# Hydrology & Irrigation : Precipitation, Evaporation and Evapotranspiration Study Notes

By Deepanshu Rastogi|Updated : November 8th, 2021

Complete coverage of syllabus is very important aspect for any competitive examination but before that important subject and their concept must be covered thoroughly. In this article we are going to discuss the fundamental of Precipitation, Evaporation and Evapotranspiration which is very useful for SSC JE and other AE-JE Exams.

## Precipitation & General aspects of Hydrology

#### Index of Wetness

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

#### Aridity index

Where

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)

where

Cv = Coefficient of variation,

∈ = Allowable % Error,

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

= mean of rainfall value

#### Estimation of missing rainfall data

where,

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.

Where,

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 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

Thus,

E = K(es-ea)

Where,

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

Where,

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.

Where,

Hn = Net heat energy received by the water surface

HHc(1-r)-Hb

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.

#### Evapo-Transpiration

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)-w2

Where,

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.

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