This  section  of  the  CD-ROM contains additional  material
supporting the information in

Chapter 4:
A Method for Determining the Solar Global and Defining the
Diffuse and Beam Irradiation on a Clear Day

of the book:
Modeling Solar Radiation at the Earth's Surface.
Recent Advances

published by Springer-Verlag, Heidelberg

November 2007
-------------------------------------
Stepwise description of data analysis

It  is  assumed that there are available databases for solar
global irradiance and for either solar beam or solar diffuse
irradiance.   The  databases may contain  either  hourly  or
daily values (the third database can be calculated from  the
two available databases).

It  should be emphasized the work presented in this  chapter
is  based on programs that have been developed during the 20
years   that   the  author  have  been  doing  collaborative
research.   Even  the programming language  and  statistical
packages  utilized in the data analysis have changed  during
the  years.   Consequently, there does not  exist  a  single
cohesive   input/output  program  to  perform  the  analysis
described  in  this chapter.  In lieu of this,  the  authors
have  decided  to describe the step-by-step  procedure  they
applied  to  produce the results described in this  chapter.
In  fact, most of the programs utilized are quite simple and
uncomplicated.   We  apologize  to  the  readers   for   the
deficiency.

Step 1: The   individual  databases  for  solar  global  and
        normal  beam irradiance are organized on  multi-year
        monthly  basis, viz., each database is divided  into
        12  monthly subsets of daily values.  The  data  are
        arranged  in  columns in the following  order:  Code
        (irradiance type), Station #, Year, Month,  day  and
        24  individual hours.  Missing values are  indicated
        by  9999,  cf.,  Step  1 Excel file  for  horizontal
        solar global radiation.
Step 2: The   two  individual  databases  are  then   cross-
        referenced in order to remove any days for  which  a
        single  hour  of data is missing.  The  direct  beam
        irradiance database is converted to horizontal  beam
        and   deducted  from  the  horizontal  solar  global
        irradiance  to  calculate  the  horizontal   diffuse
        irradiance.   The months are tabulated  individually
        for  each  year  and  a statistical  program  (e.g.,
        SPSS, Mathlab or similar) is applied to each of  the
        subsets  both  on a single year month and  a  multi-
        year month basis.  The output of the application  of
        such   a   statistical  program  to  the  individual
        subsets  includes  the following: average,  standard
        deviation,   coefficient  of  variation,   skewness,
        kurtosis,   maximum  value  (single  and  multi-year
        values),   minimum  value  (single  and   multi-year
        values),   absolute   maximum,   absolute   minimum,
        average maximum and average minimum.
Step 3: The application of the Iqbal filter as described  in
        Table  4.2  to  define a clear day  based  upon  the
        monthly  subsets  of  the  solar  global  irradiance
        data.   This  results in 12 subsets of solar  global
        irradiance on a clear day corresponding  to  the  12
        monthly  subsets.  The statistical  program  applied
        in  Step 2 is then applied to the monthly clear  day
        subsets  to  obtain  the monthly average  clear  day
        solar  global  irradiance as defined  by  the  Iqbal
        filter   (the  other  statistical  results  is   not
        relevant  to  this study).  The application  of  the
        Iqbal  filters produced, in addition,  subsets  from
        the    original    beam   and   diffuse    databases
        corresponding  to those days defined  by  the  Iqbal
        filter as clear days.
Step 4: A  program was written to determine the solar global
        irradiance  predicted  by the  models  described  in
        Section  2.2,  Eqs.  4.1-4.7.  The  monthly  average
        clear day solar global irradiance was determined  by
        averaging the values calculated for each day of  the
        month.
Step 5: A  program  was  written  to determine  the  Berlynd
        coefficient `f', which determined the value  of  the
        Berlynd  coefficient which gave the  best  agreement
        between  the calculated value for Gc, cf., Eq.  4.8,
        and  that  measured on a clear day as determined  by
        the   Iqbal   filter.   Viz.,  this  procedure   was
        repeated  for each clear day in a monthly clear  day
        subset  and the corresponding monthly value for  `f'
        is  defined as the average value for all  the  clear
        days.
Step 6: The  results  of  Step  7,  i.e.,  the  monthly  `f'
        values, enable one to calculate the clear day  solar
        global  irradiance  for any day within  a  month  by
        applying Eq. 4.8.
Step 7: It   is   then  possible  to  arrange  six   vectors
        consisting  of  the following daily  values:  global
        irradiance,  beam  irradiance,  diffuse  irradiance,
        clear  day  global  irradiance  (cf.,  Step  7)  and
        extraterrestrial irradiance.  This  enables  one  to
        determine  clearness index (KT),  clear  day  global
        index  (Kc,  Eq. 4.9), clear day horizontal  diffuse
        index  (Kd,c,  Eq.  4.11) and clear  day  horizontal
        beam index (Kb,c, Eq. 4.12).
