Geology Reference
In-Depth Information
r
1
N
X
N
2
Root Mean Squared Error
RMSE
¼
1
ð
Q
m
Q
o
Þ
ð
7
:
6
Þ
;
i
¼
P
i
¼
1
ð
Q
o
Q
m
Þ
N
Mean Bias Error
MBE
¼
ð
7
:
7
Þ
;
Variance of the distribution of differences S
2
which expresses the variability of
(Q
o
-
Q
m
) distribution about MBE
P
i
¼
1
ð
Q
o
Q
m
MBE
Þ
2
S
d
¼
ð
7
:
8
Þ
N
1
where Q
m
is the modeled or estimated evaporation/evapotranspiration from a data-
based model, Q
o
is the observation evaporation/evapotranspiration,
Q
m
is the
Q
o
is the average of the
average of the estimated evaporation/evapotranspiration,
observed radiation, and N is the number of observations.
7.4 Modelling with Traditional Reference
Evapotranspiration Models
This section gives the mathematical details of the ET
0
models and their modeling
results for different time interval data such as hourly, daily, monthly, and yearly.
We have used three popular Penman
Monteith (PM) models such as FAO56-PM,
ASCE-PM, and CIMIS-PM, along with the newly proposed Copais Approach.
-
7.4.1 Mathematical Details of the ET
0
Models
7.4.1.1 FAO-56 Penman
Monteith (FAO56-PM) Model
-
The FAO-56 PM equation for hourly time step is
37
e
0
0
408
D
ð
R
n
G
Þþc
T
hr
þ
273
u
2
ð
ð
T
hr
Þ
e
a
Þ
:
ET
0
¼
ð
7
:
9
Þ
D
þ cð
1
þ
0
34u
2
Þ
:
where ET
0
is the reference evapotranspiration (mm h
−
1
),
Δ
the saturation slope
C
−
1
), R
n
the net radiation at the grass surface
vapor pressure curve at T
hr
(kPa
°
(MJm
−
2
h
−
1
), G the soil heat
flux density (MJ m
−
1
h
−
1
),
ʳ
the psychrometric
C
−
1
), T
hr
the mean hourly air temperature (
constant (kPa
C), u
2
the average
hourly wind speed at 2 m height (m s
−
1
), e
0
(T
hr
) the saturation vapor pressure at T
hr
(kPa), and e
a
the average hourly actual vapor pressure (kPa).
°
°
