2. 7. Meteorological factors determining ETo PPT chapter 2 of 2.pdfWhere ET0 is in mmd-1. Rs is the incoming solar short wave radiation in MJm-2d-1. Constant 2.45 is the latent heat

2. 7. Meteorological factors determining ETo

� ETo is a function of air temperature, radiation , temperature, humidity and wind speed data for daily, weekly, ten-day or monthly calculations

Solar radiation

� The largest energy source for evapotranspiration process

� The amount reaching the surface is determined by its location and time of the year

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� The actual solar radiation reaching the evaporating surface depends on the turbidity of the atmosphere and the presence of clouds

Air temperature

� Source: solar radiation absorbed by the atmosphere and heat emitted by the earth

2. 7. Meteorological factors determining ETo

Air humidity

� Water content of the air

� The difference between the water vapour pressure at the evapotranspiring surface and the surrounding air is the determining factor for the vapour removal.

Wind speed

2

Wind speed

� Removes the saturated vapour pressure above the evaporating surface.

� The (average) daily wind speed (m s-1) measured at 2 m above the ground level is required.

2. 7. Empirical methods of estimating ETo

� The FAO groups of scientists have screened 31 empirical formulae for predicting the ETo the following six methods will be discussed, which are used under different climatic conditions:

1. Pan evaporation2. Blaney-criddle method3. Hargreaves Method4. Thornthwaite Method

3

4. Thornthwaite Method5. Radiation method, and6. Modified penman method

� The modified Penman method was considered to offer the best results with minimum possible error in relation to a grass reference crop.

� Three major steps involved in the estimation of ET of the crop:

* Estimation of reference evapotranspiration (ETo)* Determination of the crop coefficient (kc), and* Appropriate adjustments to management and crop environment condition.

2. 7. Empirical methods of estimating Eto1. Pan evaporation

� Evaporation pans provide a measurement of the combined effectof temperature, humidity, windspeedand sunshine on the reference crop evapotranspiration ETo

� Many different types of evaporation pans are being used. The best known

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pans are being used. The best known pans are the Class A evaporation pan.

� To relate pan evaporation to ETo, empirically derived pan coefficients are suggested

Kpan*EpanEto =

� Class A evaporation pan, the K pan varies between 0.35 and 0.85. Average K pan = 0.70. Normally details of the pan coefficient are usually provided by the supplier of the pan.

2. 7. Empirical methods of estimating Eto2. Blaney –Criddle Method:

� ETo calculated by using measured temperature data only. � This method is not very accurate; it provides a rough estimate or "order

of magnitude" only � Especially under "extreme" climatic conditions in windy, dry, sunny

areas, the ETo is underestimated (up to some 60 percent), while in calm, humid, clouded areas, the ETo is overestimated (up to some 40

5

calm, humid, clouded areas, the ETo is overestimated (up to some 40 percent).

)8*46.0( += TmeanPEToLatitu

deNorth Jan Feb Mar Apr May Jun

eJuly Aug Sep

tOct Nov Dec

South

July Aug Sept

Oct Nov Dec Jan Feb Mar Apr May June

60° 0.15 0.20 0.26 0.32 0.38 0.41 0.4 0.34 0.28 0.22 0.17 0.1355 0.17 0.21 0.26 0.32 0.36 0.39 0.38 0.33 0.28 0.23 0.18 0.1650 0.19 0.23 0.27 0.31 0.34 0.36 0.35 0.32 0.28 0.24 0.2 0.1845 0.20 0.23 0.27 0.30 0.34 0.35 0.34 0.32 0.28 0.24 0.21 0.240 0.22 0.24 0.27 0.30 0.32 0.34 0.33 0.31 0.28 0.25 0.22 0.2135 0.23 0.25 0.27 0.29 0.31 0.32 0.32 0.3 0.28 0.25 0.23 0.2230 0.24 0.25 0.27 0.29 0.31 0.32 0.31 0.3 0.28 0.26 0.24 0.2325 0.24 0.26 0.27 0.29 0.30 0.31 0.31 0.29 0.28 0.26 0.25 0.2420 0.25 0.26 0.27 0.28 0.29 0.3 0.3 0.29 0.28 0.26 0.25 0.2515 0.26 0.26 0.27 0.28 0.29 0.29 0.29 0.28 0.28 0.27 0.26 0.2510 0.26 0.27 0.27 0.28 0.28 0.29 0.29 0.28 0.28 0.27 0.26 0.265 0.27 0.27 0.27 0.28 0.28 0.28 0.28 0.28 0.28 0.27 0.27 0.270 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

ETo = Reference crop evapotranspiration (mm/month) T mean = mean monthly (°C) p = mean monthly percentage of annual daytime hours

2. 7. Empirical methods of estimating Eto3. Hargreaves Method:

� Requires only maximum and minimum daily air temperature observations

� temperatures are in 0C and ET in mm/day, Ra is the extraterrestrial

( ) ( ) amean RTTTET 8.170023.0 5.0minmax0 +−=

6

� temperatures are in C and ET in mm/day, Ra is the extraterrestrial short wave radiation in mm/day

� The Hargreaves method should agree within 15% of Modified Penman-Monteith calculations.

� Temperature difference is used to consider relative humidity, since they have linear relation.

2. 7. Empirical methods of estimating Eto4. Thornthwaite Method:

� Used to predict monthly evapotranspiration from mean monthly temperature

a

o I

TE

= 1016

5.112

1 5∑=

=i

iTI

7

� Originally developed for the climatic conditions of the east-central US. It was subsequently modified to accommodate a range of climates.

32 000000675.00000771.00179.049.0 IIIa +−+=

Where: ETo = Monthly reference crop evapotranspiration (mm/month) T = Mean monthly temperature (°C) a = is the location dependant coefficientI = is the heat index described below

2. 7. Empirical methods of estimating Eto5. Radiation Methods:

� Radiation methods use solar radiation coupled with air temperaturedata to estimate the reference evapotranspiration ETo.

�The Priestley-Taylor (1972) equation has the form

λγα GR

ET no

−+∆∆=

8

� The Makkink (1957) method is commonly used in western Europe

Where ET0 is in mmd-1. Rs is the incoming solar short wave radiation in MJm-2d-1. Constant 2.45 is the latent heat of vaporization at about 20 oC

λγ+∆Whereα is usually taken as 1.26. ET0 is in mmd-1, Rn is the net radiation, G the soil heat flux in MJm-2d-1, λ the latent heat of vaporization in MJkg-1 and γ and g are as defined for the Penman equations (kPa0C-1)

12.045.2

61.0 −+∆∆= s

o

RET

γ

2. 7. Empirical methods of estimating Eto6. Modified penman method:

� In 1990 experts and researchers was organized by FAO, to review FAO 24 methodologies on crop water requirement.

( )( )2

2

34.01273

900)(408.0

U

eeUT

GRET

asn

o ++∆

−+

+−∆=

γ

γ

9

whereETo :reference evapotranspiration [mm day-1],Rn :net radiation at the crop surface [MJ m-2 day-1],G :soil heat flux density [MJ m-2 day-1],T :mean daily air temperature at 2 m height [°C],U2 :wind speed at 2 m height [m s-1],es :saturation vapour pressure [kPa],ea :actual vapour pressure [kPa],es - ea :saturation vapour pressure deficit [kPa],∆ :slope vapour pressure curve [kPa °C-1],γγγγ :psychrometric constant [kPa °C-1].

( )234.01 U++∆ γ

2. 7. Empirical methods of estimating Eto5. Modified penman method ...

Energy balance

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Shortwave radiation is colored purple and longwave radiation is in red.

2. 7. Empirical methods of estimating Eto5. Modified penman method . . .

� The equation uses standard climatological records (solar radiation (sunshine), air temperature, humidity and wind speed) and site location

Net radiation (Rn)

� Measured by pyranometers, radiometers or solarimeters

� The difference between incoming and outgoing radiation of both short and long

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wavelengths. (+ve daytime and –ve nighttime)

Rn = Rns - Rnl

The net radiation (Rn) is the difference between the incoming net shortwave radiation (Rns) and the outgoing net longwave radiation (Rnl) [MJ m-2 day-1]

Net shortwave radiation (Rns)

� is the difference between incoming and outgoing shortwave radiation expressed as:

Rns = (1-α)Rs

Rns net shortwave radiation [MJ m-2 day-1], Rs the incoming solar radiation [MJ m-2 day-1]. α albedo or reflection coefficient, which is 0.23 for the hypothetical grass reference crop


Solar radiation (Rs)

� Not measured, it can be calculated with the Angstrom formula which relates solar radiation to extraterrestrial radiation and relative sunshine duration:

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Rs :incoming shortwave radiation [MJ m-2 day-1], n :actual duration of sunshine [hour], N :maximum possible duration of sunshine or daylight hours [hour],Ra :extraterrestrial radiation [MJ m-2 day-1], as and bs : constants, the values as = 0.25 and bs = 0.50 are recommended.


Extraterrestrial radiation for daily periods (Ra)� Solar radiation reaching the earths atmosphere. On average the extraterrestrial

irradiance is 1367 (W/m2). varies by ±3% as the earth orbits the sun.� Ra, for each day of the year and for different latitudes can be estimated from the

solar constant, the solar declination and the time of the year by:

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Earth-Sun inverse relative distance (dr)Average 1.496 x 1011 m defined as one astronomical unit (1 AU).

Ra :extraterrestrial radiation [MJ m-2 day-1],Gsc :solar constant = 0.0820 MJ m-2 min-1,dr :inverse relative distance Earth-Sun,ωs :sunset hour angle [rad],ϕ :latitude [rad], +ve N and –ve for S hemisphereδ :solar decimation [rad].

+= JCosd r 365

2033.01

πJ is the number of the day in the year between 1 and 365


Earth rotating on its axis of rotation

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solar declination ( δδδδ)

Angle between center of the earth to center of sun to the equatorial planeJ is the number of the day in the year


The sunset hour angle ( ωωωωs)

� To describe the earth's rotation about its polar axis, we use the concept of the hour angle

� Angular distance between the meridian of the observer and the meridian whose plane contains the sun. ωs = arccos [-tan (ϕ) tan (δ)]

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Daylight hours (N)

� maximum possible duration of sunshine or daylight hours.

� In the absence of any clouds, the actual duration of sunshine is equal to the daylight hours (n = N) and the ratio is one

ϕ :latitude [rad] δ :solar decimation [rad]ωs :sunset hour angle [rad]


Net longwave radiation (Rnl)� The solar radiation absorbed by the earth is converted to heat energy

then emitted with wavelenghts longer than those from the sun. � The emitted longwave radiation is absorbed by the atmosphere or is lost

in the space.� The atmosphere temperature increases consequently the atmosphere

radiates its own energy

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radiates its own energy� Consequently, the earth's surface both emits and receives longwave

radiation. The difference between outgoing and incoming longwave radiation is called the net longwave radiation, Rnl.

Rnl :net outgoing longwave radiation [MJ m-2 day-1],σ :Stefan-Boltzmann constant [4.903 10-9 MJ K-4 m-2 day-1],Tmax, :K maximum absolute temperature during the 24-hour period [K = °C + 273.16],Tmin, :K minimum absolute temperature during the 24-hour period [K = °C + 273.16],

ea :actual vapour pressure [kPa],Rs :solar radiation [MJ m-2 day-1],Rso :clear-sky radiation [MJ m-2 day-1].


Clear-sky solar radiation (Rso)

� Solar radiation reaching the earth without cloud conditions � The calculation of the clear-sky radiation, Rso, when n = N

Rso = (0.75 + 2 l0-5z)Ra

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Rso :clear-sky solar radiation [MJ m-2 day-1], Z :station elevation above sea level [m]. Ra : extraterrestrial radiation [MJ m-2 day-1]


Air temperature (T)

� Measured at 2 m above the ground surface under shelter to protect the instrument from direct exposure from direct solar heating.

2minmax TT

T+=

18

Where:

Tmax and Tmin are min and max air temperature over a 24-hour period (°C)

Slope of saturation vapour pressure curve ( ∆)

� For the calculation of evapotranspiration, the slope of the relationship between saturation vapour pressure and temperature, ∆, is required.

2T =

∆ at air temperature T [kPa °C-1],T mean air temperature [°C],

( )23.237

3.237

27.17exp6108.04098

+

+=∆

T

T

T


Mean saturation vapour pressure (es)

� As saturation vapour pressure is related to air temperature, it can be calculated from the air temperature.

where( )

+=

3.237

27.17exp6108.0

T

TTeo

19

where

e°(T) saturation vapour pressure at the air temperature T [kPa],

T air temperature [°C],

Actual vapour pressure (ea)

� The actual vapour pressure can also be calculated from the relative humidity. Depending on the availability of the humidity data, different equations should be used.

+ 3.237T

2

)()( max meanoo

s

TeTee

+=

2100

)(100

)( minmax

MaxMin

oo

a

RHTe

RHTe

e+

=


Psychrometric constant ( γγγγ)The psychrometric constant, γ, is given by: where

γγγγ :psychrometric constant [kPa °C-1],P :atmospheric pressure [kPa],λ :latent heat of vaporization, 2.45 [MJ kg-1],c :specific heat at constant pressure, 1.013 10-3 [MJ kg-1 °C-1],

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cp :specific heat at constant pressure, 1.013 10-3 [MJ kg-1 °C-1],ε :ratio molecular weight of water vapour/dry air = 0.622.

Latent heat of vaporization ( λ)� Energy required to change a unit mass of water from liquide water to

water vapour in a constant pressure and temperature


Atmospheric pressure (P)� is the pressure exerted by the weight of the earth's atmosphere.� Evaporation at high altitudes is promoted due to low atmospheric

pressure.

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where P :atmospheric pressure [kPa],z :elevation above mean sea level [m],


Soil heat flux (G)

� For a magnitude of day or ten-day soil heat flux beneth the grass surface is relatively small.

Gday≈ 0

� For month period

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� For month period

Gmonth, i= 0.07 (Tmonth, i+1 – Tmonth, i-1) or

Gmonth, i = 0.14 (Tmonth, i – Tmonth, i-1)

Tmonth, i :mean air temperature of month i [°C],Tmonth, i-1 :mean air temperature of previous month [°C],Tmonth, i+1 :mean air temperature of next month [°C].


Wind profile relationship� Wind speed is measured with anemometers. � Wind speed is slowest at the surface and increases with height. � To adjust wind speed data obtained from instruments placed at elevations other

than the standard height of 2m, a logarithmic wind speed profile is used

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U2 :wind speed at 2 m above ground surface [m s-1],Uz :measured wind speed at z m above ground surface [m s-1],Z :height of measurement above ground surface [m].


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2. 7. Empirical methods of estimating EtoRemarks

� Weather measurements should be made at 2 m (or converted to that height)

� No weather-based evapotranspiration equation can be expected to predict evapotranspiration perfectly under every climatic situation due to simplification in formulation and errors in data measurement.

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Exercise 1

Documents

2. 7. Meteorological factors determining ETo PPT chapter 2 of 2.pdfWhere ET0 is in mmd-1. Rs is the incoming solar short wave radiation in MJm-2d-1. Constant 2.45 is the latent heat