Water Resource Engineering

 

 

CE2202

Water Resources Engineering

Note Prepared by D.Sravani

 

HYDROLOGY 1.1 Introduction  Hydrology is an earth science. It encompasses the occurrence, distribution, movement, and properties of the water on the earth and their environmental relations. Hydrology has both applied and pure science aspects. On the one hand, it is an important science that studies how the water flows on the Earth. On the other hand, understanding of fundamental hydrologic processes is necessary for proper use and protection of water resources.  Water is also an agent for many other processes (weathering, transport of chemicals, erosion, and deposition). Hydrology is the study of several physical processes;  

Atmospheric processes: cloud condensation, precipitation.

 

Surface processes: snow accumulation, overland flow, river flow, lake storage.

 

Subsurface processes: infiltration, soil-water storage, groundwater flow.

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Interfacial processes: evaporation, transpiration, sediment water exchange.

Hydrologists are traditionally concerned with the supply of water for domestic and agricultural use and the prevention of flood disasters. However, their field of interest also includes hydropower generation, navigation, water quality control, thermal pollution, recreation and the protection and conservation of nature. In fact, any intervention in the hydrological regime to fulfill the needs of the society belongs to the domain of the hydrologist. This does not include the design of structures (dams, sluices, weirs, etc.) for water management. Hydrologists contribute however, to a functional design (e.g. location and height of the dam)  by developing design criteria and to water resources management by establishing the hydrological

boundary

conditions

to

planning

(inflow

sequences,

water

resources

assessment). Both contributions require an analysis of the hydrological phenomena, the collection of data, the development of models and the calculation of frequencies of occurrence.

 

1.2 History of Hydrology Water is the prime necessity for all forms of life. Human civilization has progressed from early era with utilization of available water resources. Civilization flourished wherever water was available, and it collapsed wherever water resources depleted. It is learnt from Vedic literature that ground water was abundantly utilized for use. Archaeological excavations at Mohan Jodaro reveal that people of Indus valley (3000 B.C.) had good knowledge of ground water development through wells. Later, surface water resources available through rivers, lakes, ponds were developed. People of Vedic period had knowledge of the hydrologic cycle. As more and more water was needed, people learnt the principles of hydrology by experience and consequently, reservoirs were built to store rain water for use in the period of dry season. Indus valley and Nile valley also had the knowledge of hydrology. Until 1950, pragmatic considerations dominated hydrology. Theoretical approaches in hydrology have been increasingly developed due to the development of digital computers since 1950. The focus now is on how best to optimize the use of existing surface-water  projects  projec ts and ground-w ground-water ater reso resources. urces. Challenge for the 21st century in hydrology will still be maintaining water quantity and quality against to the increasing stress on water resources by the increasing world  population,, contam  population contamination, ination, human induced induced climateclimate-hydrol hydrology ogy change change,, and extrem extremee even events ts (flood and drought). In India, the period of empiricism may be taken to have started sometime in the middle of nineteenth century and continued up to first quarter of twentieth century. During this period, development of empirical formulae, tables, and curves took place through investigators like Binnie, Ryves, Dickens, Inglis, Lacey etc.  

1.3  Application Fields Hydrological science has both pure and applied aspects. Understanding the engineering hydrology science is essential for  

Sustainable agriculture (foods for the growing population)

 

Environmental Environ mental protection protection and management management

 

Water resources development and management

 

 

Prevention and control of natural disasters

 

Control problems of tidal rivers and estuaries

 

Soil erosion and sediment transport and deposition

 

Mitigation of the negative impacts of climatic change

 

Water supply and

 

Flood and drought control

Traditional water management has focused on providing freshwater resources to the needs of humans, livestock, commercial enterprises, agriculture, mining, industry, and electric power.

1.4 Scope of Hydrology The study of hydrology helps us to know (i) The maximum probable flood that may occur at a given site and its frequency; this is required for the safe design of drains and culverts, dams and reservoirs, channels and other flood control structures. (ii) The water yield from a basin - its occurrence, quantity and frequency, etc; this is necessary for the design of dams, municipal water supply, water power, river navigation, etc. (iii) The ground water development for which a knowledge of the hydrogeology of the area, i.e., of the formation soil, recharge facilities like streams and reservoirs, rainfall pattern, climate, cropping pattern, etc. are required.

(iv) The maximum intensity of storm and its frequency for the design of a drainage project in the area

1.5 World’s Water Resources Water resources engineering uses hydrologic principles in the solution of engineering  problems arising from human exploitation of water resource resourcess of the earth. The engineering hydrologist, or water resources engineer, is involved in the planning, analysis, design, construction and operation of projects for the control, utilization and management of water resources. Hydrologic calculations are estimates because mostly the empirical and approximate methods are used to describe various hydrological processes.

 

The World‘s total water resources are estimated as a s 1.36 × 108 Μ ha-m. ha -m. Of these global water resources, about 97.2% is salt water mainly in oceans, and only 2.8% is available as fresh water at any time on the planet earth. Out of this 2.8% of fresh water, about 2.2% is available as surface water and 0.6% as ground water. Even out of this 2.2% of surface water, 2.15% is fresh water in glaciers and icecaps and only of the order of 0.01% is available in lakes and streams, the remaining 0.04% being in other forms. Out of 0.6% of stored ground water, only about 0.25% can be economically extracted with the present drilling technology (the remaining being at greater depths). It can be said that the ground water potential of the Ganga Basin is roughly about forty times the flow of water in the river Ganga.

1.6 Water resources of India The important rivers of India are shown in Fig. 1.1 and their approximate water potentials are given below: Sl.no.

River basin

Water potential (M ha-m)

1

West flowing flowing rivers like Narmada and Tapti

30.55

2

East flowing rivers like Mahanadi, Godavari, Krishna,

35.56

Cauvery and Pennar 3

The Ganges and its tributaries tributaries

55.01

4

Indus Indus and its tributaries tributaries

7.95

5

The River Brahmaputra Brahmaputra

59.07

Total

188.14

The rivers of north India are perennial (i.e., the water in sufficient quantity flows in them throughout the year) since they receive the snow melt runoff in summer. Rivers of  peninsular India (south India) receive only ru noff due to t o ra rainfall infall and have a good flow only during monsoons; many of them are either dry or have negligible flow during most of the remaining part of the year. The average annual rainfall of India is around 114 cm.

 

  Figure 1.1 River basins of India

1.7 Uses of Water resources engineering Engineering Hydrology or water resources engineering helps in the following ways  

Hydrology is used to find out maximum probable flood at proposed sites e.g. Dams.

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The variation of water production from catchments can be calculated and described by hydrology.

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Engineering hydrology enables us to find fi nd out the relationship between a catchment‘s surface water and groundwater resources

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The expected flood flows over a spillway, at a highway culvert, culvert, or  or in an urban storm drainage system can be known by this very subject.

 

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It helps us to know the required reservoir capacity to assure adequate water for irrigation or municipal water supply in droughts condition.

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It tells us what hydrologic hardware (e.g. rain gauges, stream gauges etc) and software (computer models) are needed for real-time flood forecasting.

1.8 Hydrologic cycle Water in our planet is available in the atmosphere, the oceans, on land and within the soil and fractured rock of the earth‘s crust. crust . Water molecules from one location to another are driven  by the solar energy.

Moisture circulates from the earth into the atmospher atmospheree through

evaporation and then back into the earth as precipitation. In going through this process, called the Hydrologic Cycle. Water is conserved –  conserved  –  that  that is, it is neither created nor destroyed. It would perhaps be interesting to note that the knowledge of the hydrologic cycle was known at least by about 1000 BC by the people of the Indian Subcontinent. This is reflected  by the fact that one verse of Chhandogya Chhandog ya Upanishad (the Philosophical reflections of the Vedas) points to the following: ―The rivers… all discharge their waters into the sea. They lead from sea to sea, the cclouds louds raise them to the sky as vapor and release them in the form of rain…‖ rain…‖  The earth‘s total water content in the hydrologic cycle is not equally distributed (figure 1.2).

Figure 1.2 Total global water content and global fresh water distribution

 

The oceans are the largest reservoirs of water, but since it is saline it is not readily usable for requirements of human survival. survival. The freshwater content is just a fraction of the total water available. Again, the fresh water distribution is highly uneven, with most of the water locked in frozen polar ice caps. The hydrologic cycle or water cycle consists of four key components 1.

Precipitation

2.

Runoff

3.

Storage

4.

Evapotranspiration

Figure 1.3 shows a schematic representation of the hydrologic cycle.

Figure 1.3 The hydrologic cycle A convenient starting point to describe the cycle is in the oceans. Water in the oceans evaporates due to the heat energy provided by solar radiation. The water vapour moves upwards and forms clouds. While much of the clouds condense and fall back to oceans as rain there they condense and precipitate onto the land mass as rain, snow, hail, sleet etc. A  part of precipitation may evaporate back to the atmospher a tmospheree e ven while falling. Another part may be intercepted by vegetation, structures and some part move down to the ground surface. A portion of the water that reaches the ground enters the earth‘s surface through infiltration. Vegetation sends a portion of the water from under the ground surface back to the

 

atmosphere through the process of transpiration. transpiration. The  The ground water may come to the surface through springs and other outlets after spending a considerably longer time than the surface flow. The portion of the precipitation which by a variety of paths above and below the surface of the earth reaches the stream channel is called runoff. runoff. Once  Once it enters into the stream channel, runoff becomes stream becomes stream flow.  flow.   The main components of the hydrologic cycle can be broadly classified as transportation components (precipitation, evaporation, transpiration, infiltration and runoff) and storage components (storage on land surface like depressions, ponds, lakes, reservoirs etc., soil moisture storage and ground water storage). Schematically, the interdependency of the transportation components can be represented as in figure 1.3.

Figure 1.4 Transportation components of the hydrologic cycle It is important to note that the total water resources of the earth are constant and the sun is the source of energy source of energy for hydrologic cycle. Recognition of the various processes such as evaporation, precipitation and ground water flow helps one to study the science of hydrology in a schematic way.

1.9 Precipitation The term  precipitation denotes all forms of water that reach that reach the earth from the atmosphere. The usual forms of precipitation are rainfall, snowfall, hail, frost and dew. Of all these, first two contributes significant amount of water. Rainfall being predominant form of  precipitation causing stream flow, especially the flood flow iin n a majority of rivers in India,

 

unless otherwise stated the term rainfall is used synonymously with precipitation. The magnitude of precipitation varies with time and space. Uses of precipitation data includes  

Runoff estimation analysis

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Groundwater recharge analysis

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Water balance studies of catchments

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Flood analysis for design of hydraulic structures

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Real-time flood forecasting

1.10 Forms of Precipitation Drizzle —  Drizzle  —  a  a light steady rain in fine drops (0.5 mm) and intensity 0.5 mm, maximum size —  size  —  6  6 mm) from the clouds. Glaze —  Glaze  —  freezing  freezing of drizzle or rain when they come in contact with cold objects. Sleet —  Sleet  —  frozen  frozen rain drops while falling through air at subfreezing temperature. Snow —  Snow  —  ice   ice crystals resulting from sublimation (i.e., water vapour condenses to ice) Snowflakes —  Snowflakes  —  ice   ice crystals fused together. Hail  —   small lumps of ice (>5 mm in diameter) formed by alternate freezing and melting, when they are carried up and down in highly turbulent air currents. Dew —  Dew  —   moisture moisture condensed from the atmosphere in small drops upon cool surfaces. Frost —  Frost  —  a   a feathery deposit of ice formed on the ground or on the surface of exposed objects  by dew or water vapour that has ha s frozen Fog  —   a thin cloud of varying size formed at the surface of the earth by condensation of atmospheric vapour (interfering with visibility) Mist —  Mist  —  a  a very thin fog

 

.1.11 Types of precipitation  Frontal precipitation

A front  is  is the interface between two distinct air masses. It results from the lifting of warm and moist air on one side of a frontal surface over colder, denser air on the other side. A front may be warm front or cold front depending upon whether there is active or passive accent of warm air mass over cold air mass.

Figure 1.5 Frontal precipitation Convective Precipitation

Convective precipitation is caused by natural rising of warmer, lighter air in colder, denser surroundings. Generally, this kind of precipitation occurs in tropics, where on a hot day, the ground surface gets heated unequally, causing the warmer air to lift up as the colder air comes to take its place. The vertical air currents develop tremendous velocities. Convective  precipitation occurs occur s in the form of showers of high int intensity ensity and short duration.

Figure 1.6 Convectional lifting

 

Orographic Precipitation

Orographic precipitation is caused by air masses which strike some natural topographic  barriers like mountains, and cannot move forward and hence rise up, causing condensation and precipitation. All the precipitation we have in Himalayan region is because of this nature. It is rich in moisture because of their long travel over oceans.

Figure 1.7 Orographic precipitation Cyclonic Precipitation  

Cyclone is a large low pressure region with circular wind motion. This type of precipitation is due to lifting of moist air converging into a low pressure belt, i.e., due to pressure differences created by the unequal heating of the earth‘s surface. Here the winds blow spirally inward counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. There are two main types of cyclones - tropical cyclone (also called hurricane or typhoon) of comparatively small diameter of 300-1500 km causing high wind velocity and heavy  precipitation, and the extra-tropical cyclone of large diameter up to 3000 km causing wide spread frontal type precipitation.

1.12 Measurement of Precipitation Measurement of precipitation is an important component of all hydrologic studies. Precipitation is expressed in terms of depth to which rainfall water would stand on an area if all the rain were collected on it. Thus 1 cm of rainfall over a catchment area of 1 represents a volume of water equal to

   . The precipitation is collected and measured in

a raingauge. Raingauges are classified as 1.   Non Recording type a.  Symons gauge

  

 

2.  Recordi Recording ng type a.  Tipping-bucket type  b.  Weighin Weighing g bu bucket cket type c.   Natural-Syphon type typ e The non-recording rain gauge  used in India is the Symon‘s rain gauge (Fig. 1.8). It consists of a funnel with a circular rim of 12.7 cm diameter and a glass bottle as a receiver. The cylindrical metal casing is fixed vertically to the masonry foundation with the level rim 30.5 cm above the ground surface. The rain falling into the funnel is collected in the receiver and is measured in a special measuring glass graduated in mm of rainfall; when full it can measure 1.25 cm of rain. The rainfall is measured every day at 08.30 hours IST. During heavy rains, it must be measured three or four times in the day, lest the receiver fill and overflow, but the last measurement should be at 08.30 hours IST and the sum total of all the measurements during the previous 24 hours entered as the rainfall of the day in the register. Usually, rainfall measurements are made at 08.30 hr IST and sometimes at 17.30 hr IST also. Thus the non recording or the Symon‘s rain gauge gives only the total depth of rainfall for the  previous 24 2 4 hours (i (i.e., .e., daily rainfall) and does not giv givee the intensity and d duration uration o off rainfall during different time intervals of the day. It is often desirable to protect the gauge from being damaged by cattle and for this  purpose a barbed wire fence may be erected ar around ound it.

Figure 1.8 Symon‘s rain gauge  gauge  

 

Recording Rain Gauge

This is also called self-recording, automatic or integrating rain gauge. This type of rain gauge figures. 1.9, 1.10 and 1.11, has an automatic mechanical arrangement consisting of clockwork, a drum with a graph paper fixed around it and a pencil point, which draws the mass curve of rainfall Fig. 1.12. From this mass curve, the depth of rainfall in a given time, the rate or intensity of rainfall at any instant during a storm, time of onset and cessation of rainfall, can be determined. The gauge is installed on a concrete or masonry platform 45 cm square in the observatory enclosure by the side of the ordinary rain gauge at a distance of 2-3 m from it. The gauge is so installed that the rim of the funnel is horizontal and at a height of exactly 75 cm above ground surface. The self-recording rain gauge is generally used in conjunction with an ordinary rain gauge exposed close by, for use as standard, by means of which the readings of the recording rain gauge can be checked and if necessary adjusted. There are three types of recording rain gauges - tipping bucket gauge, weighing gauge and float gauge. Tipping bucket rain gauge-  This consists of a cylindrical receiver 30 cm diameter with a

funnel inside (Fig. 1.9). Just below the funnel a pair of tipping buckets is pivoted such that when one of the bucket receives a rainfall of 0.25 mm it tips and empties into a tank below, while the other bucket takes its position and the process is repeated. The tipping of the bucket actuates on electric circuit which causes a pen to move on a chart wrapped round a drum which revolves by a clock mechanism. This type cannot record snow. Weighing type rain gauge- In this type of rain-gauge, when a certain weight of rainfall is

collected in a tank, which rests on a spring-lever balance, it makes a pen to move on a chart wrapped round a clockdriven drum (Fig. 1.10). The rotation of the drum sets the time scale while the vertical motion of the pen records the cumulative precipitation. Float type rain gauge - In this type, as the rain is collected in a float chamber, the float

moves up which makes a pen to move on a chart wrapped round a clock driven drum (Fig. 1.11). When the float chamber fills up, the water siphons out automatically through a siphon tube kept in an interconnected siphon chamber. The clockwork revolves the drum once in 24 hours. The clock mechanism needs rewinding once in a week when the chart wrapped round

 

the drum is also replaced. This type of gauge is used by IMD (Indian Meteorological Department). The weighing and float type rain gauges can store a moderate snow fall which the operator can weigh or melt and record the equivalent depth of rain. The snow can be melted in the gauge itself (as it gets collected there) by a heating system fitted to it or by placing in the gauge certain chemicals such as Calcium Chloride, ethylene glycol, etc.

Figure 1.9 Tipping bucket gauge

Figure 1.10 Weighing bucket type

Figure 1.11 Float type rain gauge

 

  Figure 1.12 Mass curve of rainfall

1.13 Graphical representation of rainfall The variation of rainfall with respect to time may be shown graphically by (i) a hyetograph, and (ii) a mass curve.   A hyetograph is a bar graph showing the intensity of rainfall with respect to time (Fig. 1.13) and is useful in determining the maximum intensities of rainfall during a particular storm as is required in land drainage and design of culverts.

Figure 1.13 Hyetog H yetograph raph

 

A mass curve of rainfall (or precipitation) is a plot of cumulative depth of rainfall against time (Fig. 1.14). From the mass curve, the total depth of rainfall and intensity of rainfall at any instant of time can be found. The amount of rainfall for any increment of time is the difference between the ordinates at the beginning and end of the time increments, and the intensity of rainfall at any time is the slope of the mass curve (i.e., i = ∆P/∆t) at that time. A mass curve of rainfall is always a rising curve and may have some horizontal sections which indicate periods of no rainfall. The mass curve for the design storm is generally obtained by maximizing the mass curves of the severe storms in the basin.

Figure 1.14 Mass curve of rainfall

1.14 Rain-gauge network The following figures give a guideline as to the number of rain-gauges to be erected in a given area or what is termed as ‗rain‗rain -gauge density‘  density‘   Area

Rain-gauge Rain -gauge densit density y

Plains

1 in 520 k 

Elevated regions

1 in 260 260-390 -390 k 

    

 

Hilly and very heavy rainfall areas

1 in 130 Km2 preferably with 10% of the rain-gauge stations equipped with the self recording type

, while in more

In India, on an average, there is 1 rain-gauge station for every 500 k 

.

developed countries, it is 1 station for 100 k 

The aim of the optimum rain-gauge network design is to obtain all quantitative data averages and extremes that define the statistical distribution of the hydro meteorological elements, with sufficient accuracy for practical purposes. When the mean areal depth of rainfall is calculated by the simple arithmetic average, the optimum number of rain-gauge stations to be established in a given basin is given by the equation (IS, 1968) 2

c   N    v      p  Where, N = optimum number of raingauge stations to be established in the basin Cv = Coefficient of variation of the rainfall of the existing rain gauge stations (say, n)  p = desired degree of percentage error er ror in the estimate of the average av erage depth of rainfall rainf all o over ver the basin The number of additional rain-gauge stations (N – n) n) should be distributed in the different zones (caused by isohyets) in proportion to their areas, i.e., depending upon the spatial distribution of the existing raingauge stations and the variability of the rainfall over the basin. Saturated Satura ted Network Net work Design

If the project is very important, the rainfall has to be estimated with great accuracy; then a network of rain-gauge stations should be so set up that any addition of rain-gauge stations will not appreciably alter the average depth of rainfall estimated. Such a network is referred to as a saturated network.

 

Example:  The normal annual rainfalls of a basin are 88cm, 104cm, 138cm, 78cm and 56cm.

Determine the optimum number of rain-gauge stations to be established in the basin if it is desired to limit the error in the mean value of rainfall to 10%. Solution:

Arithmetic mean,

 x  =

Standard deviation,

 =    = 92.8cm

  



=

station

n 1



2

 

 = 30.7cm   

Normal annual rainfall, x (cm)

A B C D E

C v =



 x  x

  464

difference ( x  x )

88 104 138 78 56

Diffe Difference rence ( x  x )

-4.8 11.2 45.2 -14.8 -36.8

2

23 125 2043 219 1354 ∑( x  x ) =3767.4 2

  = ×100 = 33.1%   x

The optimum number of rain-gauge stations to limit the error in the mean value of rainfall to  p=10%. 2

2

c   33.1    N    v   =   = 11   10    p 

∴ Additional rain-gauge stations to be established = N  –  n n = 11 –  11 –  5  5 = 6 1.15 Estimation of missing rainfall data Many precipitation stations have short breaks in their records because of absence of the observer or because of instrumental failures. It is often necessary to estimate this missing record. In the procedure used by the U.S. Environmental Data Service, precipitation amounts

 

are estimated from observations at three stations as close to and as evenly spaced around the station with the missing record as possible. If the normal annual precipitation at each of the index stations is within 10% of that for the station with the missing record, a simple arithmetic average of the precipitation at the index stations provides the estimated amount. Normal ratio method-  If the normal annual precipitation at any of the index stations differs

from that at the station in question by more than 10%, the normal-ratio method is used. In this method, the amounts at the index stations are weighted by the ratios of the normal-annual precipitation  precip itation values. That is, precipitation Px at station X is:

 p x 

Nx N x  N x   P1 P 2 P n  1   N x P P P  . . . . . .      n 2  1  n N N    n  N1 N2 Nn  N n  2  1

Where N1, N2… N n = normal annual rainfall of index stations  N x = normal annual rainfall of missing station n = number of index stations Example:  A precipitation station X was inoperative for some time during which a storm

occurred. The storm totals at three stations A, B and C surrounding X, were respectively 6.60, 4.80 and 3.70 cm. the normal annual precipitation amounts at stations X, A, B and C are respectively 65.6, 72.6, 51.8 and 38.2 cm. Estimate the storm precipitation for station X. Solution: If  I f N x, N A, N B and NC are the average annual precipitation amounts at X, A, B and

C and PA, PB  and PC  are the storm totals of stations A, B and C surrounding X, the storm  precipitation P at station X is i s given by

 p x 

1

 N x

3

 N A

 PA

 PB

Nx NB

 P C 

N x 



N C  

 

65.6 65.6 65.6    1  = 6.11cm  4.8   3.7  6.6   3 72.6 51.8 38.2 

 p x 

 

Arithmetic mean method-  If the normal annual precipitation at various stations is within

about 10% of the normal annual precipitation at station X, then a simple arithmetic average  procedure  proce dure is followed followed to estimate estimate  Px  Px.. Thus

 p x 

1  M 

 P1  P2  ...P m   

1.16 Double mass curve The trend of the rainfall records at a station may slightly change after some years due to a change in the environment (or exposure) of a station either due to coming of a new  building, fence, planting of trees or cutting of forest nearby, which affect the catch of the gauge due to change in the wind pattern or exposure. The checking for inconsistency of a record is done by the double-mass curve technique. This technique is based on the principle that when each recorded data comes from the same parent population, they are consistent. The consistency of records at the station in question (say, X) is tested by a double mass curve curve by plottting plottting the cumulative annual (or seasonal) rainfall at station X against the concurrent cumulative values of mean annual (or seasonal) rainfall for a group of surrounding stations, for the number of years of record.

Figure 1.15 Double mass curve

 

Since the past response is to be related to the present conditions, the data (accumulated precipitation of the station x, i.e., ΣP x  and the accumulated values of the average of the group of the base stations, i.e., i.e ., ΣPav) are usually assembled in reverse chronological order. Values of ΣP x  are plotted against ΣPav for the concurrent time periods, Fig. 1.15. A definite break in the slope of the resulting plot points to the inconsistency of the data indicating a change in the precipitation regime of the station x. The precipitation values at station x at and beyond the period of ch change ange is corrected using the relation,

 pcx  P x

S c S a

 

where, Pcx = corrected value of precipitation at station x at any time t Px = original recorded value of precipitation precipitation at station x at time t. Sc= corrected slope of the double-mass curve Sa = original slope of the curve. Thus the older records of station x, have been corrected so as to be consistent with the new  precipitation regime regi me of the station x.

1.17 Calculating Average Rainfall The time of rainfall record can vary and may typically range from one minute to one day for non recording gauges, recording gauges, on the other hand, continuously record the rainfall and may do so so from one day one w week, eek, depending on the m make ake of instrument. For any time duration, the average depth of rainfall falling over a catchment can be found by the following three methods.  

The Arithmetic Mean Method

 

The Thiessen Polygon Method

 

The Isohyetal Method

1.  The arithmetic-mean method

The arithmetic-mean method is the simplest method of determining areal average rainfall. It involves averaging the rainfall depths recorded at a number of gages. This

 

method is satisfactory if the gages are uniformly distributed over the area and the individual gage measurements do not vary greatly about the mean.

  P   

 pave 

n

Where, P  Where,  P aave ve = average depth of rainfall over the area

 P = sum of rainfall amounts at individual raingauge stations n = number of rain gauge stations in the area

Figure 1.16 Representation of the rainfall recorded in the four rain gauges in ‗mm‘   Average rainfall as the arithmetic mean of all the records of the four rain gauges, as shown  below

 = 10 mm  This method is fast and simple and yields good estimates in flat country if the gauges are uniformly distributed and the rainfall at different stations do not vary very widely from the mean. These limitations can be partially overcome if topographic influences and aerial representativity are considered in the selection of gauge sites.

 

2.  The Thiessen polygon method

This method attempts to allow for non-uniform distribution of gauges by providing a weighting factor for each gauge. The stations are plotted on a base map and are connected by straight lines. Perpendicular bisectors are drawn to the straight lines, joining adjacent stations to form polygons, known as Thiessen polygons (Fig. 1.17). Each polygon area is assumed to  be influenced influenced by the raingauge station inside inside it, i.e., if P1, P2, P3, ...Pi  are the rainfalls at the individual stations, and A1, A2, A3,...Ai. are the areas of the polygons surrounding these stations, (influence areas) respectively, the average depth of rainfall for the entire basin is given by

 pave 

   A P     A i i i

Where,

 A = Total area of the basin i

The results obtained are usually more accurate than those obtained by simple arithmetic averaging. The gauges should be properly located over the catchment to get regular shaped  polygons.  polyg ons. Howev However, er, one of the serious serious limitations limitations of the Thiessen Thiessen meth method od is its nonflexibility since a new Thiessen diagram has to be constructed every time if there is a change in the raingauge network.

Figure 1.17 Thiessen polygon method (a) Rainfall recorded (b) Areas of influences

 

For the given example, the ―weighted‖ average rainfall over the catchment is determined as,

    = 10.40 mm  3.  The isohyetal method  

In this method, the point rainfalls are plotted on a suitable base map and the lines of equal rainfall (isohyets) are drawn giving consideration to orographic effects and storm morphology, Fig. 1.18. The areas may be measured with a planimeter if the catchment map is drawn to a scale. scale.

The average rainfall between the succesive isohyets taken as the average

of the two isohyetal values are weighted with the area between the isohyets, added up and divided by the total area which gives the average depth of rainfall over the entire basin, i.e.,

 

Pave  =   ∑ (Area between two adjacent isohyets)  isohyets)   × (mean of the two adjacent isohyets values)

Figure 1.18 Isohyetal method (a) recorded rainfall (b) Isohyets and areas enclosed  between two consecutive isohyets i sohyets For the problem shown in Figure 1.18, the following may be assumed to be the areas enclosed between two consecutive isohyets and are calculated as under: 2

Area I = 40 km  

 

2

Area II = 80 km   2

Area III = 70 km   2

Area IV = 50 km   2

Total catchment catchment area = 240 km   The areas II and III fall between two isohyets each. Hence, these areas may be thought of as corresponding to the following rainfall depths: Area II : Corresponds to (10 + 15)/2 = 12.5 mm rainfall depth Area III : Corresponds to (5 + 10)/2 = 7.5 mm rainfall depth For Area I, we would expect rainfall to be more than 15mm but since there is no record, a rainfall depth of 15mm is accepted. Similarly, Similarl y, for Area IV, a rainfall depth of 5mm has to be taken. Hence, the average precipitation by the isohyetal method is calculated to be

  =9.89 mm  1.18 Depth-Area-Duration curves In designing structures for water resources, one has to know the areal spread of rainfall within watershed. However, it is often required to know the amount of high rainfall that may  be expected over the catchment. It may be observed that usually a storm event would start with a heavy downpour and may may gradually reduce as time passes. Hence, the rainfall depth is not proportional to the time duration duratio n of rainfall observation. Similarl Similarly, y, rainfall over a small area may be more more or less uniform. But if the area is large, then due due to the variation of rain falling in different parts, the average rainfall would be less than that recorded over a small  portion below the high rain ra in fall occurring within the area. Due to these facts, a Depth-Area Depth-Area-Duration (DAD) analysis is carried out based on records of several storms on an area and, the maximum areal precipitation for different durations corresponding to different areal extents. The result of a DAD analysis is the DAD curves which would look as shown in Figure 1.19

 

  Figure 1.19 A typical Depth-Area-Duration (DAD) Curve. For a rainfall of a given duration, the average depth decreases with the area in an exponential fashion given by

 P  P0e Where

 KAn

 

2

 P   =

average depth in cm over an area A km  

 P 0  =

highest amount of rainfall in cm at the storm centre and k and n are constants for a given region

1.19 Intensity-Duration-Frequency curves For many engineering problems such as run off disposal and erosion control, it is necessary to know the rainfall intensities of different durations and different recurrence intervals. The relationship between intensity, storm duration and frequency at any location can be obtained from the analysis of rainfall records available at that location. First of all, the rainfall intensity record of selected rainfall duration, say 10 minutes, is collected for a location and the frequency analysis is carried out to obtain the rainfall intensity for different frequencies. The process is then repeated for other durations, and one can obtain a plot as shown in figure 1.20.

 

It has been found that intensity-duration-frequency curve can be represented by the following mathematical expression

t  

 KT b ( D  a) n

 

In which i = the intensity of rainfall (cm/hr) T = the th e recurrence interval and D = the duration of rainfall Constants K, b, a and n do not have fixed value

Figure 1.20 A typical Rainfall Intensity Duration frequency (IDF) curve Two new concepts are introduced here, which are: •  Rainfall intensity This is the amount of rainfall for a given rainfall event recorded at a station divided by the time of record, counted from the beginning of the event. •  Return period This is the time interval after which a storm of given magnitude is likely to recur. This is determined by analyzing past rainfalls from several events recorded at a station. A related term, the frequency of the rainfall event (also called the storm

 

event) is the inverse of the return period. Often this amount is multiplied by 100 and expressed as a percentage. Frequency (expressed as percentage) of a rainfall of a given magnitude means the number of times the given event may be expected to be equaled or or exceeded in 100 years.

1.20  Probable Maximum Precipitation (PMP) The values of extreme rainfall events are important from the water resources engineering point of view. This is the amount of rainfall over a region which cannot be exceeded over at that place. The PMP is obtained by studying all the storms that have occurred over the region and maximizing them for the most critical atmospheric conditions. The PMP will of course vary over the Earth‘s surface according to the local climatic factors.  Naturally, it would be expected to be mu much ch higher in the th e hot humid equatoria equatoriall regions than iin n the colder regions of the mid-latitudes when the atmospheric is not able to hold as much moisture. PMP also varies within India, between the extremes of the dry deserts of Rajasthan to the ever humid regions of South Meghalaya plateau.   From the statistical studies, PMP can be estimated from the following equation

 PMP  P  K         Where

 P   =

mean of annual maximum rainfall series

  

= standard deviation of the series K = frequency factor, which is usually in the neighbourhood of 15