Precipitation, Evaporation and Evapotranspiration Study Notes

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

C_v = 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,…N_x..N_n are normal annual precipitation of 1,2,…x…n respectively.

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

And P_x is the rainfall of station x.

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

If any of N₁, N₂, N₃…N_n > 10% of N­_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…P_n 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…P_n are the rainfall data of areas A₁, A₂…A_n. 

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, e_s and the actual vapour pressure in the air e_a .Thus

Thus,  

E = K(e_s-e_a)

Where,

E = Rate if evaporation (mm/day)

e_s = Saturation vapour pressure of air (mm)

e_a = Actual vapour pressure of air (mm)

e_s-e_a Saturation deficiency

Measurement of Evaporation

1. ISI standard pan     Lake evaporation = C_p × pan Evaporation
   Where, C_p pan coefficient
   = 0.8 for ISI pan
   = 0.7 for class A-Pan
2. Empirical Evaporation Equations (Meyer’s Formula)
                                                     
   Where, k_m = Coefficients which accounts for size of water body.
   = 0.36 (for large deep water)
   ∼ 0.50 (for small and shallow waters)
   e_s = Saturation vapour pressure of air in mm of Hg.
   e_a = 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 + V_is + V_ig = V_og + V_os+E + ΔS + T_L

Where,

P=Daily precipitation on the water surface.

V_is = Daily surface inflow into lake.

V_os = Daily surface outflow from lake.

V_ig = Daily underground inflow into the lake.

V_og = 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_L = 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,  

H_n = Net heat energy received by the water surface

H_n = H_c(1-r)-H_b

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

H_b = Back radiation from water body

H_g = Heat flux into the ground

H_S = Heat stored in water body

H_i = 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.

H_n = Net radiation in mm of evaporable water per day

E_a = 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, 

w₁ = 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.