Method of determining consumptive use or evapotranspiration

A. Direct method

a) Water balance method:

• Water balance method is a measurement of continuity of flow of water.
• The method consists of drawing up a balance sheet of all the water entering and leaving a particular catchment or drainage basin.
• The equation can be written as:

ET= I+P-RO-DP+CR+SF+SW

Where,

I= irrigation, P= Precipitation, SFI=Surface flow into the control volume

LI = Subsurface lateral flow into the control volume, GW =Ground water seepage into the control volume

ET=Evapotranspiration, RO=Surface flow out of the control volume

LO =Subsurface lateral flow out of the control volume

L=Leaching requirement, Dp =Deep percolation

b) Lysimeter method:

• A water tight tank of cylindrical shape having a diameter about 2 m and depth of 3 m is placed vertically in ground.
• The tank is filled with soil sample.
• Bottom of the tank consists of sand layer and a pan for collecting surplus water.
• The consumptive use is measure by the amount of water required for the satisfactory growth of the plants with in tank.

Cu = W_a – W_d

Where, W_a = Water applied

W_d = water drained off.

B. By using empirical formula

a) Penman Equation to Estimate PET:

Mathematically,

Where,

ET= Daily potential evapotranspiration (mm/day)

Δ= Slope of the saturated vapor pressure verses temperature curve at the mean air temperature(mm Hg/oc)

Hn= Net incoming solar radiation or energy expressed in mm of evaporated water per day

Ea= Aerodynamic component(parameter includes wind velocity and saturation deficit; mm/day)

r= Psychromatric constant(=0.49mm Hg/oc)

And in the above equation, net radiation (Hn) is estimated by following equation;

 H_n=H_c(1-r)(a+bn/N)-σTa⁴(0.56-o.092√e_a)(0.1+0.9n/N)

Where;

H_c= Mean incident solar radiation at the top of the atmosphere on a horizontal surface, expressed in mm of evaporated water per day

r= Reflection coefficient (albedo) of a given area

a= A constant depending upon the latitude & is given by a=0.29cosɵ

b= A constant having the average value 0.52

n= Actual duration of bring sunshine in hours

N= Maximum possible hours of bright sunshine(mean value) & is function of latitude

σ= Stefen-Bolzman constant 2.01×10-9 mm/day

T_a= Mean air temperature in 0K

e_a= Actual vapor pressure in the air in mm of Hg.

• The parameter E_a (aerodynamic component is estimated as

Ea=0.35[1+(V₂/160)]+(es-ea)

Where;

V₂= Mean wind velocity of 2m above the ground in km/day

e_s= Saturated vapor pressure

e_a= Actual mean vapor pressure

b) Modified Penman equation:

• Doorenbos and Pruitt (1975) proposed a modified Penman method for estimating fairly, accurately the reference crop ET and gave the tables to facilitate the necessary computation.
• Mathematically,

E_tp= W R_n + (1-w) f(u) (e_s-e_a)

Where,

E_tp = Unadjusted potential evapotranspiration in mm/day

W= Temperature related weighing factor (dimensionless) (table)

R_n= Net radiation in mm of evaporable water per day

(1-w) = Temperature & elevation related weighing factor for effect of wind & humidity on ET (table)

f(u)= Wind related function (table)

e_s= Saturated vapor pressure

e_a= Actual vapor pressure

c) Blaney-criddle method

• Blaney and criddle developed a simplified formula in which CU of water is related with temperature and day time hours.

CU=ΣKTP/100……….in English unit

CU=KP(0.46T+8.13)……….in English unit

Where

CU = Monthly consumptive use of water for a given period in inch

K= Empirical consumptive use crop coefficient or a month

W= Temperature related weighing factor dimensionless (table)

T= Mean monthly temperature in ^oF

P= Monthly day light hour express as percentage of day light hour of the year

d) Thornthwaite method

Thornthwaite proposed a formula for ET calculation when data other than temperature are not available.

E=1.6 [10 x T/I]4

Where

E= Potential ET in mm/month

T= Mean monthly temperature in oC

I= Annual or seasonal heat index

I=Σi=[T/5]1.514…………………..i is monthly heat index

a= Empirical constant=0.000000675 I3-0.0000771 I2+0.01792 I+0.49239

E is corrected by Multiplying it by correction factor given in table to give PET.

This method is not so applicable and gives false reading at zero degree Celsius.

e. Radiation method

Doorebnos and Pruitt proposed a formula for calculation of consumptive use of water based on the data given about temperature and sunshine.

Cu=a+bwR_s

Where

Cu= Consumptive use of water in mm per day

w= Weightage factor which depends on temperature & altitude

R_s= Solar radiation in terms of mm of evaporable water per day

a,b= Constants given in table