Estimation Methods of Evaporation. Examples for Revision

TABLE OF CONTENTS

1.0 Introduction

2.0 Evaporation

3.0 Principles of Evapotranspiration

4.0 Estimation Methods of Evaporation
4.1 Energy Balance Method
4.2 Aerodynamic Method
4.3 Combination Method
4.4 Priestley-Taylor Method

5.0 Sample Problems

References:

1.0 Introduction

Evaporation is the process that liquid water enters the atmosphere as water vapour and replenishes the humidity of the air.¹ It is also considered as the pathway in which the water travels from its liquid state back into the hydrologic cycle as an atmospheric water vapor. Water bodies such as oceans, seas lakes and rivers provide nearly 90% of the moisture in the atmosphere through evaporation, as some study reveals.²

The ebook discusses the principles of evaporation as one of the processes in the hydrologic cycle and the different methods to estimate the evaporation rate. Four (4) different methods namely; the energy balance, aerodynamics, combination method and priestley-taylor method are included in the discussion.

2.0 Evaporation

Evaporation occurs when water is heated, thus the evaporation process needs the heat from the sun. Evaporation also helps form the clouds, and then the clouds will release the moisture in the form of rain or snow. When precipitation falls, it is again waiting to be evaporated, and that is how the water cycle starts all over again.³ In a simple point of view, evaporation is the process by which liquid turns into gas.⁴

Two factors influencing evaporation:⁵

- Supply of energy to provide the latent heat of vaporization (Solar radiation)
- Wind velocity and specific humidity,

Meteorological factors affecting evaporation:⁶

1) Solar radiation
2) Wind
3) Relative humidity
4) Temperature

3.0 Principles of Evapotranspiration

Vegetation needs water, and its water demand differs on its kind of specie. The water required by a certain vegetation to grow passes through its roots and to the stem and eventually transpired into the atmosphere. If the land surface is covered with vegetation, the evaporation and transpiration simultaneously occurs which is known as the process of evapotranspiration.⁷

Evapotranspiration is the collective process of evaporation from the land surface and the transpiration from vegetation.⁸ Aside from the two factors influencing evapotranspiration as mentioned previously, evapotranspiration is also influenced by another factor which is the supply of moisture at the evaporatove surface.⁹ In general, the term evapotranspiration is the totality of evaporation and transpiration.

The Potential Evapotranspiration (PET) is the amount of evaporation calculated from a well vegetated surface.¹⁰ “Potential evapotranspiration is the evaporation from an extended surface of a short green crop which fully shades the ground, exerts little or negligible resistance to the flow of water, and is always well supplied with water.”¹¹

Potential evapotranspiration (PE), assumes no control of water, is defined as a measure of the ability of the atmosphere to remove water from the surface by the processes of both the evaporation and transpiration.¹²

4.0 Estimation Methods of Evaporation

The following are the different methods used in the estimation of evaporation rate.¹³

4.1 Energy Balance Method

Abbildung in dieser Leseprobe nicht enthalten

(Eq.1)

If the sensible heat flux Hs and the ground heat flux, G are both zero, Equation 2 can be used.

Abbildung in dieser Leseprobe nicht enthalten

(Eq.2)

where:

Er = evaporation rate

Rn = net radiation

Iv = latent heat of vaporization

Iv = 2500 – 2.36T

T = Temperature

Pw = density of water

The energy balance method (latent heat flux) is calculated as the residual term in the general energy balance equation.¹⁴

4.2 Aerodynamic Method

¹⁵ The first factor controlling the evaporation is the heat energy which was the main concern of the Energy balance method, but the second controlling factor is the ability to transport vapor. Aerodynamic method is concerned on this factor which is governed by the humidity gradient and wind speed.¹⁶

Abbildung in dieser Leseprobe nicht enthalten

)(Eq. 3)

Abbildung in dieser Leseprobe nicht enthalten

(Eq. 4)

where:

Ea = evaporation rate

B = vapor transfer coefficient

ea = vapor pressure

eas = vapor pressure at the surface

z0 = roughness height

u2 = wind speed

4.3 Combination Method

¹⁷ Evaporation rate can also be computed by combining the two previous methods of Energy Balance and Aerodynamic methods.

Abbildung in dieser Leseprobe nicht enthalten

(Eq. 5)

where:

Abbildung in dieser Leseprobe nicht enthalten

(Eq. 6)

Abbildung in dieser Leseprobe nicht enthalten

(Eq. 7)

Δ = gradient of saturated vapor pressure

g = psychrometric constant

Er = Evaporation rate from Energy balance method

Ea = Evaporation rate from Aerodynamics method

Cp = specific heat at constant pressure

Kh = heat diffusivity

Kw = vapor diffusivity

Kh/Kw = commonly taken equivalent to 1

4.4 Priestley-Taylor Method

Abbildung in dieser Leseprobe nicht enthalten

(Eq. 7)

where:

Abbildung in dieser Leseprobe nicht enthalten

¹⁸ The Priestley-Taylor equation is useful for conditions where weather inputs for the such as relative humidity and wind speed are not available.¹⁹

The Priestley-Taylor coefficient, a, is the fraction of surface moisture available for evaporation. Several authors had presented different methods for the determination of a such as Holtslag and Van Ulden (1983), Steiner et al. (1991) and German (2000).²⁰

5.0 Sample Problems

Problem 1:

Assuming there is no sensible heat in an open water surface, determine the evaporation rate (Er) using the following data:

Net Radiation – 190 W/m[2]

Air temperature - 20[0]C

Use the energey Balance Method.

Solution:

Abbildung in dieser Leseprobe nicht enthalten

The density of water should be taken from Table 1 with respect to its temperature. Using the 20[0]C air temperature, the density of water is 998 kg/m[3]. In case the air temperature is not included in the table, you may use interpolation.

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¹ Kara Rogers, Evaporation, Encyclopaedia Britannica, https://www.britannica.com/science/evaporation

² Howard Perlman, The Water Cycle: Evaporation, U.S. Geological Survey's (USGS) Water Science School, 2016, https://water.usgs.gov/edu/watercycleevaporation.html

³ Evaporation, National Geographic, https://www.nationalgeographic.org/encyclopedia/evaporation/

⁴ eSchoolToday (2017), https://www.eschooltoday.com/water-cycle/what-is-evaporation-of-water.html

⁵ Ven Te Chow, David Maidment, Larry Mays, Applied Hydrology, International Edition (1988), McGraw-Hill Book Company

⁶ E.M. Wilson, Engineering Hydrology, 4th Edition, 1990, Macmillan International Higher Education

⁷ E.M. Wilson, Engineering Hydrology, 4th Edition, 1990, Macmillan International Higher Education, p 35

⁸ Ven Te Chow, David Maidment, Larry Mays, Applied Hydrology, International Edition (1988), McGraw-Hill Book Company, p 80

⁹ Ibid, p 81

¹⁰ Ibid

¹¹ M B Kirkman, Potential of Soil and Plat Water Relations, Academic Press, 2005, https://www.sciencedirect.com/science/article/pii/B9780124097513500268

¹² Pidwirny, M. (2006). "Actual and Potential Evapotranspiration". Fundamentals of Physic Geography, 2nd Edition. http://www.physicalgeography.net/fundamentals/8j.html

¹³ Ven Te Chow, David Maidment, Larry Mays, Applied Hydrology, International Edition (1988), McGraw-Hill Book Company, p 83

¹⁴ A. Ershadi, M.F. McCabe , J.P. Evans, J.P. Walker, Evaluation of energy balance, combination, and complementary schemes for estimation of evaporation, Proceedings of IAHS Lead Symposia held during IUGG2011 in Melbourne, Australia, July 2011) (IAHS Publ. 3XX, 2011), http://users.monash.edu.au/~jpwalker/papers/iugg11.pdf

¹⁵ Ven Te Chow, David Maidment, Larry Mays, Applied Hydrology, International Edition (1988), McGraw-Hill Book Company, p 84

¹⁶ Ibid

¹⁷ Ibid, 86

¹⁸ Ibid, 89

¹⁹ Priestley-Taylor Equation, 2009,CRA-CIN http://bioma.jrc.ec.europa.eu/components/componentstools/evapotranspiration/help/Priestley-Taylor.html

²⁰ Priestley-Taylor Coefficient, 2009,CRA-CIN http://bioma.jrc.ec.europa.eu/components/componentstools/evapotranspiration/help/Priestley-Taylor_coefficient.html