Chapter 4. Precipitation – Elementary Engineering Hydrology

4

Precipitation

Chapter Outline

4.1 DEFINITION

All water flowing or stored on the land surface or subsurface is derived directly or indirectly from precipitation, i.e. rainfall including snowfall. It is one of the important basic processes in the hydrological cycle.

Precipitation is the general term for all the moisture emanating from the clouds and falling on the ground. Precipitation data are of utmost importance to hydrologists as they form the basis of all hydrological studies. Variation of rainfall distribution over time and space creates extreme problems like droughts and floods. Study of precipitation, therefore, requires great attention.

4.2 DIFFERENT FORMS OF PRECIPITATION

The different forms of precipitation are as follows:

  • Drizzle: It consists of water drops less than 0.5 mm in diameter and intensity less than 1 mm/h.
  • Rain: It consists of water drops of 0.5 mm and above.
  • Cloudburst: It is rainfall, which is exceptionally of very high intensity.
  • Hail: It is precipitation in the form of balls or lumps of ice with diameter from 0.5 mm up to 5.0 cm.
  • Snow: It is precipitation in the form of ice crystals or thin flakes of ice resulting directly from the water vapour.
  • Sleet: It is a mixture of ice and rain.
  • Dew: It forms on the ground directly by condensation during the night when the surface has been cooled due to outgoing radiation.
  • Glaze: It is the ice coating when drizzle or rain freezes as it comes in contact with cold objects at the ground.
  • Fog: It is a low-level cloud that touches the ground.
  • Smog: It is a mixture of smoke and fog.

Precipitation of high intensity occurring over a substantial time covering a large area is normally termed as a storm.

4.2.1 Terminal Velocity of a Raindrop

As a raindrop starts falling under gravity, the velocity is low. The air resistance is a function of velocity. As the raindrop starts falling under gravity, the velocity of fall of the raindrop goes on increasing so also the air resistance. A stage is reached when the air resistance and the weight of the raindrop are equal and opposite. When this stage is reached, the raindrop starts falling with a constant velocity.

This constant velocity is called the terminal velocity of the raindrop and is a function of the diameter of the raindrop. The terminal velocity for different diameters of the raindrop is given in Table 4.1.

When the raindrop diameter is more than 5.5 mm, because of the resistance offered by air during its fall, it deforms and splits. The air resistance of a falling body depends on the area exposed to air. The volume contained by the surface area per unit weight is maximum in case of a sphere. Hence to have minimum resistance, it is nature’s tendency to have a spherical shape for a raindrop.

 

Table 4.1 The terminal velocity for different diameters of raindrops

Serial no.
Diameter of raindrop (mm)
Terminal velocity (m/s)
1
1.0
4.4
2
2.0
5.9
3
3.0
7.0
4
4.0
7.7
5
5.0
7.9
6
5.5
8.0
4.3 PROCESS OF PRECIPITATION

Four conditions are necessary for the formation of precipitation. These are:

  1. Mechanism to cool the air
  2. Mechanism to produce condensation
  3. Mechanism to produce growth of droplets
  4. Mechanism to produce accumulation of moisture of sufficient quantity

4.3.1 Mechanism to Cool the Air

Water vapour is the most essential for the formation of precipitation. Generally, it is available in the atmosphere.

Air near the ground surface and the oceans carries a lot of moisture. When this air is heated, it becomes lighter and rises up in the atmosphere along with the water vapour and, naturally, as it rises it gets cooled.

Cooling of water vapour is necessary so that the vapour gets saturated and helps in condensation.

4.3.2 Mechanism to Produce Condensation

When the air gets cooled it condenses. Condensation of the water vapour in the high atmosphere takes place on a hygroscopic nucleus.

Hygroscopic nuclei may be defined as very small particles that have an affinity for water. These are very small particles of dust of the size 10−3 to 10 micron (1 micron = 10−3 mm). Sodium chloride, sulphur trioxide and cement particles have affinity for water. These hygroscopic nuclei are available in atmosphere in abundance. The condensation may take place even before the air is saturated with vapour.

Condensation depends on the curvature of the nucleus. When, due to condensation, the raindrop size increases, the curvature is reduced and thus the affinity to attract water vapour also reduces. When the raindrop size equals to 10−3 mm, the effect of curvature and hygroscopicity becomes negligible.

4.3.3 Mechanism of Droplet Growth

Clouds can be considered as colloidal or in suspension. A tendency of the droplet thus formed to remain small and not to fall on the earth is termed as colloidal stability. On the other hand, if these droplets tend to combine to form bigger size droplets sufficient to overcome the air resistance to fall on the earth then it is termed as colloidal instability.

Therefore, for precipitation colloidal instability is necessary. The small droplets, of size less than 10−3 mm formed due to condensation coalesce (combine to form a bigger one), which is due to the following two reasons:

  1. Gravitational coalescence process The small droplets formed due to condensation are in suspension and move in a haphazard manner in any direction. The speed of movement of different particles is different and thus the particles collide with each other. During this collision, the larger particles grow at the cost of the smaller ones. When the size of the droplet is sufficient to overcome the air resistance, it falls down.

    This process is more predominant in tropical countries where the cloud temperature is well above 0 °C.

  2. Ice crystal theory In the high atmosphere where condensation takes place, the temperature is 0 °C or even lower. The droplets thus formed are in the form of ice crystals or even water droplets. There is a difference in saturation pressure over the ice crystals and the water droplets. Thus evaporation of water droplets and condensation over the ice crystals occurs.

    This process is comparatively slow and occurs in very cool (super cooled) clouds, i.e. having temperatures lower than 0 °C.

4.3.4 Mechanism to Produce Accumulation of Moisture

If a vertical column of atmosphere from land or from sea is considered, the amount of water vapour remains the same or slightly more than during and after rains. Thus to have rains there should be continuous inflow of water vapour into the vertical column from the sides. This flow is known as convergence and is observed during precipitation.

4.4 FACTORS AFFECTING PRECIPITATION

The factors affecting precipitation at a specific location are as follows:

  • Height of the station
  • Presence of mountains and their relative position
  • Nearness of large lakes or oceans
  • Forestation or urbanization
  • Prevalent wind direction
  • Sunspots

4.4.1 Height of Station

Normally temperature decreases with the altitude, and hence the moisture holding capacity of the air decreases. So also, the temperature reduces with the altitude and less moisture is available for precipitation. Thus, generally, higher the altitude lesser will be the precipitation. There are some exceptions to this tendency, but these exceptions have special conditions associated with them.

4.4.2 Presence of Mountains and their Relative Position

Mountains having their ridges across the direction of the flow of wind cause lifting of air. As the air containing moisture is lifted up, the temperature reduces and causes precipitation on the windward side. This is the case of orographic precipitation.

Of course, precipitation reduces on the leeward side of the mountains.

If the mountain range is oriented parallel to the movement of air, it does not affect the precipitation.

4.4.3 Nearness of the Oceans and Seas

A place near a large water body will have a higher relative humidity because of continuous supply of water vapour. If other favourable conditions exist, then it will ensure higher precipitation. So also, as the air moves towards land, precipitation will occur due to vertical movement of moisture and due to cooling. Normally coastal areas receive higher precipitation as compared to the interior ones.

4.4.4 Forestation and Urbanization

In the forest area, transpiration is more and the temperature is less. Thus, due to the forestation, precipitation tends to increase. Higher precipitation helps in an increase in forestation. The African and Amazon forests are good examples. The heat from the urban area is more and naturally the vapour-holding capacity of the air increases.

Precipitation due to urbanization, therefore, reduces.

4.4.5 Prevalent Wind Direction

Areas that receive winds from equatorial or warm oceans receive higher precipitation. Winds travelling from the cold areas receive little precipitation. The coasts near the equator facing east or west are rich in precipitation, whereas coasts facing north or south poles receive less precipitation.

The precipitation over India is named according to the direction from which the wind is blowing.

4.4.6 Sunspots

There are spots on the Sun and scientists have observed that these sunspots have a cycle of variation of 11 years, i.e. the nature of the sunspots are repeated after every 11 years. Some scientists believe that there is a correlation between the hydrological cycle and the sunspots cycle, but have failed to prove any exact correlation.

4.4.7 Precipitation Cycle

It was formerly assumed that the precipitation cycle in India repeats after 35 years. However, after scanning the observed data, it is now noticed that no such cycle of precipitation after 35 years is prevalent.

4.5 TYPES OF PRECIPITATION

The different types of precipitation are as follows:

  • Cyclonic precipitation
  • Convective precipitation
  • Orographic precipitation

In nature, the effect of these types is interrelated and hence precipitation of any specific type cannot be exactly identified.

4.5.1 Cyclonic Precipitation

Very often, low-pressure belts are developed as a result of thermal variations in some regions, and hence air from the surrounding area flows towards these low-pressure belts. The air rushing from the surroundings changes into a whirling mass because of the rotary motion of the earth. The movement of such whirling air results in cyclone formation. Some features of a cyclone are mentioned below:

  • A cyclone may be defined as a whirling mass of air at the centre of which the barometric pressure is low.
  • It is also known as hurricane, blizzard, typhoon and tornado according to the whirling speeds. An anticline similarly whirls round a high-pressure centre.
  • A cyclone comprises of a very large mass of air spread over an area from 10 km2 to as high as 1500 km2 moving with a velocity of 100 km/h or even more.
  • The whirling air mass carries water vapour with it. The central portion of the cyclone acts as a chimney through which the air gets lifted, expanded and cooled, and the water vapour gets condensed causing precipitation.

Thus, precipitation caused due to a cyclone is known as cyclonic precipitation and may result into a drizzle or into heavy precipitation covering a large area.

4.5.2 Convective Precipitation

On a hot day, the ground surface is heated unequally and so is the air near the ground surface. This causes air that is heated more to rise in atmosphere, to cool and then to condense resulting into precipitation. Such type of precipitation is called convective precipitation and normally covers a small area for a short duration but has a high intensity.

4.5.3 Orographic Precipitation

When the winds carrying sufficient water vapour are obstructed by a range of hills or mountains, they are mechanically lifted up. During this lifting, the air is cooled and condensation takes place. This results in heavy precipitation on the windward side and the precipitation on the leeward side reduces substantially.

The precipitation caused due to the obstruction by mountains is called orographic precipitation. In India, precipitation is mostly due to this type.

Figure 4.1 shows a specific case of orographic precipitation.

Fig. 4.1 Orographic precipitation

4.5.4 Artificial Precipitation

Precipitation can also be achieved artificially. Many times it happens that there is sufficient water vapour in the atmosphere and all other conditions are also favourable for precipitation, but there may be a deficiency of the hygroscopic nuclei, which are essential for the formation of raindrops.

A nucleus is essential for the formation of a raindrop. Artificial precipitation can be produced by providing the required hygroscopic nuclei. The hygroscopic nuclei for such artificial precipitation used so far are:

  • Dry ice (solid CO2)
  • Silver iodide
  • Sodium chloride
  • Portland cement

This process of artificial formation of clouds is also known as cloud seeding. Cloud seeding is accomplished by the following methods:

  • Emitting the hygroscopic nuclei with the help of special guns or through high-level chimneys
  • Using aeroplanes for spreading the nuclei
  • Using rockets by using suitable delivery systems (these nuclei are taken to the desired height followed by explosions)

Artificial rain-inducing system is not much prevalent because it has the following three major disadvantages.

  1. It is a very costly process.
  2. It may affect rainfall in the adjoining area.
  3. The success rate is not very high.
4.6 MEASUREMENT OF PRECIPITATION

The instrument used to measure rainfall is known as rain gauge. All forms of precipitation are measured on the basis of the vertical depth of water that would accumulate on a plain surface, if the precipitation remains where it falls. It is measured in millimetres or tenths of millimetres.

In olden days, a rain gauge was known as hyetometer, ombrometer or pluviometer.

4.6.1 History of Precipitation Measurement

The earliest systematic hydrological measurements ever made were probably those of precipitation. There is evidence that precipitation was measured as far back as 400 bc. However, precipitation measurements done by Mr Townley in 1671 are available even now.

The measurement of precipitation is never subjected to check either by repetition or by duplication and hence care should be taken during its measurement. So also, rainfall measurement forms the basic data on which all the designs are based and hence utmost accuracy has to be observed during its measurement. The precipitation per unit time is the intensity of precipitation.

It is measured as mm/h or cm/day.

4.6.2 Considerations for Selecting Site for a Rain Gauge

The following considerations should be followed while installing a rain gauge:

  • The site should be an open-level ground.
  • Clear distance between the obstruction and the rain gauge should be at least twice the height of the obstruction. In no case, it should be nearer to the rain gauge than 30 m.
  • The site should be representative of the area.
  • Roof installation and windward slopes should be avoided.
  • The serious factor that affects the rainfall measurement is wind velocity, its vertical as well as horizontal components. Obstruction to either should be avoided.
  • The rain gauge should be installed upright in a vertical mode.

A gauge inclined at 10° with vertical will catch 1.5% less rainfall as compared to that in a vertical direction. Some engineers consider that the rain gauge should be kept perpendicular to ground and the rainfall thus calculated may be multiplied by the cosine of the angle of inclination of the ground surface. However, this is not practicable and hence avoided.

The best site would be a level ground with trees and bushes all around, which serve as windbreak. However, care should be taken that these trees and bushes do not affect the catch of the rain gauge and the distance between the two is more than twice their height.

4.6.3 Hyetograph

A bar chart of time versus precipitation is known as hyetograph. The ordinate graph presents the rainfall in a year drawn to some scale at the corresponding year.

Specific and ordinate graphs are shown in Figs. 4.2 and 4.3, respectively.

Fig. 4.2 Mass curve and hyetograph of precipitation

Fig. 4.3 Ordinate graph of precipitation

4.6.4 Mass Curve of Precipitation

A mass curve of precipitation is a cumulative plot of the accumulated precipitation.

A mass curve is shown in Fig. 4.2.

The slope of the mass curve is the intensity of rainfall at that time. When there is no rainfall, the mass curve is horizontal.

Example 4.1

The hourly precipitation data during a storm are as follows:

Plot

  1. Hyetograph
  2. Mass curve

Solution:

The mass curve coordinates will be as follows:

The hyetograph and the mass curve are shown in Fig. 4.2.

4.6.5. Types of Rain Gauges

The different types of rain gauges are as follows:

  • Non-recording rain gauge
  • Recording or automatic rain gauge
  • Radar

The rainfall observed at a station by a rain gauge is known as point rainfall or station rainfall. The rainfall observed by the non-recording or recording rain gauges is point rainfall and hence these gauges are known as point precipitation gauges. The third one, i.e. by the radar, gives an instantaneous picture of the rainfall over an area and not the point precipitation.

4.6.5.1 Non-recording rain gauge

The standard Symons’s rain gauge is shown in Fig. 4.4.

The gauge consists of a funnel with sharp edges and the rainfall is collected in the cylinder, which has a narrow neck and splayed base, resting on the ground. The volume of the water collected in specific time divided by the area of the funnel, gives the depth of the rainfall during this period.

In order to avoid this division, the cylinder is calibrated and rainfall can be measured immediately. The various dimensions of the rain gauge are shown in Fig. 4.4. Normally, the observations are taken at 8:30 a.m. every day, which indicates the rainfall during the 24 h of the previous day.

Fig. 4.4 Non-recording rain gauge

Disadvantages in the non-recording rain gauge

The disadvantages in the non-recording rain gauge are as follows:

  • It records the precipitation only during the observation period and not the intensity of precipitation.
  • If the rainfall is heavy, the cylindrical collecting bottle may overflow and thus may not record the entire quantum of precipitation.

4.6.5.2 Automatic rain gauges

In this case the rainfall is recorded automatically using different mechanisms. The different types of automatic rain gauges are as follows:

  • Siphon bucket-type rain gauge
  • Tipping bucket-type rain gauge
  • Weighing bucket-type rain gauge

All these automatic rain gauges record not only the rainfall but also its intensity.

Siphon bucket-type rain gauge

The rainfall is collected in a float chamber through a funnel. The funnel has a sharp rim. The float chamber contains a light float that rises in the chamber as rainfall is collected in the chamber.

Thus, the level of the float is indirectly a measure of the rainfall.

The vertical movement of the float is recorded by a mechanism on a paper chart fixed on a drum, by a pen. This pen rests on the chart. This chart is kept rotating at a uniform speed on the drum by a spring wound mechanism. The drum makes one rotation a day.

Thus, the chart records time on the x-axis and rainfall on the y-axis.

There is a small compartment by the side of the float chamber. This is connected by a small opening at the bottom. This is known as the siphon chamber. A small vertical pipe is used that works as a siphon. This siphon is used to empty the chamber to avoid the increase in size of the float chamber. As the level of water in the float chamber reaches a specific level, the siphon starts working and water in the float chamber is drained. The float moves down to its lowest position. Along with the float, the pen moves down and draws a vertical line on the chart. As the rain water is again collected in the float chamber due to rainfall, the float moves and with it the pen too.

Normally, the paper on the drum is replaced everyday at 8:30 a.m. Figure 4.5 shows the details of a siphon bucket-type rain gauge and the rainfall chart. The chart is the mass curve of precipitation.

Fig. 4.5 Siphon bucket-type rain gauge

The vertical line indicates that the siphon has worked and a horizontal line indicates no precipitation. The slope of the chart indicates the intensity of rainfall.

The siphoning action requires 15 seconds and record of rainfall during this period is lost. So also the rainfall record may be lost during the time taken in changing the paper, if there is rainfall during that time.

Example 4.2

The chart fixed to an automatic float-type rain gauge is shown in Fig 4.5

Find

  1. Hourly precipitation
  2. Daily precipitation
  3. Time when the siphon was operated
  4. Period of no precipitation
  5. Maximum intensity of precipitation

Solution:

  1. The hourly precipitation as read from the chart will be as follows:
  2. Total daily precipitation: 10.0 + 8.0 = 18.0 mm
  3. Time when siphon operated: 20 h, i.e. 8 p.m.
  4. Time of no precipitation: 13–14

                                                  14–15

                                                  2–3

                                                    3–4

                                                    Total 4 h

  5. Maximum intensity: 1.8 mm/h from 1 to 2 h

Tipping bucket-type rain gauge

The details of a tipping bucket-type rain gauge are shown in Fig. 4.6.

In this type, the rainwater received through the funnel is collected alternately in twin buckets. When one bucket receives water and the water level reaches a specific level, it tips along a pivot and discharges into a measuring jar. As the bucket tips, the other twin bucket receives the rainwater. Both the buckets receive the rainwater alternately and discharge into the same measuring bucket.

The funnel diameter, the bucket size and shape are so designed that the bucket may tip after it has received a rainfall of 25 mm. The tipping of the bucket is recorded by an electric circuit or by some mechanism on a drum. The measuring jar is calibrated to give the depth of rainfall.

This rain gauge gives the total precipitation during the specific period. The intensity of rainfall can be worked out from the time required to tip the bucket as well as the number of tippings of each bucket. However, for low intensity of rainfall, the results may not be very accurate since no-rainfall period is not recorded in this rain gauge.

Fig. 4.6 Tipping bucket-type rain gauge

Weighing bucket-type rain gauge

The details of a weighing bucket-type rain gauge are shown in Fig. 4.7.

The rainfall is collected through a funnel into a bucket resting on a platform. The weight of water thus collected is transformed through a mechanism to a pen, which makes a trace on a paper fixed on a drum. The drum is driven mechanically by a spring clock and makes one revolution a day at a uniform speed. Thus, the trace of the pen on the paper records the weight of rainwater and indirectly the rainfall.

Fig. 4.7 Weighing bucket-type rain gauge

Fig. 4.8 Chart of weighing bucket-type rain gauge

After a certain amount of precipitation, the mechanism reverses the travel of the pen. However, the movement of the drum remains unaltered. Figure 4.8 shows a typical rainfall chart of a weighing bucket-type rain gauge.

The horizontal line indicates the no-rainfall period. Reversal of line has to be taken into account. With this, the total precipitation as well as the intensity of precipitation can be calculated accurately.

This type of rain gauge can be used for the measurement of snow, rainfall, hail, and so on.

Example 4.3

The chart fixed to an automatic weighing bucket-type rain gauge reads as in Fig. 4.8:

Find

  1. Hourly precipitation
  2. Daily precipitation
  3. Time when the pointer reverted
  4. Period of no precipitation
  5. Maximum intensity of precipitation

Solution:

  1. The hourly precipitation as read from the chart will be as follows:
  2. Total daily precipitation: 100 + (100 − 52) = 148 mm
  3. Time when the pointer reverted: 4 h
  4. Period of no precipitation: 8–9

                                                    9–10

                                                    Total 2 h

  5. Maximum intensity of precipitation: 30 mm/h from 4 to 5 h

Difference between the record graph papers

The difference between the record graph papers of siphon-type rain gauge and weighing-type rain gauge is as follows:

  1. The pen, in the case of a float-type, records the vertical movement of float and the graph paper is a squared graph paper. However, in case of weighing-type, the weight of water collected on the platform is transferred to the pen through a point and hence its movement is along the arc of a circle with pivot as the centre.
  2. In the case of float-type, when the level of water in the collection chamber reaches the specific limit, the siphon operates and the pen records a vertical line up to the x-axis. On the contrary, when the weight of water collected on a platform reaches the specific limit, the mechanism reverts and the graph records precipitation in the negative direction.

4.6.5.3 Radar measurement of rainfall

Radar is an acronym and its full form is RAdio Detection And Ranging. It was originally designed to detect the location of aircrafts flying in the air.

High frequency electromagnetic waves are radiated in the atmosphere and the reflections of these waves due to the rainfall (which is known as echo) are recorded on a radarscope.

The intensity of rainfall, its duration and also the coverage can be estimated by scanning the intensity of radiation of the electromagnetic waves, the echo due to rainfall, the time of travel, and so on. The range of a radar is about 200 km. This procedure is very costly and requires high-level instrumentation.

4.6.6 Difficulties in the Measurement of Precipitation

The difficulties experienced in the measurement of precipitation are as follows:

  • The rain gauge itself may cause eddy currents and may affect the catch of the rain gauge.
  • There may be some evaporation from the water collected in the rain gauge.
  • Some of the precipitation water may be lost in wetting the sides of the funnel or the measuring flask.
  • In some case, the splash into or out of the gauge may modify the true value of rainfall.

4.6.6.1 Rainy days

When the rainfall during a day is 2.5 mm or more the day is known as rainy day.

4.6.6.2 Classification of intensity of rainfall

The rainfall intensity is classified as follows:

  1. Up to 2.5 mm/h: Light rain
  2. 2.5–7.5 mm/h: Medium rain
  3. 7.5 mm/h and above: Heavy rain

4.6.6.3 Average precipitation

The average precipitation, whether it is annual, seasonal or even daily, is taken as the average of the last 30 years. It is revised after every 10 years by deleting the previous 10-year data and adding the recent 10-year data.

4.6.6.4 Index of wetness

Index of wetness is the ratio of rainfall in a given year and annual average precipitation. When this index is less than one, it is called a bad year or a deficient year or a dry year. When it is more than one, it is called a good year or a surplus year or a wet year. When it is one, it is a normal year.

4.7 SUPPLEMENTING RAINFALL DATA

Sometimes there might be breaks or gaps in the rainfall data of some stations. These gaps may be due to the following reasons:

  • Absence of an observer
  • Instruments failure
  • Unapproachable circumstances such as flooding or washing out of the approach road, etc., resulting in non-recording of the rainfall

The missing rainfall data may be supplemented by the following methods:

  • Arithmetic average method
  • Normal ratio method
  • Weighted average method

4.7.1 Arithmetic Average Method

When the data of a rain gauge station, e.g. ‘A’, is missing for a year, consider the adjacent rain gauge stations—B, C and D. If the rainfall at these adjacent stations B, C and D is within 10% of the average rainfall of A (less or more), then the simple arithmetic average of these adjacent stations of the year may be considered as the missing rainfall of A for that year.

where, n = Number of adjacent rain gauge stations

PB, PC, PD = Precipitation at B, C and D for the period for which the data is missing at A

Example 4.4

In a catchment area, daily precipitation was observed by 11 rain gauge stations. On 2 August 2005, the observations indicated that one rain gauge was out of order. The observations taken by the 10 rain gauge stations are as follows:

Estimate the missing data at H.

Solution:

Since there is not much variation in the precipitation data, a simple arithmetic average of the precipitation observed at the 10 remaining stations was taken as under.

4.7.2 Normal Ratio Method

If the rainfall of station A is missing for a year and the variation of the adjacent rain gauge stations B, C and D is more than 10%, then simple principle of linearity is used to evaluate the missing rainfall of A as follows:

where, NA = Average of A excluding the missing period

   NB NC = Average of B and C excluding the missing period

    PB PC = Precipitation at B and C during the missing period

           n = number of adjacent rain gauge stations considered

For this method, a minimum of three adjacent rain gauge stations are considered.

Example 4.5

The average annual precipitation at five rain gauge stations in a catchment is as follows:

However, the precipitation at station P was not available for the year 1996 because the rain gauge was out of order. The precipitation observed at the other stations for 1996 was as follows:

Evaluate the precipitation at P during 1996.

Solution:

4.7.3 Weighted Average Method

The station of which the data is missing, e.g. A, is considered as the origin and the adjacent rain gauge stations are considered and their distances from A are calculated or measured on a map.

It is assumed that the rainfall variation between these two stations A and B is inversely proportional to the square of the distance between them.

Thus,

where, r1, r2 and r3 = the distances from A of the adjacent stations B, C and D

   PB, PC and PD = the rainfall at the adjacent stations B, C and D for the missing period.

This method is also known as United States National Weather Service (USNWS) method.

Example 4.6

The location coordinates in km of the five rain gauge stations w.r.t. × are as follows:

The annual precipitation at X for the year 2005 is missing. The annual precipitation at the remaining four stations for 2005 is as follows:

Evaluate the missing precipitation at X for the year 2005.

Solution:

The relative positions of the stations A, B, C and D w.r.t. X are shown in Fig. 4.9.

AX = √(202 + 252) = 32.01 km

BX = √(402 + 152) = 42.72 km

CX = √(302 + 202) = 36.05 km

DX = √(252 + 152) = 29.15 km

Fig. 4.9 Estimation of missing precipitation data

4.8 CONSISTENCY VERIFICATION OF RAIN GAUGE

It may happen that the rainfall recorded by a rain gauge station is doubtful. It then becomes necessary to verify the rainfall record of this station. This is known as verification of consistency of a rain gauge. This may by due to the following reasons:

  • Change in the location of the rain gauge
  • Change in the surroundings, namely, growth of trees, buildings, and so on.
  • Change in the instrument
  • Fault developed in the rain gauge

The verification can be done by the double mass curve method.

4.8.1 Double Mass Curve Method

On a simple graph paper, the mass curve of the precipitation of the doubtful station, e.g. ‘A’ versus the mass curve of the average precipitation for the remaining rain gauge stations whose data are available for the corresponding period is plotted.

Fig. 4.10 A double mass curve plotted for a specific study

Normally, one should get a straight line through origin if the record at A is correct. If there is inconsistency at A from a particular year, the slope of the straight line may change from that year. It may, therefore, be concluded that the records of A are incorrect from that year and need modification.

The slope of the straight line is maintained and extended and the record of A is corrected accordingly. This procedure cannot be applied for studies for storm rainfall or daily rainfall.

A double mass curve plotted for a specific study is shown in Fig. 4.10.

Example 4.7

The average annual precipitation data of six rain gauge stations in a catchment area during 1991–2000 are as follows:

The data observed at station C were doubtful because of some topographical changes there. Verify whether the data observed at C is consistent and correct it, if necessary.

Solution:

The mass curve coordinates of precipitation at C and also the combined mass curve coordinates of precipitation at A, B, D, E and F will be as follows:

Fig. 4.11 Double mass curve of precipitation

A graph of mass curve of precipitation at A, B, D, E and F versus mass curve of precipitation at C was plotted on a simple graph paper. It was noticed that the curve follows a straight line up to 1997. It changes its slope from 1997.

This means that due to the change in topography at C, the observations from 1997 were incorrect. The straight line graph up to 1997 was extended further and the precipitation at C was corrected (as shown in Fig. 4.11) from this extended graph for the respective years and entered in the table.

4.9 AVERAGE DEPTH OF PRECIPITATION

The precipitation over a catchment area is never uniform. This becomes quite clear from the figures of the average depth of precipitation of the various rain gauge stations in the catchment area. One of the basic requirements in the study of a catchment area is the average depth of precipitation over the entire catchment.

This is also known as equivalent uniform depth of rainfall. The average depth of precipitation can be calculated by the following methods:

  • Arithmetic mean method
  • Thiessen polygon method
  • Isohyetal method

4.9.1 Arithmetic Mean Method

This method is very simple. The arithmetic mean of average precipitation values of all the rain gauges within the catchment area is determined, namely,

where, Pav = Average precipitation over the catchment area

PA, PB, PC = Average precipitation at various rain gauge stations A,B,C, …

This method may be adopted when the catchment area is flat and there is not much variation in the average values of the precipitation of all the rain gauge stations. This method is very simple for calculations. However, no weightage is given neither to the influence area of the individual rain gauge nor the topography. This method is also known as unweighted mean method.

4.9.2 Thiessen Polygon Method

A. M. Thiessen suggested this method in 1911 and hence this method takes this name after him. A regular step-by-step procedure is as follows:

  1. Mark the catchment area correctly on a sheet of paper.
  2. Mark correctly the locations of all the rain gauge stations within the catchment area. Other rain gauge stations outside the area but nearby, if any, having hydrological homogeneity may also be considered. Join the adjacent rain gauge stations by straight lines so as to divide the catchment area into triangles. (Whenever a quadrilateral is to be divided, the shorter diagonal is preferred.)
  3. Draw perpendicular bisectors of all the sides of the triangles. The three perpendicular bisectors of a triangle will meet at a point inside the triangle. Near the ridge line of the catchment, the perpendicular bisector lines may be extended beyond the ridge line.

Thus, every rain gauge station will be surrounded by a polygon and it is presumed that the rain gauge station has got an influence on the area of the polygon surrounded by it.

The area of each polygon is measured. The area of influence lying inside the catchment area of the rain gauge, located outside the catchment, should also be considered. The average precipitation over the catchment area is worked out as follows:

where, Pav = Average precipitation over the catchment area

PA, PB, PC = Average precipitation at various rain gauge stations

AA AB AC = Area of the polygon surrounding the rain gauge stations A, B and C

A = Catchment area = AA. + AB + AC + …

Pav can also be mentioned as follows:

and the factors called Thiessen’s weights.

In this method, weightage to each rain gauge is given depending upon its influence area. Rain gauges having hydrologic homogeneity outside the area, if any, are also considered for more accuracy. However, no consideration is given to the topography.

Example 4.8

Figure 4.12 shows a typical layout of a catchment area ABCDF. Six rain gauge stations are established at A, B, C, D, E and F, as shown in the figure. The precipitation observed at these six stations in July 2004 is as follows:

Find the average precipitation over the catchment during July 2004 by Thiessen’s polygon method.

Fig. 4.12 Rain gauge stations surrounded by a polygon

Solution:

Join the locations of the adjacent rain gauge stations, AB, BC, CD, DA, AE, BE, CE, DE, DF and FA, and draw their perpendicular bisectors. The perpendicular bisectors will meet at P, Q, R, S, T, V and W.

Thus, each rain gauge station will be surrounded by a polygon and its area will be as follows:

Therefore, average precipitation over catchment in July 2004 is as follows:

4.9.3 Isohyetal Method

An isohyet may be defined as a line joining locations having equal rainfall. Isohyets are drawn by the method of simple interpolation of average value of precipitation similar to the level contours.

The step-by-step procedure to calculate average depth of precipitation by isohyetal method is as follows:

  1. On a sheet of paper, mark correctly the catchment area.
  2. Show the locations of the rain gauge stations on the map and mention their average precipitation. Rain gauge stations outside the catchment area if any, but nearby, having hydrologic homogeneity may also be marked. Join these rain gauge stations to divide the catchment area into triangles.
  3. Isohyets may be drawn at suitable equal intervals by assuming a straight line variation between the two adjacent rain gauge stations.
  4. The area between two isohyets inside the catchment area should be measured accurately.
  5. The average precipitation of the area between two isohyets may be calculated as follows:

where, P1 = Average precipitation between two isohyets

          A = Higher value between the two consecutive isohyets

          B = Lower value between the two consecutive isohyets

         i = Isohyetal interval (A–B)

         a = Length of higher value of isohyet A within the catchment’s area

         b = Length of lower value of isohyet B within the catchment’s area

However, this procedure is complicated.

Alternately, the average precipitation of the area between the two isohyets is calculated by taking a simple mean of the two isohyets, i.e..

For the area between the higher value isohyet (A) and the ridge line, it is not possible to calculate the average precipitation. In such case, the average is considered as A only. Similarly the average precipitation for the area between the lower value isohyet and the ridge line is considered as only B.

Thus, the average of the catchment area may be calculated as follows:

where, Pav = Average precipitation over a catchment

         P1 = Average precipitation between two consecutive isohyets

           A1 = Area between two consecutive isohyets within the catchment area

         A = Catchment area = A1 + A2 + A3 + …

Drawing isohyets is to some extent a skilled job. While drawing isohyets, one may consider the topographical efect, and such other things. Since rain gauges outside the area, but nearby, having hydrologic homogeneity are considered, this isohyetal method is more accurate.

Use of the three methods followed for a specific study is indicated in Fig. 4.13.

Fig. 4.13a Arithmetic mean method

Fig. 4.13b Thiessen polygon method

Fig. 4.13c Isohyetal method

Example 4.9

The daily precipitation data observed at four rain gauge stations located inside a catchment area on 2 August 2005 are as follows:

So also the daily precipitation data observed at four other rain gauge stations that are meteorologically similar but outside the catchment area on the same day are as follows:

Fig. 4.14 Rain gauge surrounded by a polygon inside the catchment area

Figure 4.14 shows the catchment area and the locations of the rain gauge stations. If the catchment area is 54 km2, find the daily average precipitation over the catchment.

Solution:

The average daily precipitation over the catchment will be calculated by three different methods as stated below.

  1. Arithmetical mean method
  2. Thiessen’s polygon method
  3. Isohyetal method
  1. Arithmetical mean method The average daily precipitation of the catchment area will be the average of the four rain gauge stations located inside the catchment area.

  2. Thiessen’s polygon method Join the locations of the adjacent rain gauge stations by straight lines as, AB, AH, BH, BC, BD, CD, DE, DF, EF, FG, GH and HF.

    Draw perpendicular bisectors of these lines to meet

    • Inside the catchment area at M, N, P, Q, R, S
    • The catchment area boundary at a, b, c, d, e, f, g, h, i, j, k, l, m, n, y

    Each rain gauge will be surrounded by a polygon inside the catchment area and its area will be as follows:

    Therefore, the average daily precipitation over the catchment area on 2 August 2005 will be

  3. Isohyetal method Taking into consideration the location of the rain gauge stations inside (B, D, F, H) as well as outside the catchment area (A, C, E, G) and the precipitation recorded by them, isohyets of 30, 35, 40, 45, 50 mm are drawn and area between them was measured accurately (Fig. 4.15).

    Fig. 4.15 Isohyetal method

    Therefore, the average daily precipitation over the catchment area on 2 August 2005

4.10 RAIN GAUGE DENSITY

Rainfall is the most fundamental data used in the hydrological studies and hence a well distributed network of rain gauge stations is essential. The average area of influence of the rain gauge stations is indicated as rain gauge density or network density. The density of rain gauge stations in an area may be decided taking into consideration the following points:

  • Variation in the rainfall in the area. If the area is plain and if there is not much variation in rainfall, the number of rain gauge stations may be small.
  • The nature of study for which rainfall data is required
  • Cost involved in establishing and maintaining the rain gauge stations

4.10.1 Minimum Density of Rain Gauge Stations

The BIS has recommended the following criteria:

  • One rain gauge per 520 km2 in plain areas. (For area in the path of low pressure systems, denser network is necessary.)
  • One rain gauge per 260–390 km2 for area where average elevation of the area above mean sea level is 1000 m and above.
  • One rain gauge per 130 km2 in hilly areas with heavy rainfall. (Higher density recommended wherever necessary.)

The BIS has recommended the following procedure to calculate the optimum number of rain gauges in a catchment area.

n = Number of rain gauge stations existing in an area

P1, P2, P3, …, Pn = Average rainfall of the ‘n’ rain gauge stations

Now,

N = Number of optimum rain gauge stations

x = Percentage permissible error in the estimation of average rainfall.

Additional rain gauge stations = Nn

It may be noted that both Cv and x be mentioned as percentages.

The additional rain gauge stations may be located in addition to the existing rain gauge stations, so that they all are evenly distributed over the entire catchment area.

Example 4.10

In a catchment area covering 100 km2, the average annual precipitation observed at five rain gauge stations is as under.

Find the number of additional rain gauge stations and also the rain gauge density if the permissible error is 10%.

Solution:

Since permissible error is 10%,

Number of rain gauge stations required = (Cv/10)2 = (26.06/10)2

                                                                           = 6.79

Additional rain gauge stations required = 6.79 − 5 = 1.79 ≈ 2

Rain gauge density = 100/7 = 14.30 km2/rain gauge.

Example 4.11

In a catchment area covering 5600 km2, the zone-wise existing rain gauge stations were as follows:

Additional nine rain gauge stations are to be installed. Indicate the zone-wise distribution of these nine additional rain gauge stations.

Solution:

The total number rain gauge stations in the catchment N will be 7 + 9 = 16.

The additional nine rain gauge stations will be distributed proportional to the area of the zones and also taking into consideration the number of existing rain gauge stations, as follows.

4.10.2 Moving Average Curve

The hyetograph plotted in a usual way will not indicate any trend or cyclic pattern. A moving average curve proposed will smoothen the variables and indicate the trend or the cyclic pattern, if any.

It is also known as moving mean curve.

The moving average period ‘m’ is generally odd, for example 3 or 5, depending upon n where n is the number of observations.

If X1, X2, X3, …, Xn is the sequence of rainfall of n values, then the moving average curve coordinates are as follows (m = 3).

when X = n, number of Y terms = n + 1 − m,

when m = n, it will be a simple arithmetic average

and when m = 1, it will be a normal hyetograph.

The 3-year moving average for a specific study is shown in Fig. 4.16.

Example 4.12

The average annual precipitation in millimetres observed over a catchment area from 1980 to 1995 is as follows:

 

1149, 1260, 1425, 1680, 1200, 1400, 1645, 1500,
1155, 945, 875, 1080, 1480, 1625, 1500, 1470

 

Construct a 3-year moving average curve and plot it along with the original data.

Fig. 4.16 Three-year moving average

Solution:

The first, 3-year moving average curve coordinate

The second, 3-year moving average curve coordinate

Thus, the 3-year moving average curve coordinates will be as under.

1278, 1455, 1435, 1426, 1415, 1515, 1433,

1200, 991, 966, 1145, 1395, 1535, 1531

The number of coordinates in the 3-year moving average curve = 16 − 3 + 1 = 14. The 3-year moving curve and the original curve will be as shown in Fig. 4.17.

Fig. 4.17 Three-year moving curve and the original curve

4.11 PROBABLE MAXIMUM PRECIPITATION

For an area, the maximum depth of precipitation that may occur for a specific duration is known as possible maximum precipitation or probable maximum precipitation. The usual short form used is PMP. This data is required for estimating maximum possible flood from a catchment area. The PMP for a known duration can be correlated as follows:

 

PMP = Pa + K × sx

 

where, Pa = Average precipitation over the area

        sx = Standard deviation of rainfall series

        K = A constant for the area and is in the neighbourhood of 15.

The data of world’s greatest rainfall was analysed and it was observed that it follows a curve PMP = 42.16 × D0.475

where, PMP = Precipitation in centimetres

             D = Duration in hours

4.11.1 Relation Between the Extremes and the Average Precipitation

It is observed that normally over a period

The maximum annual rainfall = 1.51 × average annual rainfall

The minimum annual rainfall = 0.60 × average annual rainfall.

4.11.2 Station Year Method

In case of a specific study, the data of rainfall may be required for a long period. This data may not be available in some cases. It is then assumed that the rainfall data of n rain gauge stations for 1 year is equivalent to the data of one rain gauge station for n years and the study is continued. This approach is known as station year method.

4.11.3 Recurrence Interval of a Storm

The number of years within which a given storm may equal or even exceed is known as recurrence interval or return period and normally is denoted by Tr.

Suppose the record at a station or over an area is available for n years, then the precipitation data may be arranged in the descending order.

The serial number of a specific value of precipitation in the descending order is known as ranking of the storm, e.g. m. Then the return period of that specific value of precipitation, Tr = n/m. This means that this precipitation value or more than this occurs m times in n years.

Probability

Probability generally denoted by p is reciprocal of the return period, i.e. p = m/n = 1/Tr.

Frequency

Probability expressed in terms of percentage is frequency, i.e. frequency = p × 100 = m/n × 100

Example 4.13

The precipitation in millimetres observed at a rain gauge station for the last 32 years is as follows: 988, 966, 935, 1007, 992, 1050, 975, 920, 1035, 990, 1095, 1015, 986, 927, 1003, 1055, 1135, 955, 1001, 1045, 1090, 997, 1040, 1100, 948, 972, 1012, 950, 1070, 982, 929, 960

Find

  1. The return period and frequency of the precipitation of 997 mm
  2. The precipitation of return period of 1.33 and its frequency

Solution:

The precipitation figures in millimetre were arranged in a descending order as follows:

  1. The serial order of 997 mm is 16

    Therefore, its return period = 32/16 = 2 and its frequency = 1/2 × 100 = 50%.

  2. Return period = 1.33 = n/m = 32/m

    Therefore, m = 24. The precipitation figure at serial no. 24 is 966 mm and its frequency will be = 24/32 × 100 = 75%.

4.12 INTENSITY DURATION ANALYSIS

It is observed that most intense storms last for a short time. As the intensity reduces, the duration of the storm increases and vice versa. The study of intensity and its duration is known as intensity duration analysis.

4.12.1 Intensity-Duration Curve

For an area, the available data of the duration and its intensity is analysed and a graph of duration versus intensity is plotted. This graph is known as intensity-duration curve or intensity-duration graph.

It is observed that this graph normally follows the following equation:

where, I = Intensity in mm/h

        t = duration in minutes

C,a,b = constants for the specific area.

The intensity duration graph prepared for a specific study is shown in Fig. 4.18.

Fig. 4.18 Intensity-duration curve for a specific study

Example 4.14

A storm occurred over a catchment area as under:

Plot the maximum intensity-duration curve.

Solution:

The maximum intensity-duration curve will be as shown in Fig. 4.19.

Fig. 4.19 Maximum intensity-duration curve

4.12.2 Intensity-Frequency-Duration Analysis

If for a catchment area sufficient data, for example for more than 50 years, is available, this data is analysed for each storm, for its intensity, frequency as well as its duration. This analysis may be presented as shown in Fig. 4.20.

These graphs are for a specific catchment area and may change for different catchments depending upon their hydrologic character.

Fig. 4.20 Intensity-frequency-duration curve

4.12.3 Isopluvial Map

The intensity-frequency-duration, curves are prepared for various adjoining areas. A combined map for the large area can be prepared for a maximum rainfall depth for various combinations of a return period and duration.

Such maps for a region for various rainfall depths, return periods and duration are called isopluvial maps. An isopluvial map is shown in Fig. 4.21.

Fig. 4.21 Isopluvial map of South India

Fig. 4.22 Depth-area-duration curve

4.12.4 Depth-Area-Duration Analysis

In some cases, the average depth of storm and its duration is required for a specific area. Such study is called depth-area-duration analysis. The normal short form is DAD study. Every storm has a centre having maximum precipitation, e.g. Po, and the average precipitation over a specific area, e. g. Pa. Naturally (PoPa) is always positive, and its value increases with bigger catchments and decreases with smaller catchments.

For a catchment, this value may differ for cyclonic, convective, as well as orographic precipitation. A specific study done for an area is shown in Fig. 4.22.

Normally, for each duration, the equation suggested by Horton is

          Pa = Po−(KA)n

where, Po = Maximum precipitation

        Pa = Average precipitation

         A = Area in sq. km

       K,n = Constants

4.12.5 Transposition of a Storm

Sometimes, data about storms are not available for a catchment under study, e.g. catchment A. However, sufficient data about the storms are available for another catchment B, which are meteorologically homogeneous.

A storm occurring over B is considered to be applicable and occurring over A and further studies are continued for A. This procedure is called transposition of storm. However, this may not be applicable for hilly catchments.

4.13 PRECIPITATION OVER INDIA*

Rainfall over India is very erratic in terms of both time and space. The coefficient of variation of the annual rainfall varies between 15 and 36, and hence it is said that India’s prosperity is a gamble in the monsoon’s rains.

The average annual precipitation over India is 1140 mm. Both the maximum and the minimum precipitations in the world are observed in India. The important features affecting precipitation over India are the following:

  1. The orographic features
  2. The wind currents

The seasons in the Indian subcontinent can be divided into four major seasons.

  1. South-west monsoon (June to September)
  2. Post-monsoon (October to December)
  3. Winter season (January to February)
  4. Pre-Monsoon (March to May)

The chief characteristics of these seasons are as follows.

4.13.1 South-West Monsoon

The south-west monsoon is the principal rainy season of India. Over 70% of the annual precipitation occurs over the Indian subcontinent during this season.

Except for the south-eastern part of the peninsula and Jammu and Kashmir, the rest of the country experiences heavy rains during this season. The monsoon enters into the Indian subcontinent through the southern part of Kerala towards the end of May or beginning of June with a very good degree of regularity in the statistical sense.

Under normal monsoon conditions, the distribution clearly shows the marked influence of the effect of orography of the Western Ghats, Khasi-Jantia hills, the Vindhyas, and the Himalayas. These are the regions with heavy precipitation. There is an increase in precipitation from the west coast up to the Western Ghats and then it decreases rapidly. For example, Goa gets over 2000 mm of precipitation, while Pune gets less than 600 mm. Immediately, south of Vindhyas again is the region of heavy precipitation decreasing southwards. There is a constant decrease of precipitation over the Gangetic plane from east to west decreasing from over 1000 mm over West Bengal to less than 100 mm over west Rajasthan. There is another region of heavy precipitation over the foothills of Himalayas reducing sharply towards the west of north-west, with almost negligible in the Ladakh valley that is on the leeward side.

4.13.2 Post-Monsoon

As the southwest monsoon retreats, low-pressure areas develop in the Bay of Bengal and a northeasterly flow of air that picks up moisture in the Bay of Bengal is formed. This air mass strikes the east coast of the southern peninsula, particularly Tamil Nadu, and causes precipitation in those areas. In addition, during this period several tropical cyclones form in the Bay of Bengal and to a lesser extent in the Arabian Sea. These strike the coastal areas and cause intense precipitation.

 

Fig. 4.23 Isohyetal map of India

Courtesy: India Meteorological Department

 

4.13.3 Winter Rains

Near about the end of December, disturbances originating in the mid-east travel eastwards across Afghanistan and Pakistan, known as western disturbances. They cause moderate to heavy precipitation and snowfall in the Himalayas and Jammu and Kashmir. Some light precipitation occurs in the northern planes. Some precipitation is also experienced in the Tamil Nadu region due to low- pressure areas formed in the Bay of Bengal.

4.13.4 Pre-Monsoon

There is hardly any precipitation during this season. Convective cells cause some thunderstorms, mainly in Kerala, West Bengal and Assam. Some cyclone activity, primarily in the eastern coast, also occurs. Figure 4.23 shows the average annual precipitation over India.

REVIEW QUESTIONS
  1. Define precipitation. Explain its importance in the study of hydrology.
  2. What are the different forms of precipitation?
  3. Discuss the factors affecting precipitation.
  4. Explain the different types of precipitation.
  5. Explain artificial precipitation. Why is it not followed on a large scale in India?
  6. Discuss the considerations for selecting the site for a rain gauge.
  7. Explain the different types of rain gauges. Discuss their merits and demerits.
  8. Explain with the help of a neat sketch, the working of a non-recording rain gauge. Discuss its merits and demerits.
  9. Explain with the help of a neat sketch, the working of a siphon bucket-type rain gauge.
  10. Explain with the help of a neat sketch, the working of a tipping bucket-type rain gauge.
  11. Explain with a neat sketch, the working of a weighing bucket-type rain gauge.
  12. Discuss the difficulties experienced during the measurement of precipitation.
  13. Why supplementing of rainfall data is required? State the different methods in use.
  14. Explain verification of consistency of a rain gauge.
  15. Explain the double mass curve method.
  16. How the average precipitation over a catchment is calculated? Discuss the different methods with their merits and demerits.
  17. Explain the ISI standards for rain gauge density in a catchment. Also, discuss the procedure to calculate the optimum number of rain gauge stations in a catchment.
  18. What is a moving average curve? What are its advantages? Explain the procedure to draw it.
  19. Explain the depth-area-duration analysis.
  20. What is an intensity-duration curve?
  21. Write a detailed note on precipitation over India.
  22. Write a note on frequency of a storm.
  23. Write short notes on the following:
    1. Terminal velocity
    2. Orographic precipitation
    3. Cloud seeding
    4. History of measurement of precipitation
    5. Use of radar for measurement of precipitation
    6. Index of wetness
    7. Classification of the intensity of rainfall
    8. Rain gauge density
    9. Probable maximum precipitation
    10. Station year method
    11. Recurrence interval of a storm
    12. Isopluvial map
    13. Transposition of a storm
  24. Differentiate between
    1. Record graph sheets of siphon bucket-type rain gauge and a weighing bucket-type rain gauge.
    2. Forms of precipitation and types of precipitation.
    3. Cyclonic precipitation and orographic precipitation.
    4. Non-recording-type rain gauge and recording-type rain gauge.
    5. Siphon-type rain gauge and weighing-type rain gauge.
NUMERICAL QUESTIONS
  1. During a storm, the hourly precipitation data observed was as follows:

    Plot the following:

    1. Hyetograph
    2. Ordinate graph
    3. Mass curve

    Ans: The hourly mass curve coordinates are as follows:

  2. The precipitation coordinates in mm observed on an automatic float-type rain gauge are as follows:

    Find:

    1. Daily precipitation
    2. Time when siphon operated
    3. Time of no precipitation
    4. Maximum intensity of precipitation

    Ans:

    1. Daily precipitation 5 142 mm
    2. Time when siphon operated 5 At 21 h
    3. Time of no precipitation 5 between 13 and 14 h and 2, 3 and 4 h
    4. Maximum intensity of precipitation = 15 mm/h between 15 and 16 h
  3. The precipitation coordinates observed on a weighing-type automatic rain gauge were as follows:

    Find:

    1. Daily precipitation
    2. Time when siphon operated
    3. Time of no precipitation
    4. Maximum intensity of precipitation

    Ans:

    1. Daily precipitation = 138 mm
    2. Time when siphon operated = At 21 h
    3. Time of no precipitation = Between 14 and 15 h and 1, 2 and 3 h
    4. Maximum intensity of precipitation = 18 mm/h between 11 and 12 h
  4. Five rain gauge stations located in a catchment indicate the average annual precipitation as follows:

    The precipitation at B was missing for the year 1998 since the rain gauge was out of order. The precipitation observed at other stations for 1998 are as follows:

    Calculate the missing data for B for the year 1998.

    Ans: 2348 mm

  5. The location coordinates in km of five rain gauges w.r.t. P are as follows:

    The annual average precipitation at the Station P was missing for the year 2004.

    The average annual precipitation at other stations for the year 2004 is as follows:

    Evaluate the missing precipitation at P for the year 2004.

    Ans: 2750 mm

  6. The annual precipitation of the rain gauge Station A for the year 1990–1999 was as given below. Similarly, the average annual precipitation of the remaining five rain gauge stations for the same period was as given below. The precipitation recorded at A was doubtful because there were changes at the location. Verify the precipitation at A is consistent and correct it if necessary.

    Ans: The precipitation data at Station A is wrong from the year 1996 and the corrected precipitation figures from 1990 in mm are 1388, 1412, 1398, 1443, 1384, 1456, 1412, 1489, 1464, 1427, respectively.

  7. A catchment area is in the form of an equilateral triangle ABC of side 10 km. Four rain gauge stations are located at A, B, C and D. Station D is the centroid of the triangle. The average annual precipitation observed at these stations in mm are 1145, 1252, 1184 and 1056, respectively. Find the average annual precipitation of the catchment area by all the three methods.

    Ans: 1101 mm

  8. The average annual precipitations of the five rain gauge stations in a catchment are as follows:

    If the catchment covers an area of 110 km2 , find the number of additional rain gauge stations required. Acceptable permissible error is 10%.

    Ans: 4

  9. The average annual precipitation in mm observed over a catchment area for the last 16 years is as follows:

    1154, 1265, 1430, 1683, 1205, 1390, 1650, 1497, 1160, 940, 870, 1080, 1490, 1630, 1505, 1475

    Construct a 3-year moving average curve and compare with the original data.

  10. The average annual precipitation in mm observed at a rain gauge station for the last 32 years is as follows:

    966, 992, 920, 1045, 1012, 1070, 960, 935, 1050, 1035, 1015, 948, 972, 950, 929, 1007, 975, 990, 1095, 986, 988, 927, 1003, 1055, 982, 1135, 955, 1001, 1040, 1090, 997, 1100

    Find:

    1. The return period and the frequency of the precipitation of 1045 mm
    2. The precipitation of the return period of 2 and its frequency

    Ans: (i) 4, 25%
    (ii) 997, 50%

  11. The storm occurred over a catchment area is a under:

    Plot the Maximum intensity duration curve

MULTIPLE CHOICE QUESTIONS
  1. The terminal velocity of a raindrop depends upon
    1. Diameter of the raindrop
    2. Velocity of air
    3. Temperature of the air
    4. Specific gravity of water
  2. Cyclone is also known as
    1. Hurricane
    2. Tornado
    3. Typhoon
    4. All the above
  3. Raindrop is always
    1. Spherical
    2. Conical
    3. Elliptical
    4. Cubical
  4. Hygroscopic nuclei used for artificial rain are of
    1. Dry ice
    2. Silver iodide
    3. Sodium chloride
    4. Portland cement
    5. Any of the above
  5. Artificial rain method is normally not followed because
    1. It is a costly process.
    2. It may affect the rainfall in the adjoining area.
    3. The success rate is not very high.
    4. All the above.
  6. In case of a siphon bucket-type rain gauge, the siphon acts when
    1. The rain stops
    2. The rain starts
    3. Water in the float chamber reaches a specific level
    4. After a specific time.
  7. In case of a mass curve of rainfall, when there is no rainfall, the graph is a
    1. Vertical line
    2. Blank
    3. Horizontal line
    4. Downward line
  8. In case of a tipping bucket-type rain gauge, the bucket tips when
    1. The rain starts
    2. The bucket receives a rainfall of 25 mm
    3. The rain stops
    4. After a specific time
  9. In case of a weighing-type rain gauge, when the water level reaches a specific level in the chamber
    1. The pointer moves down
    2. The pointer reverses its movement
    3. The pointer stops
    4. The drum stops its rotational movement
  10. Cloud seeding is accomplished by the following methods
    1. Emitting the hygroscopic nuclei
    2. Using the aeroplanes for spreading with the help of a special gun the nuclei
    3. Using rockets by suitable delivery systems
    4. Any of the above
  11. In India, the precipitation received is mostly
    1. Cyclonic precipitation
    2. Convective precipitation
    3. Orographic precipitation
    4. None of the above
  12. Clear distance between the rain gauge and the obstruction should be equivalent to at least
    1. Height of the obstruction
    2. Twice the height of the obstruction
    3. Three times the height of the obstruction
    4. Four times the height of the obstruction
  13. A plot of time versus rainfall is called a
    1. Hydrograph
    2. Hyetograph
    3. Isohyet
    4. None of the above
  14. An isohyet is a line joining
    1. Equal precipitation intensity
    2. Equal precipitation depth
    3. Equal storm duration
    4. Equal height of stations
  15. The characteristics of convective precipitation are
    1. High intensity and long duration
    2. High intensity and low duration
    3. Low intensity and low duration
    4. Low intensity and long duration
  16. The chart fixed to an automatic rain gauge gives
    1. A rainfall hyetograph
    2. An intensity-duration curve
    3. An isohyetal map
    4. A precipitation mass curve
  17. The average annual precipitation over India is
    1. 1000 mm
    2. 1500 mm
    3. 1140 mm
    4. 1350 mm
  18. Orographic precipitation occurs due to lifting of air mass because of
    1. Presence of mountain barriers
    2. Extratropical cyclones
    3. Density difference of air mass
    4. Difference of air temperature
  19. The double mass curve technique is followed to
    1. Check the consistency of rainfall at a station
    2. Find average rainfall of a station
    3. Find number of rain gauge stations required in a catchment
    4. Estimate the missing data of rainfall of a station
  20. The probable maximum precipitation is given by the relation
    1. PMP = Pa + Kσ
    2. PMP = Pa
    3. PMP = Pa e
    4. PMP = Pa e−Kσ
  21. A rain gauge inclined at 10° will catch
    1. 0.5% less as compared to vertical
    2. 1.0% less as compared to vertical
    3. 1.5% less as compared to vertical
    4. 2.0% less as compared to vertical
  22. In olden days, a rain gauge was also known as
    1. Hyetometer
    2. Ombrometer
    3. Pluviometer
    4. All of the above
  23. Radar means
    1. Radio Detection and Recording
    2. Radio Detection and Ranging
    3. Radiation Detection and Recording
    4. Radiation Detection and Ranging
  24. A day is known as rainy day when the rainfall during the day is
    1. 2.5 mm or more
    2. 5.0 mm or more
    3. 7.5 mm or more
    4. 10.0 mm or more
  25. Average precipitation over a catchment can be calculated by
    1. Arithmetic mean method
    2. Thiessen’s polygon method
    3. Isohyetal method
    4. Any of the above methods
  26. The density of rain gauge stations in a catchment is decided considering
    1. Variation of rainfall in that area
    2. The nature of study for which rainfall data are required
    3. Cost involved in establishing and maintaining the rain gauge stations
    4. All the above considerations
  27. Over a period, the maximum annual rainfall is equal to
    1. 1.26 times the average annual rainfall
    2. 1.51 times the average annual rainfall
    3. 1.75 times the average annual rainfall
    4. 1.95 times the average annual rainfall
  28. A raindrop deforms and splits because of the resistance of air when it is more than
    1. 4.0 mm
    2. 5.5 mm
    3. 7.5 mm
    4. 10.0 mm
  29. Over a period the minimum annual rainfall is equal to
    1. 0.50 times the average annual rainfall
    2. 0.60 times the average annual rainfall
    3. 0.70 times the average annual rainfall
    4. 0.80 times the average annual rainfall
  30. Sunspots have a cycle of variation of
    1. 7 years
    2. 9 years
    3. 11 years
    4. 13 years
  31. The frequency of a storm in years is given by
    1. nm
    2. n + m
    3. n × m
  32. The equation of the intensity-duration curve is
  33. A mass curve is a graphical representation of
    1. Rainfall intensity versus time in chronological order
    2. Accumulated rainfall versus time in chronological order
    3. Accumulated rainfall intensity versus time in chronological order
    4. None of the above
ANSWERS TO MULTIPLE CHOICE QUESTIONS

1. a      2. d      3. a      4. e      5. d      6. c      7. c      8. b      9. b      10. d      11. c      12. b      13. b      14. b      15. b      16. d      17. b      18. a      19. a      20. a      21. c      22. d      23. b      24. a      25. d      26. d      27. b      28. b      29. b      30. c      31. d      32. a      33. b