Geology Reference
In-Depth Information
5.4.1 Data Analysis and Model Input Selection Based
on the Gamma Test
The Gamma Test is able to provide the best mean square error that can possibly be
achieved using any nonlinear smooth models. In this study, different combinations
of input data were explored to assess their in
uence on the solar radiation modelling
(Fig.
5.19
). There were 2
n
1 meaningful combinations of inputs; from which, the
best one can be determined by observing the Gamma value, which indicates a
measure of the best MSE attainable using any modelling methods for unseen
smooth functions of continuous variables. Figure
5.19
, we can see some very
interesting variations of the best MSE (
−
ʓ
) with different input combinations. The
minimum value of
was observed when we used all the available input data sets
viz. Extraterrestrial Radiation (ETR), daily precipitation (P), daily mean tempera-
ture (T
mean
), daily maximum temperature (T
max
), daily minimum temperature (T
Tmin])
)
and daily mean wind velocity (U). As mentioned earlier the gradient (A) is con-
sidered as an indicator of model complexity. A model with low MSE and low
gradient is considered as the best scenario for the modelling. V-ratio is the measure
of degree of predictability of the given outputs using available inputs. The smaller
value of V-ratio was observed when we considered all the inputs.
The quantity of available input data to predict the desirable output was analysed
using the M-test. The M-Test results would help us to determine whether there were
suf
ʓ
cient data to provide an asymptotic Gamma estimate and subsequently a reli-
able model. The M-Test analysis results are shown in Fig.
5.20
. The test produced
an asymptotic convergence of the Gamma statistic to a value of 0.0354 at around
770 data points (i.e. M = 770). The variation of
the Standard Error
(SE)
Fig. 5.19 The gamma test results on the daily sunshine data set (variations of indices with
different input combinations) (The scenario 1 includes inputs like [ETR, Tmax, U, Tmean, Tmin,
P]. The scenario 2 includes inputs like [Tmax, UTmean, Tmin, P]. The scenario 3 includes inputs
like [ETR, U, Tmean, Tmin, P]. The scenario 4 includes inputs like [ETR, Tmax, Tmean, Tmin, P].
The scenario 5 includes inputs like [ETR, Tmax, U, Tmin, P]. The scenario 6 includes inputs like
