Analytical Methods of Evaporation Estimation

Analytical Methods of Evaporation Estimation
Analytical Methods of Evaporation Estimation

Analytical Methods of Evaporation Estimation

 The analytical methods for the determination of lake evaporation can be broadly classified into three categories as

  •    Water budget method,
  •    Energy-balance method, and
  •    Mass-transfer method.

Water-Budget Method

 The water-budget method is the simplest of the three analytical methods and is also the least reliable. It involves writing the hydrological continuity equation for the lake and determining the evaporation from a knowledge or estimation of other variables. Thus, considering the daily average values for a lake, the continuity equation is written as

P + VIS + VIG = VOS + VOG + EL + ΔS +TL


  • P = daily precipitation 
  • VIS = daily surface inflow into the lake
  • VIG =daily groundwater inflow
  • VOS = daily surface outflow from the lake
  • VOG = daily seepage outflow
  • EL = daily lake evaporation
  • ΔS = increase in lake storage in a day 7 daily transpiration loss
  • TL =daily transpiration loss

All quantities are in units of volume (m') or depth (mm) over a reference area. Equation (3.6) can be written as

EL=P+(VIS-VOS)+(VIG-VOG)-TL-ΔS                                                                       (3.7)

 In this, the terms P. V V, and AS can be measured. However, it is not possible to measure V V and T, and therefore these quantities can only be estimated Transpiration losses can be considered to be insignificant in some reservoirs. If the unit of time is kept large, say weeks or months, better accuracy in the estimate of E is possible. In view of the various uncertainties in the estimated values and the possibilities of errors in measured variables, the water-budget method cannot be expected to give very accurate results. However, controlled studies such as at Lake Hefner in USA (1952) have given fairly accurate results by this method.

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. Considering the water body as in below Fig. the energy balance to the evaporating surface in a period of one day is give by

Hn = Ho + He + Hg + Hs + Hi 

Hn = net heat energy received by the water surface 
=He (1-r)-Hb

Energy balance in water body
fig:-Energy balance in water body

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

  • Hb = back radiation from water body
  • Ha=sensible heat transfer from water surface to air
  • He=heat energy used up in evaporation


where ρ =density of water L=latent heat of evaporation , EL=evaporation in mm

  • Hg=heat flux into the ground
  • Hs=heat stored in water body
  • Hi=net heat conducted out of the system by water flow

All the energy terms are in calories per square mm per day. If the time periods are short, the terms Hs, and Hi, can be neglected as negligibly small. All the terms except Ha, can either be measured or evaluated indirectly. The sensible heat term, which cannot be readily measured is estimated using Bowen's ratio β given by the expression

β=Ha/(ρLEL) =6.1 x 10-4 x pa ((Tw-Ta)/(ew-ea))

where p =atmospheric pressure in mm of mercury,

ew=saturated vapour pressure in mm of mercury

ea=actual vapour pressure of air in mm of mercury.

 Temperature of water surface in ︒C and 

, temperature of air in ︒C From Eqs (3.8) and (3.9) EL can be evauated as

EL = (Hn – Hg –Hs - Hi)/ (ρL(1+β))

 Estimation of evaporation in a lake by the energy balance method has been found to give satisfactory results, with errors of the order of 5% when applied to periods less than a week

Mass-Transfer Method

This method is based on theories of turbulent mass transfer in boundary layer to calculate the mass water vapour transfer from the surface to the surrounding atmosphere However, the details of the method can be found in published literature With the use of quantities measured by sophisticated (and expensive) instrumentation, this method can give satisfactory results


Following observation were made for conducting the water budget of a reservoir over a period of one month of 30 days

Average surface area 10 km2 

Rainfall = 10 cm 

Mean surface inflow rate=10m3/s 

Mean surface outflow rate= 15m3/s 

Fall in reservoir level=150m 

Pan evaporation =20 cm 

Assume pan evaporation coefficient = 0.70 


  Estimate the average seepage discharge during that month


 Area of reservoir = 10 x 10 m




VOLUME( m3) 






SURFACE OUTFLOW=15*3600*24*30 








Seepage volume = se 


Total inflow volume 


Total outflow 


Reduction in storage =10*106*1.5 




 Reduction in storage = Total inflow volume - Total outflow volume

(40,280,000+se )-(26,920,000) = 15,000,000 

se = 1,640,000 = 164 Mm3. 29687


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