### MEASUREMENT OR ESTIMATION OF EVAPORATION | HYDROLOGY

Estimation of evaporation is of utmost importance in many hydrologic problems associated with planning and operation of reservoirs and irrigation systems.

In arid zones, this estimation is particularly important to conserve the scarce water resources.

However, the exact measurement of evaporation from a large body of water is indeed one of the most difficult tasks.

The amount of water evaporated from a water surface is estimated by the following methods:

(1) Using evaporimeter data

(2) Empirical evaporation equations and

(3) Analytical methods

**(1) EVAPORATION PAN METHOD**

Evaporimeters are water-containing pans which are exposed to the atmosphere and the loss of water by evaporation is measured in them at regular intervals. Meteorological data, such as humidity, wind movement, air and water temperatures, and precipitation are also noted along with evaporation measurement.

Many types of evaporimeters are in use and a few commonly used pans are described here :

**1) US WEATHER BUREAU CLASS A PAN :**

The US Weather Bureau Class A Pan or surface pan evaporimeter along with its dimensions is shown in Figure.

The pan diameter is 120 cm, depth 25 cm and is painted white.

The pan is kept on a wooden platform as shown in the figure so that air can circulate freely.

The height of the wooden frame is kept at 15 cm above the ground surface.

The depth of water in the pan is maintained at 20 cm.

A hook gauge fixed on the stilling well of the pan is used to measure the water level. Evaporation is measured by a hook gauge in a stilling well.

Water level is measured daily.

Water is added every day up to the fixed level.

Pans of about 1.0 m diameter have higher rates of evaporation than that from a large free water surface.

It has been observed that a 3.0 m diameter pan gives a value which is nearly the same as in a nearby lake.

Lake evaporation = Pan coefficient * Pan evaporation

Average value of Pan coefficient is 0.70

**2) ISI STANDARD PAN :**

This span evaporimeter specified by IS: 5973-1970, also known as modified Class A Pan, consists of a pan 1220 mm in diameter with 255 mm of depth.

The pan is made of copper sheet of 0.9 mm thickness, tinned inside and painted white outside.

A fixed point gauge indicates the level of water. A calibrated cylindrical measure is used to add or remove water maintaining the water level in the pan to a fixed mark.

The top of the pan is covered fully with a hexagonal wire netting of galvanized iron to protect the water in the pan from birds.

Further, the presence of a wire mesh makes the water temperature more uniform during day and night.

The evaporation from this pan is found to be less by about 14% compared to that from an unscreened pan.

The pan is placed over a square wooden platform of 1225 mm width and 100 mm height to enable circulation of air underneath the pan.

Lake evaporation = Pan coefficient * Pan evaporation

Average value of Pan coefficient is 0.80

**3) COLORADO SUNKEN PAN :**

This pan, 920 mm square and 460 mm deep, is made up of unpainted galvanized iron sheet and buried into the ground within 100 mm of the top.

The chief advantage of the sunken pan is that radiation and aerodynamic characteristics are similar to those of a lake.

However, it has the following disadvantages:

- Difficult to detect leaks
- Extra care is needed to keep the surrounding area free from tall grass, dust, etc.,
- Expensive to install

Lake evaporation = Pan coefficient * Pan evaporation

Average value of Pan coefficient is 0.78

**4) US GEOLOGICAL SURVEY FLOATING PAN:**

With a view to simulate the characteristics of a large body of water, this square pan (900 mm side and 450 mm depth) supported by drum floats in the middle of a raft (4.25 m * 4.87 m) is set afloat in a lake. The water level in the pan is kept at the same level as the lake leaving a rim of 75 mm. Diagonal baffles provided in the pan reduce the surging in the pan due to wave action. Its high cost of installation and maintenance together with the difficulty involved in performing measurements are its main disadvantages.

Lake evaporation = Pan coefficient * Pan evaporation

Average value of Pan coefficient is 0.80

**(2) EMPIRICAL METHODS **

**1) MEYER'S FORMULA **

E

_{L }= Lake evaporation in mm/day

e_{w} = Saturated vapour pressure at the water surface temperature in mm of mercury

e_{a} = Actual vapour pressure of overlying air at a specified height in mm of mercury

V_{9 } = Monthly mean wind velocity in km/h at about 9 m above ground and

K_{M} = Coefficient accounting for various other factors with a value of 0.36 for large deep waters and 0.50 for small, shallow waters.

**2) ROHWER'S FORMULA **

Rohwer's formula considers a correction for the effect of pressure in addition to the wind-speed effect and is given by :

E_{L } = Lake evaporation in mm/day

e_{w} = Saturated vapour pressure at the water surface temperature in mm of mercury

e_{a} = Actual vapour pressure of overlying air at a specified height in mm of mercury

p_{a} = Mean barometric reading in mm of mercury

V = Mean wind velocity in km/h at ground level, which can be taken to be the velocity at 0.6 m height above ground

These empirical formulae are simple to use and permit the use of standard meteorological data.

However, in view of the various limitations of the formulae, they can at best be expected to give an approximate magnitude of the evaporation.

**(3) ANALYTICAL METHODS**

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

**1) 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 + V_{is}
+ V_{ig} = V_{os} + V_{og} + E_{L} + △S + T_{L}

P = Daily precipitation

V_{is} = Daily surface inflow into the lake

V_{ig} = Daily groundwater inflow

V_{os} = Daily surface outflow from the lake

V_{og} = Daily seepage outflow

E_{L} = Daily lake evaporation

△S = Increase in lake storage in a day

T_{L} = Daily transpiration loss

All quantities are in units of volume (m³) or depth (mm) over a reference area.

Equation can be written as :

E_{L}
= P + (V_{is} - V_{os} ) + (V_{ig} – V_{og} ) -
△S - T_{L}

In this, the terms P, V_{is} , V_{os} and △S can be measured. However, it is not possible to measure V_{ig} , V_{og} and T_{L} 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 is possible.

**2) 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 shown in Figure, the energy balance to the evaporating surface in a period of one day is given by :

H_{n}
= H_{a} + H_{e} + H_{g} + H_{s} + H_{i}

where H_{n}
= Net heat energy received by the water surface

= H_{c} (1 – r) - H_{b}

H_{c} (1 – r) = incoming solar radiation into a surface of reflection coefficient (albedo) r

H_{b} = back radiation (long wave) from water body

H_{a} = sensible heat transfer from water surface to air

H_{e} = heat energy used up in evaporation

= ρLE_{L }

where

ρ = density of water, L = latent heat of evaporation and E_{L} = evaporation in mm

H_{g} = heat flux into the ground

H_{s} = heat stored in water body

H_{i} = net heat conducted out of the system by water flow (advected energy)

All the energy terms are in calories per square mm per day. If the time periods are short, the terms H, and H, can be neglected as negligibly small. All the terms except

H can either be measured or evaluated indirectly. The sensible heat term H, which cannot be readily measured is estimated using Bowen's ratio β given by the expression

p_{a} = atmospheric pressure in mm of mercury

e_{w} = saturated vapour pressure in mm of mercury

e_{a} = Actual vapour pressure of air in mm of mercury

T_{w} = temperature of water surface in °C and

T_{a} = temperature of air in °C

E_{L }can be evaluated as

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.

**3) MASS TRANSFER METHOD :**

When wind flows on the surface, a boundary layer is formed. The method is based on turbulent mass transfer in this boundary layer to calculate the mass of water vapour transferred from the surface to the surrounding atmosphere.

It is also known as vapour flow approach or aerodynamic approach. It is assumed that wind velocity in the vertical is logarithmic and atmosphere is adiabatic.

The evaporation is expressed as :

E_{L} = Evaporation in mm/h

z_{1} , z_{2} = Arbitrary levels about water surface levels in metres

e_{1}
, e_{2} = Vapour pressures at z_{1} , z_{2} in mm Hg

v_{1}
, v_{2} = wind velocity at z_{1} , z_{2} in km/h

T= Average temperature in °C between z_{1} , z_{2}

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