poster - International Conference of Agricultural Engineering

two types of reference surfaces representing clipped grass and alfalfa, and for daily or hourly
time step. This equation is simplified to a reduced form of the ASCE–PM. The equation is
expressed as:
900
0.408 (
Rn
G)
U
2
( es
ea
)
ET
T 273
o
(1)
(1 0.34U
2
)
where ET o is standardized grass reference evapotranspiration (mm day-1), R n is calculated
net radiation at the crop surface (MJ m -2 d -1 ), G is soil heat flux density at the soil surface
(MJ m -2 d -1 ), T is mean daily air temperature at 2 m height (°C), U 2 is mean daily wind speed
at 2 m height (m s-1), e s is saturation vapor pressure (kPa), calculated for daily time steps as
the average of saturation vapor pressure at maximum and minimum air temperature, ea is
mean actual vapor pressure (kPa), Δ is slope of the saturation vapor pressure-temperature
curve (kPa °C -1 ), γ is psychrometric constant (kPa °C -1 ), Units for the 0.408 coefficient are m 2
mm MJ -1 . All the calculations of daily values (R n , e s , e a ) and other parameters were made by
ASCE-EWRI (2005).
2.3. Sensitivity analyses and sensitivity coefficients
In ecological and hydrometeorological studies (e.g., McCuen, 1974; Saxton, 1975; Beven,
1979; Anderton et al., 2002) a number of sensitivity coefficients have been defined
depending on the purpose of the analyses. For example, Saxton (1975) mathematically
differentiated the equation under investigation to derive equations for the rate of change of
the independent variable with respect to each dependent variable. Smajstrla et al. (1987)
defined the sensitivity coefficient as the slope of the curve of ET o versus the climatic variable
being studied. Slopes computed in this manner represented the rates of change in ET o with
respect to change in the climatic variable. For multi-variable models (e.g., the Penman-
Monteith equation), different variables have different dimensions and different ranges of
values, which makes it difficult. In general, a model of evapotranspiration can be written as:
ET f p p , p ,...,
(2)
o 1, 2 3
p N
where
i
p is input data variable and N is the number of parameters and input data variables.
The error in ET o ( ETo
) that results from errors in the pi
can then be expressed as:
ETo
ETo
f p1 p1, p2
p2
,..., pN
p
N
(3)
Expanding equation 3 in Taylor series and ignoring second-order terms and above, leads to:
ETo
ETo
ETo
ETo
p1
p2
... pN
(4)
p
p
p
1
ET
where the differential
p
2
i
o
N
is the absolute sensitivity of the estimation of
p
i
, and
pi
is the
individual error associated with p
i (Beven, 1979).
Following McCuen (1974) and Beven (1979), the partial derivative is transformed into a nondimensional
form to display the sensitivity for the variables:
ETo
/ ETo
ETo
pi
S lim
/
P i
pi
pi
pi
ETo
(5)
Δp 0
i
where S
P is the sensitivity coefficient represents the fraction of the change in p
i
i that is
transmitted through to the estimate of ET o . However, the relative coefficients are sensitive to
the values of p and ET o . p in this study represents air temperature, solar radiation, relative
i
i
humidity and wind speed. Basically, a positive/negative sensitivity coefficient of a variable
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