In this module we will talk about water resources engineering. Now all of us are aware of the

importance of water and the scarcity of water resources. So we must use the resources available

to us optimally and before doing that we must know how or in what forms water is available,

its special and temporary distribution and for that the first thing which we will discuss

is the hydrologic cycle.

As you can see in this figure, the hydrologic cycle or the water cycle consists of various

forms and movements of water. Now let us start with this ocean. In the ocean due to the southern

radiation, there is a lot of evaporation of water. When it goes up it condenses and then

there is some precipitation in the form of either rain or snow. We will discuss these

forms little later.

When the rainfall occurs, there might be some evaporation directly from the rain and the

rest of it when it falls on the surface either goes into the ground as infiltration or it

runs off in the rivers or deposits in the lakes. Now these rivers then run to the ocean

and this cycle continues. There are lot of components of these this cycle which we are

interested in. For example if we are working in the field of irrigation engineering we

would like to know how much water is going into the ground and from where the plants

can take their water? For example, for this module concerned about the water resources,

then we should know how much water is going into the rivers so that we can control the

floods or we can avoid a lack of water for irrigation other areas. So let us look at

some components of this precipitation.

We will start with discussion of precipitation, its various forms. In India we would typically

worry about rain, snow and hail. All of us know what is rain snow of course we have seen

in India it's not lot but in some of the western countries and colder climates snow

is also an important part of the precipitation. Hail, drizzle, sleet and clays are all different

parts of precipitation. In your chemistry classes you must have seen the precipitation

of solids and liquids. So in similar form you can think of rain as precipitation of

liquid in gas. So in the atmosphere there is lot of water vapour, when it cools down,

the condensation causes that water vapour to drop in the form of rain or snow or hail

depending on the temperature at that time. Various forms have sub classifications. Also

for example rain can be classified as light medium or heavy depending on how much rain

is falling in let us say 1 hour.

When we study the mechanisms of rain, it can be caused by various different kinds of mechanisms.

The important thing is that there is a mass of water vapour which should cool down so

that the water condenses and then falls down. So for cooling, we have lot of different mechanisms.

For example the frontal mechanism where a front which is a surface or a surface of contact

between 2 different air masses of different temperature, when a warm front or warm air

for example,

this is the ground surface and there is warm air going from the side and encounters a cold

front here. Then this warm air tends to rise above the cold air, because of its smaller

density and therefore as it goes up due to adiabatic rate of cooling, this water vapour

will condense and will fall down as rain, so this is called frontal precipitation.

The surface of the earth may be warmer and therefore the air which is in contact with

the surface because of it is high temperature and low density tends to rise and sets up

the conductive current. Now when this air rises again, it goes up, it goes down and

therefore there will be some precipitation in the form of rain. The third mechanism is

called Orographic precipitation.

In this form if we have a mountain and air coming in, it will raise because of the rise

in the ground elevation. As it rises up again, the temperature decreases and there will be

some precipitation which is known as the orographic precipitation and then finally cyclonic precipitation.

This occurs especially in coastal areas where from the sea cyclones which are winds of very

high magnitude and rotating about the centre, they carry a lot of moisture from the sea

and then they come on land and will cause precipitation. Now precipitation is important,

and to know how much precipitation is occurring at a certain time, we shall discuss the measurement

of precipitation in the next topic. There are basically 2 different types of instruments,

which are known as rain gauges. One is a simple non recording and the other is recording.

Non recording means that it will not record with time of the continuous variation of rainfall.

We will go manually and may be once a day see the instrument and see how much rain has

collected and in recording type gauges, we have a continuous record of rainfall. As it

is falling, it is being recorded in the non recording rain gauge.

This figure shows a non recording. Typical non recording rain gauge in which on the top

we have a funnel to carry the rain water falling on it. This funnel then carries water into

a graduated cylinder on which we can see the markings which tells how much rain has fallen

in that period. Typically in India around 8 -- 8.30 AM, a person goes and looks at

this rain gauge and finds out how much rainfall has occurred in the previous day. So at a

fixed time, every day somebody goes and watches the amount of rainfall in the recording gauges.

We have a continuous record. There are 3 different types of rain gauges commonly used here. The

most common one is known as a tipping bucket.

In the tipping bucket rain gauge which is shown here we have a funnel which collects

rain fall and there is an arrangement here which is known as the tipping bucket which

has 2 compartments as shown here . One of the compartments is below the funnel, so it

collects all the water and then a fixed amount of water has entered into this bucket it tips

over. So then it rotates and the other compartment comes below the funnel, so this will go here

and the other compartment will come below the funnel and then it will start collecting

and when it tips, there is a magnet here which will send the signal to some recording device

and we will know how much time it took to fill one side of the bucket and we know how

much rainfall has been collected in that time. So that way it records these tips which tell

us the intensity of rainfall. The data which we obtained from these non recording and recording

gauges can be expressed or displayed in a form of a hyetograph or a mass curve.

Now a hyetograph is a plot of time versus intensity. Intensity of rainfall is typically

expressed in terms of mm per hour and sometimes cm per hour. If we have a non recording rain

gauge, then this data can be expressed as daily values of intensity. For example in

the first day, if we collect 2 mms of rain, we can express the intensity and it would

be better in that case to change it to mm per day. So we have 2 mm in the first day,

then suppose in the second day we have 3, and then it will look like this. Since we

do not know when in the day this rainfall occurred, because we are collecting data every

24 hours, we cannot show the variation within that one day. So this typically will look

like this and so on. So this is known as a hyetograph. How does the rainfall intensity

vary with time? The second type of curve which we use to show the rainfall intensity variation

is a mass curve.

The mass curve again with time shows the accumulated depth, so the intensity shows how intense

the rainfall is, how many cm or mm is per hour and a mass curve shows how much depth

has accumulated from the starting. So again we say that at this time and day, this accumulated

depth may be in mm s or cm, so in the first day if we have 2 mm of rain, it would be 2

then in the second day suppose we have another 3, then this would be 5. So this curve is

continuously increasing because it tells you the accumulated mass or depth of rainfall.

For recording gauges, we typically get a curve which directly gives us the accumulated depth.

In the recording gauge we have come across the tipping bucket. There is another one which

is not so common because it is more expensive and this is known as a weighing type in the

weighing bucket. As the rain falls on the bucket or on the rain gauge, it gets collected

and a signal is sent immediately to record how the weight is increasing with time.

So what we get is directly a mass curve of rain which would look like this. Again this

depth may be mm s or cm. Time may be in hours or day. This shows the accumulation of rain

in the rain gauge over time and if you look at this curve it tells you that there is no

rain from this point. At this point, there is some rainfall. The slope of this curve

will show you the intensity of rainfall. So wherever the slope is largest, for example

here or here the intensity of rainfall is very high and there it is flat. There is almost

no rainfall or very low intensity rainfall. So the mass curve slope will give us the hyetograph.

Now to collect the data we need to put these rain gauges in the field and therefore it

becomes important to know what should be our network.

For example, if we want to find out the rainfall over a certain area, how many rain gauges

should be put and where should they be located, then for example one option would be to locate

the gauges here or you may add more gauges here. So there are some guide lines which

tell you, in how much area how many gauges should be used. Now for example in India the

guidelines are for a 1000 km square area. If we have a plane area, 2 rain gauges are

sufficient. If you have moderate elevation for example a 1000 m elevation, then you may

need 3 to 4 rain gauges in a 1000 km square area. Because the variation of special variation

of rain is likely to be more than in the planes and for hilly areas typically we need to use

8 rain gauges for 1000 km squared area. So these guide lines should be followed whenever

we are designing a rain gauge network and another guideline is that 10 percent of the

rain gauges should be of recording type. So if we have lets say 15 gauges in this area,

1 or 2 should be recording and based on the record. Of those 1 or 2 we can estimate the

temporal variation of rainfall. On the other stations that is why this 10 percents recording

gauges are to be used.

Once we collect the data from these gauges, we have to analyse the data, so the next thing

we will discuss is the data analysis. Suppose we have a network of rain gauges like this

and we have collected a data over let us say a period of a year, then some of the data

may be missing. For example there may be a rain gauge here where we have data for every

day. But one day the person who was supposed to collect the data could not go there and

therefore we have a missing data. So the first thing we will see is how to estimate or how

to take care of the missing data. If we have collected data for a number of days but have

missed 1 day, how do we estimate that missing value? The easiest thing of course is to see

if we have missed values at 1 station but we have the values available at all the other

stations we can take mean of all the other values and say that will be the value at this

point.

So if we have m other stations, then we can say that the missing value at x could be the

mean of all the other values of precipitation on that day, and we estimate our missing value

of Px using this. But there is a problem with this method when there is a wide variation

of rain over the area. For example this gauge may be recording a higher rainfall than this

gauge in general. This is the reason why we have to look at normal precipitation at various

gauges. When we say normal precipitation, typically normal is taken as a 30 year average.

So if we are looking at let us say May 18th then we would consider what the rainfall at

those stations on May 18 over the past 30 years was and the average of those values

would be called the normal precipitation for that rain gauge for that day. So if we are

measuring the precipitation at this station on May 18th, we can estimate it based on the

mean precipitation on that day for all the gauges and they are normal values.

So the formula which we use in this case takes care of the variation in the normal rainfall

at other stations also. So it is a similar formula but now instead of estimating the

rainfall, we estimate the ratio of the rainfall with the normal rainfall and that way we can

estimate the missing value Px. The next important thing to look for is whether the data is consistent

or there is some inconsistency in data for this purpose.

We use what is known as a double mass curve. The assumption is that if the data is consistent

it should follow the same trend over a number of years compared with the other stations

in that area. So we plot a double mass curve which is accumulated precipitation, suppose

5 or 10 nearby stations versus the precipitation at the station where we want to find out whether

the data is consistent or not and if the data is consistent, typically it would follow a

straight line with minor variations. But if there is some change in the characteristics

of the catchment or if the gauge has been shifted and there is some inconsistency, then

we would see that the data does not follow a single straight line and it may deviate

from that position. So if we plot the most recent data here and if there is a break somewhere,

let say we are starting from 2006 and then we find that in 1980 there was a break in

the curve.

So it will tell us that the data is not consistent and there is some problem. Either before 1980,

the gauge was in different location and then it was shifted or there was some change in

the precipitation pattern because of some natural factors. For example there may be

lot of vegetation which was removed. So there could be a number of factors causing this

behaviour but any inconsistency in data can be obtained by the double mass curve analysis

by plotting accumulated precipitation at one station versus accumulated precipitation at

a few nearby stations. Now once we estimate the data and check that is consistent, we

go for ariel averaging.

So if we have a certain area and we want to find out rainfall over this area, the values

which we have for precipitation is only at these rain gauges and these are called point

values. Out of these point values, now we want to estimate what would be the average

rainfall over this whole area. So let us call this area A. So the problem is, given the

point rainfall values at the rain gauges, how to estimate the average rainfall over

the entire area?

There are a number of techniques. The simplest one is known as arithmetic mean and as it

is clear, arithmetic mean means we just take the mean of precipitation values at all the

stations.

Let us say we have these 8 stations. We will say that arithmetic mean or mean precipitation

or the area would be sigma of pi over 8, i = 1 to 8. So it will take the mean of all

the precipitation over the entire area. The draw back with this method although is very

simple is that we do not give any weight to the location of the gauges in that area.

If we have an area where let us say 4 gauges are here and 1 gauge is here, we take the

mean without considering that these 4 are very near. So they do not represent as much

area as this one here. So how much area does it represent? It is not accounted for in the

arithmetic mean method. So a modification or an improvement over this was proposed by

Thiessen and this is known as the Thiessen polygon method in which the relative position of various

gauges is also considered.

If we have rain gauges in an area like this, we draw perpendicular bisectors of the lines

joining the rain gauges and then we assign suppose this is rain gauge, 1, 2 and 3, we

say that area A1 is an effective area for the rain gauge 1. Similarly area A2 and area

A3 and then we compute the average precipitation. We give the weight to individual rain gauges.

So P1A1/A + P2A2/ A, this tells us that a certain rate A1/A depending on what area is

covered by rain gauge 1 is assigned to the precipitation of each rain gauge. So this

takes care of some of the draw backs of the arithmetic mean method in that it accounts

for the position of the gauges. But it does not account for variation in topography. For

example there may be mountainous area here and there may be plane area here, so if this

is a sharp change in elevation, the thiessen polygon method will not be able to account

for it.

Therefore we have another method which is called Isohyetal method which accounts for

the variation of topography. Also by looking at individual precipitation values, I am drawing

isohyets. Isohyets are nothing but lines of equal precipitation. So if we have the precipitation

values at all these stations, we could look at those values and using those values we

could draw isohyetal lines. For example this rain gauge, may be 8 mms, 10mms, and 12mms,

depending on the values of these rain gauges. So these all these rain gauges will have values

between 8mm and 10mm. This will have less than 8mm, this within 10mm and 12mm. So we

will draw the isohyets and then we will assume that the area between 2 isohyets has a rainfall

which is equal to the mean of the values of these 2 isohyets. So this area will have a

rainfall of 9 mm and by summing up the area and the rainfall over the respective areas,

we can get the average rainfall over the area in terms of P bar. Suppose P1 and P2 are the

surrounding isohyetal values and A is the area between them, then we simply sum up the

average precipitation into the area for all the isohyets in the area. Now once we get

the ariel average, we can know what is the depth of rainfall over certain area and then

we can prepare what are known as depth area duration curves.

Now these curves look like this. This is the area which may be in Km square and average depth of rainfall which may be

in mm or cm and this will show the duration of rainfall which may be 6 hours, 12 hours

and so on. So this is the duration. Now if you look at a typical storm, the intensity

will be the largest at the centre of the storm and therefore the depth will be very high.

As you increase the area, it means you are moving away from the storm centre. The intensity

decreases and therefore the depth also decrease over the area. Now if the storm is of larger

duration the depth will increase. So these kinds of curves will tell us how much of the

average depth of rainfall is to be expected over a certain area if the rainfall occurs

for a certain time which is 6 hours or 12 hours or any given time. There is sometimes

an imperical equation also given for variation of rainfall. Average depth with area is -- K

k to the power n exponential where P0 is the point rainfall value, which we obtain from

the rain gauge. But since the rain gauge will not always be at the centre of the storm we

say that this rain gauge value represents the rainfall over a 25Km squared area. This

kind of equation tells us, for any given duration the average depth decreases with area. These

values of K and M will depend on the catchment area and some typical values are given in

various text books about different areas. The other aspect which is important is to

have some kind of frequency analysis or risk analysis to see the chances of rainfall occurring

in the next 10 years or next 100 years or so. The frequency analysis is also very important

from this point of view.

So frequency analysis is nothing but deciding how frequent a rainfall would be and typically

what we do is present an intensity duration frequency curve in which we say how frequent

will the rainfall of certain intensity and certain duration be. The curve would look

like this. This is the intensity of rainfall which may be mm per hour duration typically

in hours and this denotes the frequency or the return period which may be a rainfall of once in 100 years

or once in 20 years or once in 50 years. The frequency of course would be reverse of the

time period, so we can write the time period as one over the probability of occurrence

of a rainfall and when we discuss the intensity using frequency curve, they will help us in

knowing or designing a project or some structure against a given probability of occurrence.

So if you want to design something which needs to be very safe, we may go in for 100 year

precipitation and based on that 100 year precipitation, we can find out the depth of precipitation and those curves.

We can prepare, in terms of duration, depth of rainfall and the time period. So what this

curve indicates is that for a given duration of rainfall, what will be the depth for a

given time period. One should be aware of the fact that time period of 100 years does

not mean that this rainfall will occur every 100 years. In general if we take a very long

period of record, for example 400 - 500 years, this event is likely to occur 4 or 5 times.

It is not that it will occur only once in any given 100 year period. Related to this

there is a concept of probable maximum precipitation which can occur over a given area and this

probable maximum precipitation is used in very extreme cases where we have to design

something which is very critical. For example a large dam the future of which will be catastrophic

so in that case, we can find out what the PMP is.

PMP or the probable maximum precipitation which is typically written as some factor

multiplied by the standard deviation plus the mean rainfall and generally the value

of K is taken as above 15. So the mean rainfall plus 15 times standard deviation which is

normally taken as the probable maximum precipitation for that area and this is used in critical

design to estimate what will be the maximum flood which can occur in the given catchment.

So in this lecture we have seen various aspects of precipitations but we must realise that

as water resource engineer, it is not the precipitation which is of importance to us.

It is really the run off or how much water is going into the river which is more important

to us. Although you are an agricultural engineer, the water which is going underground may be

more important to you but most of the water resources engineering projects deal with construction

of dams, canals and other things from the rivers and therefore the volume of water going

into the river is more important although it depends on precipitation. But we are more

concerned about the run off. So in today's lecture we have looked at the precipitation.

Out of this precipitation, part of it will go underground which is called infiltration,

part of it will evaporate from the surface; part of it will be lost as transpiration from

the plants. So we combine them and we call that evapo transpiration. So evapo transpiration

and infiltration are the 2 abstractions from the precipitation and most of the rest goes

to the streams or over the surface as surface run off. Part of it goes inside the ground

and again goes to the streams and ocean as underground run off or what we call base ground.

So after today's lecture in which we studied precipitation, we will look at what are the

various abstractions with infiltration, evapo transpiration and also there is some 'storage

on the surface' to see the quantity of water taken out of the precipitation and that will

help us in finding quanitity of the water going into the rivers and lakes.