Data Based Solar Radiation Modelling - Hydrological Data Driven Modelling - page 115

5.3 Data Based Six-Hourly Solar Radiation Modelling

This section tries to answer questions on which inputs should be used and how long
the training data should be for model development using 6-hourly data from the
Brue catchment with the aid of nonlinear models LLR and ANNs. In this part of the
analysis, the following six-hourly records of input parameters are considered:
horizontal extraterrestrial radiation (RN) (based on Allen et al. [ 8 ]), wet bulb
temperature (WT), air bulb temperature (DT) and atmospheric pressure (p). The
hourly extraterrestrial radiation can be estimated from the solar constant, the solar
declination, the solar time angle at the beginning and end of the period and the time
of the year by the Eq. 5.9 :

12 ð 60 Þ

R a ¼ G sc d r ½ ð x 2 x 1 Þ sin ðuÞ sin ðdÞþ cos ðuÞ cos ðdÞ ð sin ðx 2 Þ sin ðx 1 Þ Þ

p

ð 5 : 9 Þ

where R a is extraterrestrial radiation in hourly period (MJ m − 2 h − 1 ), G sc is solar
constant (0.0820 MJ m − 2 min − 1 ), d r is the inverse distance between Earth and Sun, δ
is solar declination (rad), ˆ is the latitude (rad), ˉ 1 is solar time angle at the

beginning of a period (rad), ˉ 2 is solar time angle at the end of a period (rad). 1460

6-hourly records are collected for the study after normalisation of the data. Nor-
malization is performed (i) to equalize the relative numerical signi

cance between

the input variables; (ii) to aid the analysis routines to perform ef ciently, especially

in the absence of any prior knowledge regarding the input variable relevance and
(iii) to eliminate the effect of the data units.

5.3.1 Input Data and Training Data Length Selection Using
Entropy Theory

In this section of the study, the variability of the data used is measured using the
concept of entropy. Attributes like Marginal entropy, joint entropy, conditional
entropy and transinformation are calculated for four inputs to the independent
variable of solar radiation. These values are dependent to

x, the length of class
intervals or the discretization interval for computing class frequency. It is assumed
that these input data have the normal distribution (for the convenience of the
computation). Figure 5.4 shows the histogram of the measured air dry bulb tem-
perature. When a variable is far from the normal distribution, its computation would
be very complicated and currently, there are no ready algorithms to solve this

Δ