipitation: (1) amount of precipitable water, (2) rate of convergence, and (3) vertical
motion. Meteorological models representing all three components have been developed
(Wiesner, 1970 ), but it has proved quite difficult to specify maximum rates of areal
convergence and vertical motion for the models.
The standard approach to estimating PMP (WMO, 1986) observed totals for extreme
storms are used as indicators of the maximum values of convergence and vertical motion.
The two major components of the standard approach to the PMP computation are
moisture maximization for the observed storm and storm transposition. In the first step of
moisture maximization, the goal is to increase storm rainfall amounts to reflect the
maximum possible moisture availability. In the storm transposition step, it is determined
whether a given storm, which occurred in a broad region around the basin of interest, can
be transposed to represent rainfall over the basin. The principal data required for standard
PMP computations are (1) catalog of extreme storm and (2) surface dew-point
temperature observations. Additional meteorological information, including surface and
upper-air maps, is typically used subjectively in determining storm transposition regions.
Surface dew point is used as a moisture index for moisture maximization.
2.9
Rainfall data screening
Data screening is a necessary step to check for inconsistency in rainfall records which
may be due to change in location of raingauge, change in exposure such as coming up of
new buildings and growth of trees or changes in instruments or observed procedure. A
double mass curve is a technique which is used to test the consistence of precipitation
records at a station and to adjust them if necessary. This is achieved by plotting the
accumulated precipitation at the gauge in question against the average accumulated
precipitation of a number of other nearby gauges which are influenced by the same
meteorological conditions.



A change due to meteorological causes would not cause a change in slope, as
all based stations would similarly be affected.
The obvious break in the double mass curve indicate inconsistency in the data
The double mass curve provides a correction factor to assume that the data is
reasonably homogeneous throughout its period of record.
An example of a mass curve is presented in Figure 2.7.
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Figure 2.7
Double mass curve.
The mass curve shows a change in the slope in at the indicated point. For the period after
the break the ratio of the accumulated precipitation at the test site to the accumulated
mean precipitation at the base station is 0.90. For the period before the break the ratio is
0.80. In order to correct the older records to be consistent with the more recent ones,
those from before the break are multiplied by 0.90/0.80.
2.10 Frequency analysis
Rainfall frequency analyses are used extensively for design of engineering works that
control storm runoff. These include municipal storm sewer systems, highway and railway
culverts, and agricultural drainage systems. Precipitation frequency analyses also play an
important role in a diverse range of non-structural problems involving natural hazards
associated with extreme rainfall events. The precipitation frequency analysis problem is
to compute the amount of precipitation PT in a duration D with a given probability of
occurrence p for a given year. If an event of specified duration and intensity has
probability of occurrence p for a year, the return interval T is the expected time, in years,
between events and is given by T = 1/p.
In practice, the estimation of extreme rainfall events required in the design of engineering
structures involves extraction of annual maximum rainfall values from continuos rainfall
records, for different durations for a given site. The resulting values are then fitted to a
selected statistical distribution, eg., a log-normal or Gumbel. The fitted distribution in then
used to estimate the rainfall design storms with the frequency of occurrence of say 5, 10, 25
and 50 years return period. Assuming a log-normal distribution is the one which is being
applied, the magnitude of the rainfall storm PT can be estimated from the expression
PT     .z
T
(2.6)
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Where  and  are the mean and standard deviation respectively of rainfall values
transformed in log values. zT is the frequency factor under normal distribution for return
period T. If the Gumbel distribution is applied instead, the
PT  u  . y
(2.7)
T
Where u and  are the parameters of the Gumbel distribution, and yT is the EV1 reduced
variate. The parameters of the Gumbel distribution are estimated by the method of moments
(MOM).
Mean,  = u + 0.5772
St. dev.,  = 1.28.
Details on the topic on frequency analysis are presented on chapter 9.
References
Lisley, R.K., Kohler, M.A. & Paulhus, J.L.H., 1988: hydrology for Engineers,
McGraw-Hill Book Company, London.
Myers, V., 1967: Meteorological estimation of extreme precipitation for spillway design
floods, ESSA Tech, Mem. WBTM HYDRO-5, U.S. Weather Bureau, Washington D.C.
Shaw, E.M., 1983: Hydrology in practice. Van Nostrand Reinhold, 569 p.
Wiesner, C.J., 1970: Hydrometeorology, Chapman and Hall, London.
Wisler, C.O. & Brater, E.F., 1967: Hydrology, John Wiley & Sons,London.
World Meteorological Organization, 1986: Manual for estimation of probable
maximum precipitation, Operational Hydrology Report 1, WMO No. 332, 2nd ed.,
Secretariat of the World Meteorological Organization, Geneva, Switzerland.
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