3.3 Potential evapotranspiration (ETp) and Effective
rainfall determination
Potential runoff is defined the maximum possible rate at which
evapotranspiration would occur from a large area completely and uniformly
covered with growing vegetation which is not short of water under given
atmospheric conditions (Weligepolage, 2005).
3.3.1 Estimation of Potential
Evapotranspiration
A Number of approaches have been developed for estimating the
ETp or ETref based on different theoretical concepts. Most commonly applied
methods for hydrological studies can be classified into four categories on the
basis of their data requirement (Weligepolage, 2005):
a) Temperature based methods- use only daily average air
temperature and some times the day length.
b) Radiation based methods- use both the net radiation and air
temperature data for estimating ET.
c) Combination- use net radiation, air temperature, wind speed
and relative humidity data based on the Penman-Monteith combination
equation.
d) Pan measurement- use pan evaporation with modifications
depending on wind speed, temperature and humidity.
The methods that do not require information about the nature
of the surface, estimate the reference crop evapotranspiration rate where as
others are surface specific and do require information about albedo, vegetation
height, maximum stomatal conductance, leaf area index and other factors.
The American Society of Civil Engineering (ASCE) and
Consortium of European Research Institutes have undertaken major studies to
evaluate the performance of different evapotranspiration estimation procedures
under different climatologic conditions. Both have indicated that the FAO
Penman-Monteith approach of reference crop evapotranspiration as relatively
accurate and consistent performance in evapotranspiration estimation (Allen et
al, 1998).
The following paragraph gives details on the Penman-Montheith
method where the Potential evapotranspiration is considered to be the Reference
evapotranspiration:
ET=
0 Ä + +
(1 0 . 34 )
U 2
(3)
900
0. 40 8Ä
+
+
( )
R G
-
n
U e
2 ( a
- ed)
T
273
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where; ETo =
|
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Rn
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=
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G
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=
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T
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=
|
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U2
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=
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Reference crop evapotranspiration (mm/day) Net radiation at crop
surface (MJ m-2 d-1) Roil heat flux (MJ m-2
d-1)
Average temperature (oC)
Windspeed measured at 2m height (m s-1)
(ea-ed) = Vapour pressure deficit (kpa)
=? Slope vapour pressure curve (kPa
oC-1)
? = Psychometric constant (kPa oC-1) 900 =
Conversion factor
3.3.1.1 Net radiation
The Net radiation is s determined as follows;
R n =R ns -R nl
(4)
n
R = 0 .77(0 .25 + 0 . 5 ) (5)
ns Ra
N
(6)
n
nl 2.45.10 (0.9 0.1)(0.34 0.14 )( )
= + - +
9 ed T T
4 4
R kx kn
N
G = 0.14(Tmonthn - T monthn-1) (7)
where; Rn = net radiation
Rns = net short wave radiation (MJ m-2
d-1)
Rnl = net longwave radiation (MJ m-2
d-1)
n /N = relative sunshine fraction
Tkx = maximum temperature (K)
Tkn = minimum temperature (K)
ed = actual vapour pressure (kPa)
G = soil heat flux (MJ m-2 d-
1)
Tmonth n = mean temperature in month n
(oC)
Tmonth n-1 = mean temperature in preceding month n-1
(oC)
3.3.1.2 Mean Relative Humidity
The humidity expressed as saturation vapour pressure at
dewpoint temperature (mbar) has been converted to mean daily relative humidity
from maximum and minimum temperatures according to the following
relationship:
RH RH
+ ?
RH e
= =
max min
min 2 d ? ?
50 50
+ (8)
e e ?
a Tmean a T
( ) ( max) ?
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Where ed = saturation vapour pressure at dewpoint temperature
(kPa) ea = saturation vapour pressure at minimum
temperature
ea(Tmax) = saturation vapour pressure at maximum temperature
The saturation vapour pressure is
determined according to Teten's formula: e a 0.611exp (
17.27 T T 237.3 )
= +
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(9)
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Where ea = saturation vapour pressure at temperature T
(oc) 3.3.1.3 Wind speed
The original wind data expressed in m/s are convereted into
km/day according to:
U2=U 2 ×86.4 (10)
*
Where; U2 = wind speed in km/day at 2 m
height
U2 = wind speed in m/s
*
3.3.1.4 Solar radiation
As no measured data on solar radiation are available, solar
radiation has been estimated from measured sunshine hours according to the
following relationships:
|
n
R )
p
= (0 .25 + 0 . 5
s 100
|
R (11)
a
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Where; Rs = solar radiation (MJ
m-2d-1)
Ra = extraterrestrial radiation (MJ
m-2d-1)
0.25, 0.5 = Angstrom coefficients
n
n = (12)
* 100
p N
Where; n = daily sunshine hours (hr)
np = daily sunshine percentage (percentage.)
N = day length (hours), depending on latitude and month of the
year.
From the computed ETo series, the 20%
exceedence probability (1 in 5 years-return period) values are estimated.
3.3.2 Estimation of Effective Rainfall
Effective rainfall is defined as that part of the
precipitation which is effectively used for evapotranspiration by the crop.
Four methodologies are given below to determine the effective rainfall:
a) Fixed percentage rainfall: effective
rainfall is calculated according to:
EPPT=a×PPT (13)
Where a, is a fixed percentage to be given by the user to account for
losses from runoff and deep percolation. Normally losses are around 10 to 30%,
thus a = 0.7- 0.9, EPPT is the effective precipitation and PPT, the total
precipitation
b) Dependable rain: based on an analysis
carried out for different arid and subhumid climates an empirical formula was
developed in FAO/AGLW to estimate dependable rainfall, the combined effect of
dependable rainfall (80% prob.exc.) and estimated losses due to runoff and
percolation. This formula may be used for design purposes where 80% probability
of exceedance is required. Calculation according to:
EPPT=0.6PPT-10;
forPPT<70mm (14)
EPPT = 0.8PPT - 24; for PPT >
70mm (15)
c) Empirical formula: The parameters may be
determined from an analysis of local climatic records. An analysis of local
climatic records may allow an estimation of effective rainfall. The
relationship can, in most cases, be simplified by the following equations:
EPPT= aPPT-b;
forPPT<Z(mm) (16)
EPPT=cPPT+d;
forPPT>Z(mm) (17)
Values for a, b, c and z are correlation coefficients.
d) USDA Soil Conservation Service Method: is
a method where monthly effective rainfall (in millimetre) can be calculated
from monthly total rainfall (in millimetre) according to the following
equations (18, 19); this mwthod is adopted whenever daily rainfall data are not
available.
EPPT = PPT(125 - 0.2PPT)/125; for
PPT 250 mm
< (18)
EPPT = 125 + 0.1PPT; forPPT >
250mm (19) The use of these methods depends on the
time scale of the model and the availability of data.
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