Precipitation, Evaporation and Evapo-Transpiration Study Notes for Civil Engineering

By Deepanshu Rastogi|Updated : July 22nd, 2021

This article contains basic notes on "Precipitation, Transpiration & Evapotranspiration(EPT)" topic of "Hydrology & Irrigation" subject which contains sub-topic like Index of Wetness, Aridity Index, Optimum number of Rain Gauges required, Estimation of Missing Rainfall Data, Mean Rainfall Data, Dalton's Law & Measurement of Evaporation, Water & Energy Budget Method, Evapo-Transpiration(AET) & Penman's Method, Transpiration Loss, Direct & Indirect determination method for Streamflow, Determination of Velocity and Velocity distribution profile details.

This article contains basic notes on "Precipitation, Transpiration & Evapotranspiration(EPT)"  topic of "Hydrology & Irrigation" subject which contains sub-topic like Index of Wetness, Aridity Index, Optimum number of Rain Gauges required, Estimation of Missing Rainfall Data, Mean Rainfall Data, Dalton's Law & Measurement of Evaporation, Water & Energy Budget Method, Evapo-Transpiration(AET) & Penman's Method, Transpiration Loss, Direct & Indirect determination method for Streamflow, Determination of Velocity and Velocity distribution profile details.

Precipitation & General aspects of Hydrology

Index of Wetness

  • Index of wetness =  image001
  • % Rain deficiency = 100 - % index of wetness

Aridity index



A.I = Aridity index

PET = Potential Evapo-Transpiration

AET = Actual Evapo-transpiration

  • AI ≤ 0 → Non arid
  • 1 ≤ A.I ≤ 25 → Mild Arid
  • 26 ≤ A.I ≤ 50 → Moderate arid
  • A.I > 50 → Severe Arid

Optimum Number of rain Gauge: (N)


Cv = Coefficient of variation,

∈ = Allowable % Error,

σ = Standard deviation of the data, n = Number of stations,

image004 = mean of rainfall value

 Estimation of missing rainfall data



N1, N2,…Nx..Nn are normal annual precipitation of 1,2,…x…n respectively.

P1, P2…Pn are rainfall at station 1,2,…. N respectively.

And Px is the rainfall of station x.

Case: A minimum number of three stations closed to station ‘x’



If any of N1, N2, N3Nn > 10% of x

Mean rainfall Data

To convert the point rainfall values at various into an average value over a catchment the following three methods are in use

(i) Arithmetic Avg Method: 

When the rainfall measured at various stations in a catchment area is taken as the arithmetic mean of the station values.



P1, P2…Pn are rainfall values of stations 1,2…n respectively.

In practice, this method is used very rarely.

(ii) Thiessen Polygon Method: 

In this method, the rainfall recorded at each station is given a weightage on the basis of an area closest to the station.


Where, P1, P2…Pn are the rainfall data of areas A1, A2An

The Thiessen-polygon method of calculating the average precipitation over an area is superior to the arithmetic average method.

(iii) Isohyetal Method: 

An isohyet is a line joining points of equal rainfall magnitude. The recorded values for which a real average P is to be determined are then marked on the plot at appropriate stations. Neighboring stations outside the catchment are also considered.



 Evaporation & Evapo-Transpiration

Evaporation and its Measurement

Evaporation is a cooling process in which the latent heat of evaporation of about 585 cal/gm is provided by the water body. in this process, liquid changes into gaseous phase at the free surface, below the boiling point through the transfer of heat energy.

Dalton’s Law

The rate of evaporation is proportional to the difference between the saturation vapour pressure at the water temperature, es and the actual vapour pressure in the air ea .Thus


E = K(es-ea)


E = Rate if evaporation (mm/day)

es = Saturation vapour pressure of air (mm)

ea = Actual vapour pressure of air (mm)

es-eSaturation deficiency

Measurement of Evaporation

  1. ISI standard pan
                                                                                                     Lake evaporation = Cp × pan Evaporation
    Where, Cpan coefficient
    = 0.8 for ISI pan
    = 0.7 for class A-Pan
  2. Empirical Evaporation Equations (Meyer’s Formula)
    Where, km = Coefficients which accounts for size of water body.
    = 0.36 (for large deep water)
     0.50 (for small and shallow waters)
    e= Saturation vapour pressure of air in mm of Hg.
    ea = Actual vapour pressure of overlying air in mm at Hg at the specified height of 8 m.
    V9 = monthly mean wind velocity in km/hr at about 9 m above the ground level.
  3. 1/7th power Law


Where, V1 is the wind velocity at height H1 and V2 is the wind velocity at height H2.

Water Budget Method

This is the simplest method but it is least reliable it is used for rough calculation, it is based on mass conversation principle.

P + Vis + Vig = Vog + Vos+E + ΔS + TL


P=Daily precipitation on the water surface.

Vis = Daily surface inflow into lake.

Vos = Daily surface outflow from lake.

Vig = Daily underground inflow into the lake.

Vog = Daily underground outflow from the lake.

E = Daily Evaporation

ΔS = change in storage of lake

= +ve if increase in storage

= -ve if decrease in storage

T= Daily transpiration loss from the plants on the lake.

Energy Budget Method

The energy budget method is an application of the law of conservation of energy. The energy available for evaporation is determined by considering the incoming energy. Outgoing energy and energy stored in the water body over a known time interval.



Hn = Net heat energy received by the water surface


Hc(1-r) = incoming solar radiation into a surface of reflection coefficient, r

H= Back radiation from water body

H= Heat flux into the ground

HS = Heat stored in water body

Hi = Net heat conducted out the system by water flow (advected energy)

β = Bowen’s ratio

δ = Density of water

L = Latent heat of evaporation.


While transpiration takes place, the land area in which plants stands, also loses moisture by the evaporation of water from soil and water bodies. In hydrology and irrigation practice, it is found that evaporation and transpiration processes can be considered advantageously under one head as evapo-transpiration.

The real evapo-transpiration occurring in a specific situation is called actual evapo-transpiration (AET).

  • Penman’s Method

Penman’s equation is based on sound theoretical reasoning and is obtained by a combination of the energy balance and mass transfer approach.


Where, PET = daily evaporation in mm/day.

A = slope of the saturation vapour pressure v/s temperature curve at the mean air temperature in mm of Hg per °C.

Hn = Net radiation in mm of evaporable water per day

Ea = Parameter including wind velocity and saturation deficit.

γ = Psychometric constant

= 0.49 mm of Hg/°C

It is based on mass transfer and energy balance.

Transpiration Loss (T)

T = (w1+w2)-W


w= Initial weight of the instrument

W = Total weight of water added for full growth of plant.

w2 = Final weight of instruction including plant and water

T = Transpiration loss.

Streamflow Measurement

Streamflow representing the runoff phase of the hydrologic cycle is the most important basic data for hydrologic studies.

Streamflow measurement techniques can be broadly classified into two categories as:

  1. Direct Determination and
  2. Indirect Determination.

Under each category, there are a host of methods. The important ones are listed below:

  1. Direct determination of stream discharge
    1. Area velocity methods
    2. Dilution techniques
    3. Electromagnetic method and
    4. ultrasonic method
  2. Indirect determination of streamflow
    1. Hydraulic structures, such as weirs, flumes and gated structures, and
    2. Slope- area method

Determination of Velocity

    1. Float Method: Float are generally used to determine the approximate velocity of the surface, these are floating devices which are passed through the water along the flow of the stream.

Here, Vs = surface velocity

L= Distance travelled by the float in time ‘t’.

   2. Current Meters Method: these consists of rotating elements which rotate due to reactions of stream currents. The number of revolution per second are counted. This can be used to measure point velocity of any depth.

V = aNs + b


V = point velocity
N= Number of revolution per sec. a and b are current meters constant.

Velocity Distribution

(i) image006

For turbulent flow


image008 mean velocity

Vs = surface velocity



(ii) For shallow streams

image009 where image010 point velocity at 0.6 y from the surface

(iii) For Deep streams image011

Sounding Weight

image012 W = weight in Newton

image008Average stream velocity

Y = Depth of flow in meters.

Stream Flow (discharge measurement)

(i) Area Velocity Method: 

This method of discharge measurement consists essentially of measuring the area of cross-section of the river at a selected section called the gauging site and measuring the velocity of flow throughout the cross-sectional area. The gauging site must be selected with care to assure that the stage-discharge curve is reasonably constant over a long period of about a few years.

Total discharge,



(ii) Moving Boat Method: 
In this method, a special propeller type current meter which is free to move about a vertical axis is towed in a boat at a velocity VB at right angles to stream flow. If the flow velocity is VF the meter will align itself in the direction of the resultant velocity VR making an angle θ with the direction of the boat. Further. The meter will register the velocity VR if VB IS normal VF.



Where, qi = Discharge through the ith segment.


ti = Time required to pass the boat through ith segment.

(iii) Dilution Method: 

The dilution method of flow measurement, also known as the chemical method depends upon the continuity principle applied to a tracer which is allowed to mix completely with the flow.


This technique in which Q0 is estimated by knowing C1C2C0 and Q1 is known as constant rate injection method or plateau gauging.


Q= Discharge of stream

C= Tracer intensity initially

C1 = Tracer intensity at (1)

C= Tracer intensity at (2).


Q1 and Q2 are discharge at (1) and (2) respectively.

(iv) Slope-Area Method: 

It is a very versatile indirect method of discharge estimation and requires (i) the selection of a reach in which cross-sectional properties including bed elevations are known at its ends. (ii) the value of Manning’s n and (iii) water-surface elevations at the two end sections.




Hf = Frictional losses

He = Eddy losses




ke = Eddy loss coefficients.







Where, Q = stream flow (m3/sec)



Where, k = Conveyance



 Where, A = area (m2)

 R = Hydraulic Mean Radius



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Deepanshu RastogiDeepanshu RastogiMember since Jul 2020
cracked GATE DTU AIR 1130-GATE
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N.jayasriJun 10, 2019

In std deviation formula square is missing.... Please correct it
kr rahul

kr rahulJul 29, 2019

should we read the detail nptel notes first to understand the notes given provided by grade up.
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How to view this article i am unable to view any article plz help??
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Prakash 1995Aug 23, 2019

How to download

Study material notes ????
Yashwanthraj Raj
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Transpiration loss
In the formula there is a mistake sir plz rectify it sir
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