Water Engineering Education & Applications Email:
[email protected] Website www.weea.co.za or
[email protected] Paper No. IRIG/11: Application of Penman’s Method in computing the crop-water requirement (ET crop) Crispen Mutsvangwa MSc (Eng.,); MSc Water & Environmental Management
© Copyright 2011. Water Engineering, Education & Applications
APPLICATION OF PENMAN’S METHOD IN COMPUTING THE CROPWATER REQUIREMENTS Crop-water requirements The crop-water requirement is the amount of water required by a plant during its vegetation period from germination to maturity. The total amount of water required and the timing of water applied is governed by:
• • • • •
Prevailing climatic conditions Type of crop Stage of growth Extent of root-development Soil type
Evaporation Evaporation is a process whereby water is converted to water vapour and removed from evaporating surface. Energy is required to change water molecules from liquid to vapour and mainly from solar radiation. Transpiration This is the vaporization of liquid water contained in plant tissues, mainly through stomata. Vaporisation occurs within the leaf (in the intercellular spaces) and the vapour exchange with the atmosphere is controlled by the stomata aperture. Nearly all the water taken up is lost by transpiration and only a tiny fraction is used within the plant. Evapotranspiration It is the quantity of water transpired by a plant during growth or released by plant tissue, plus moisture evaporated from the surface of the soil and vegetation. Reference evapotranspiration ( ETO), mm/day The rate of evapotranspiration from an extended surface of 8 to 15cm tall green grass cover of uniform height, actively growing, completely shading the ground and no short of water (Doorenbos and Pruit, 1977). However different crops can be used as ‘reference crops.’ Crop evapotranspiration (ET crop), mm/day mm/day The evapotranspiration of a disease-free crop growing in a large field (one or more hectares) including sufficient water and fertility and achieving full production potential of
rispen C rispen
Mutsvangwa: Water Engineering, Education Education & Applications, www.weea.co.za
Page 1 of 9
the crop under the given growing environment. It includes evaporation of water from the soil surface, evaporation from the plant surfaces and transpiration of water through plant tissues into the atmosphere. Potential evaporation for different crops will not be the same. The relationship between ET o and ETcrop is given as: ET crop = k c ET o
(1)
Where: kc =crop coefficient. The values for k c for different crops have been derived from experiments and the values of the crop coefficient are different for each crop (Fig. 1), and also differs with:
• • •
Stage of growth Crop density Crop characteristics
The kc values can be applied to ET o derived from any methods for the period under consideration and usually between 10 to 30 days. Irrigation water requirements This is the depth of water needed to meet the water loss through ET
crop.
I = ET crop − Pe
(2)
Where: Pe =effective precipitation, which is the rainfall that is useful or usable in any phase of crop production. In engineering practice, the peak water requirements are usually predicted for 10 days or monthly periods. Ideally, the length of the period should be the same as that of the irrigation interval. METHODS TO DETERMINE THE REFERENCE EVAPOTRANSPIRATION (ET O) There are several methods to determine the ET O and these include:
• • • • •
direct measurements meteorological equations combination methods empirical methods pan evaporation
Direct measurement
Crops are grown in soil tanks called lysimeters and then there is periodic determination of the root zone soil moisture and recording interval rainfall, irrigation or drainage. From the measured data, a water balance is carried out. Such data derived from field measurements under field conditions is more reliable and can be used for designing as well as calibrating of empirical formulations.
C rispen
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
Page 2 of 9
Meteorological equations/climatic
Such methods include:
• • • •
mass transfer methods infrared radiometry tracer techniques energy balance
Combination methods
They are based on energy balance and aerodynamic equations (radiation and aerodynamics). According to this theory, there is continuous evaporation if:
•
there is supply of water to be evaporated or transpired
•
there is a supply of energy to provide latent heat of vaporization
•
Mechanism for removing the produced vapour into the atmosphere.
If well calibrated, combination methods produce better results than other methods and one of the most comprehensive one is the Penman’s method (1948), and can be applied satisfactorily in most climatic regions. Empirical formulae
They are based on correlation of the reference evapotranspiration (ET O ) and meteorological factors. Some few examples are the Thornthwaite and Blaney-Criddle methods (Svehlik,1939).
Pan Evaporation method
The method is applicable for moderate short periods like 10 days. The evaporation pans provide a measurement of integrated effect of meteorological factors on evaporation under conditions of adequate water supply. The measured pan evaporation is then related to the potential ET O using pan coefficients: ET O = k p E pan
(3)
The consumptive daily use of the crop (ET crop) is then obtained by simply multiplying the measured depth of evaporation in the pan by the pan coefficient and the crop coefficient: ET crop = k p k c E pan
(4)
Where:
kp =pan coefficient kc =crop coefficient Epan =pan evaporation, mm/day The kp is a function of pan type, pan sitting, relative humidity, wind run and fetch distance. Applicability of methods Some methods produce good results for one location and unsatisfactory at other locations. It has been found that no single method using meteorological data is
C rispen
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
Page 3 of 9
universally adequate under all climatic conditions. However, as result of an expert Consultation of (FAO, 1990), the FAO Modified Penman’s method is now recommended as the standard method for the definition and computation of the reference evapotranspiration (ET o), All methods before use for planning and deign of irrigation projects need local or regional calibration.
PENMAN’S METHOD It applies the radiation balance plus aerodynamic approach to estimate ET o. Penman’s (1948) method uses the radiation balance to indicate part of energy available for evaporation and the aerodynamic term to quantify the influence of advection. The original equation of Penman is given as (Svehlik, 1977): ET O =
∆ H + γ E a ∆ + γ
Where:
(5)
=net radiation Ea =aerodynamic term =slope of the saturation vapour pressure curve at mean temperature ∆ γ =psychrometric constant: a relation between vapour pressure deficit and wet bulb depression The above equation can be written as: ET O =
∆H
γ ∆ f (u )∆e ( Rn − G ) + ∆ + γ ∆ + λ
radiation balance
∆ ∆ + γ
, mm/day
(6)
aerodynamic term
=weighting function for elevation and temperature
∆
=slope of saturation vapour pressure versus temperature curve
Rn Rn G f(u) Rs Rb
=net radiation, mm/day =soil heat flux + evaporation + air heat =G + E +H =soil heat flux, if soil is heating = wind function = incoming short wave (solar) radiation =net outgoing long wave (terrestrial) radiation =coefficient of albedo, α =0.25 for FAO Modified Penman =vapour pressure deficit, mb
α e
FAO Modified Penman’s Method Application of the original Penman’s method revealed that it is particularly applicable to cool limited regions like in England and also in hot and semi-arid regions. Doorenbos et al (1984) slightly modified the equation. The modified equation uses mean daily climatic
C rispen
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
Page 4 of 9
conditions since day and night time weather conditions considerably affect the level of evaporation. It was developed by comparing Lysimeter- measured evaporation from locations world-wide. Statistical analysis was performed to determine which additional metrological parameters would reduce the error between measured and estimated evapotranspiration. ⎡ ∆ ⎤ γ (7) ET O = c ⎢ Rn + f (u )∆e⎥ mm/day ∆ + λ ⎣ ∆ + γ ⎦ Or
ET O = c[ Rn + +(1 −
Where:
) f (u )(es − ea )]
(8)
ω=weighting
function for the effect of radiation on ETo at different elevation and temperature (Agritex, 1980). =weighting factor for the effect of wind and humidity on ETo at different temperature and altitudes (Table 1). =adjustment factor to compensate for the effect of day and night weather conditions
1-ω c
The adjustment factor, c is a function of: • Relative humidity maximum, RH max • day to night wind run ratio, U day/Unight • day time wind speed at 2m, U 2day • Solar radiation, R s Computation of the input parameters The adjustment factor , c The adjustment factor can be established can be computed from (Cuenca, 1989): U c = 0.68 + 0.0028 RH max + 0.018 Rs − 0.068U 2 day + 0.013 day + U night (9) ⎛ U day ⎞ ⎟ + 0.43 × 10 − 4 ( RH max )( R s )(U 2 day ) 0.0097 (U 2 day )⎜ ⎜ U night ⎟ ⎝ ⎠
Where:
Uday
=mean day time wind speed at 2m
Wind function, f(u) The wind function at a wind speed height of 2m is given as:
⎛
U 2 m ⎞
⎝
100 ⎠
f (u ) = 0.27⎜1 +
⎟
(10)
To convert any wind speed given at a specified height is given as: 0.2
and
C rispen
U 2 m
⎡2⎤ = U Z ⎢ ⎥ ⎣ Z ⎦
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
(11)
Page 5 of 9
Where:
Uz
=Wind speed at a specified height z
Vapour pressure deficit, ∆
∆e = es − e a Where:
(12) es ea
ea =
Where:
=saturation vapour pressure, mb =mean actual vapour pressure of air, mb
e s RH mean
100
RHmean
(13) =mean relative humidity
The following expressions for e x can be used (Svehlik, 1982). x e s = 6.1078e ,
mb
(14)
e s = 4.5812e ,
mmHg
(15)
x
e s = 33.8639 (0.00738T mean + 0.8072 ) − 0.000019 1.8 T mean + 48 + 0.001316 8
x =
2 19.8374T mean − 0.00831T mean
Where:
T mean + 273.16
(16)
(17)
Tmean = mean air temperature in oC
Values of saturation vapour, e s are also given in tables as a function of T mean. Net radiation, R n Rn = (1 − α ) R s − Rb ,
mm/day
(18)
n ⎞ ⎛ Rs = ⎜ 0.35 + 0.61 ⎟ Rbo , N ⎠ ⎝
mm/day
(19)
Where: Rs N n Rbo
=total daily clear sky radiation at the surface of earth, and can be found in tables as function of latitude. =maximum possible sunshine hours (can be found from tables as function of latitude) =actual sunshine hours =net outgoing clear sky-long wave radiation
⎡ Rs
⎤ + b⎥ Rbo ⎣ Rso ⎦
Rb = ⎢a
C rispen
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
(20)
Page 6 of 9
n ⎡ ⎤ 0 .5 4 Rb = ⎢0.9 + 0.1⎥ 0.34 − 0.44(e s ) δ (T mean ) N
⎣
Where:
a, b es
Rbo
(T = εδ
4 mx
Where:
⎦
[
]
(21)
=empirical constants =saturation vapour pressure. 4 + T min )
2
(22)
=emissivity of the surface =Boltzmann constant (4.89995x10 -3J/m2Kd
ε δ
=OC+273
(23)
ε = a1 + b1 [e s ]
(24)
K
0. 5
ε = −0.02 + 0.261 exp − 7.77 × 10 − 4 (T mean ) 2
Or
(25)
(mb/ oC)
Slope of saturation, ∆
∆ = 2[0.00738 T nean + 0.8072] − 0.00116 7
Tmean =mean temperature of air over a period of interest, oC
Where:
mb/oC
Psychrometric constant, γ γ =
e s − ea
altitude (m) 0 500 1000 2000 3000 4000
(27)
T dry − T wet
Table 1
Temp o ( C)
(26)
Values of Weighting Factor (l –W) for the Effect of Wind and Humidity on ETo at Different Temperatures and Altitudes
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
.57 .56 .54 .51 .48 .46
.54 .52 .51 .48 .45 .42
.51 .49 .48 .45 .42 .39
.48 .46 .45 .42 .39 .36
.45 .43 .42 .39 .36 .34
.42 .40 .39 .36 .34 .31
.39 .38 .36 .32 .31 .29
.36 .35 .32 .31 .29 .27
.34 .33 .31 .29 .27 .25
.32 .30 .29 .27 .25 .23
.29 .28 .27 .25 .23 .21
.27 .26 .25 .23 .21 .19
.25 .24 .23 .21 .19 .18
.23 .22 .21 .19 .18 .16
.22 .21 .20 .18 .16 .15
.20 .19 .18 .16 .15 .14
.19 .18 .17 .15 .14 .13
.17 .16 .15 .14 .13 .12
.16 .15 .14 .13 .12 .11
.15 .12 .13 .12 .11 .10
Example 1
(c)
C rispen
Compute the crop water requirement (ET crop) using the FAO-Modified Penman’s method. The following meteorological data is applicable.
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
Page 7 of 9
Dry bulb temperature Wet bulb temperature Mean actual vapour pressure of air Net outgoing long wave radiation Rb Incoming short wave radiation Rs Coefficient of albedo α Mean day time wind speed at a height of 1.5m Maximum relative humidity Minimum relative humidity Adjustment factor, C Saturation vapour pressure Crop coefficient
=25 oC =11 oC =15mb =16mm/day =35mm/day =0.25 =300km/day =85% =30% =1.2 =1.4mb =0.85
Solution:
From Penman’s equation, the ETcrop is calculated as:
⎡
⎤ γ ∆ f (u )∆e⎥ ) Rn + ∆ + γ ⎣ ∆ + γ ⎦
ETo = c ⎢(
To convert any wind speed given at a specified height is given as: U 2 m
⎡2⎤ = U Z ⎢ ⎥ ⎣ Z ⎦
0.2
⎛ 2 ⎞ = 300⎜ ⎟ ⎝ 1.5 ⎠
0.2
= 318km / day
The wind function f(u) is calculated as:
⎛ ⎝
f (u ) = 0.27⎜1 +
T mean=
x =
T max + T min
2
=
U 2 m ⎞
⎛ 318 ⎞ ⎟ = 0.27⎜1 + ⎟ = 1.13 100 ⎠ 100 ⎝ ⎠
28 + 15 2
= 21.5o C
2 19.8374T mean − 0.00831T mean
T mean + 273.16
=
19.8374 × 21.5 − 0.00831 × [21.5] 21.5 + 273.16
Saturation vapour pressure:
es = 6.1078e x = 6.1078 × e
Mean Relative humidity:
RH meam =
1.43
Mean actual vapour pressure of air:
C rispen
Rmax + Rmin
ea =
2 e s RH mean
100
=
=
2
= 1.43 = 25.59mb
85 + 30 2
= 57.5%
25.59 × 57.5 100
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
= 14.71mb
Page 8 of 9
∆ = 2[0.00738 T nean + 0.8072] − 0.00116 = 2[0.00738 × 21.5 + 0.8072] − 0.00116 = 1.57 7
7
Psychrometric constant: γ =
es − ea T dry − T wet
=
25.59 − 14.71 25 − 11
Vapour pressure deficit,
= 0.78 mb/oC
∆e
∆e = es − ea = 25.59 − 14.71 = 10.88mb Net radiation, R n Rn = (1 − α ) Rs − Rb = (1 − 0.25)35 − 16 = 10.25mm / day
1.57 0.78 ⎡ ⎤ )10.25 + 1.13 × 10.88⎥ = 11mm / day 1.57 + 0.78 ⎣ 1.57 + 0.78 ⎦
ET o = 1.02⎢(
ET crop = k c ET o = 0.85 × 11
9.4mm/day
References 1. Agritex Handbook, (1986), Department Agriculture, Zimbabwe Government 2. Doorenbos J., and Pruit W.O., (1977), Crop water requirements, FAO, Irrigation and Drainage Paper, No. 24, Rome 3. Cuenca R., (1989), Irrigation Systems Design: An Engineering approach. Prentice Hall. USA. 4. Jensen M. E., (1980), Design and Operation of Farm Irrigation Systems, American Society of Irrigation Engineers, USA 5. Penman H. L., (1948), Natural evaporation from open water, bare soil and grass, Proc. Royal Soc of London, Series A., 193, 120-146. 6. Singh V., (1995), Environmental Hydrology, Kluwer Academic Publishers, USA 7. Svehlik Z. J., (1977), Estimation of irrigation requirements, in Irrigation Development Irrigation Development Planning, Rydzewski J. R. (Ed), University of Southampton, UK. 8. Thornthwaite C. W., (1948), An approach towards a national classification of climate, Geor Rev., V38 55-94 9. http://www.fao.org/
C rispen
Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za
Page 9 of 9
