Case Study

SSM is applied independently for each station and finally parameter estimation series are obtained for a’i and b’. The lower order statistics that could not be man­aged with Angstrom equation are shown in Table 6.1 together with the classical Angstrom parameters. It is to be noted that in the application of the SSM, mode values are considered rather than arithmetic averages as used in the classical meth­ods. It is easy and practical to do statistical analysis of Angstrom equation parame­ters and variables with SSM. Also included in Table 6.1 are the relative error (RE) percentages between the classical method arithmetic average and mode values of SSM. In the CD accompanying this book the reader will find all a’ and Ъ values

Table 6.1 Statistical properties of SSM and Angstrom equation

Station Name

Angstrom

Equation

Mode,

SSM

Stand.

Dev.,

SSM

Relative Error (%)

a

Ъ

a’

Ъ’

a

b’

a, a

b, Ъ

Adana

0.33

0.29

0.31

0.31

1.27

1.75

6.05

6.42

Adiyaman

0.30

0.22

0.27

0.26

0.80

1.10

9.93

17.90

Afyon

0.40

0.28

0.34

0.29

0.78

1.95

15.20

5.78

Amasya

0.30

0.38

0.27

0.37

2.44

6.79

6.72

3.92

Anamur

0.36

0.25

0.29

0.35

1.51

2.04

21.40

26.90

Ankara

0.31

0.32

0.30

0.48

3.03

6.09

4.74

32.00

Antalya

0.33

0.38

0.33

0.32

1.98

2.78

0.60

16.20

Aydin

0.32

0.42

0.33

0.42

1.88

3.38

4.50

0.95

Balikesir

0.23

0.37

0.22

0.34

1.39

3.98

0.88

6.28

Bursa

0.27

0.33

0.24

0.35

1.25

3.09

9.62

4.03

Canakkale

0.31

0.33

0.31

0.45

3.81

4.58

2.50

27.70

Cankiri

0.35

0.32

0.11

0.25

5.92

6.86

57.30

21.60

Diyarbakir

0.23

0.48

0.43

0.42

2.09

3.06

45.00

12.73

Elazig

0.32

0.32

0.24

0.40

1.74

2.46

25.40

16.38

Erzincan

0.44

0.15

0.40

0.25

0.83

2.42

9.15

36.05

Eskijehir

0.39

0.26

0.34

0.43

0.74

1.56

13.81

39.60

Istanbul

0.30

0.35

0.28

0.55

0.90

3.34

5.08

35.50

Isparta

0.36

0.16

0.28

0.16

0.58

1.03

21.32

0.00

Izmir

0.33

0.33

0.32

0.42

1.16

1.71

1.80

22.00

Kars

0.50

0.12

0.74

0.41

1.32

2.22

33.30

70.00

Kastamonu

0.32

0.24

0.19

0.31

0.70

2.04

41.17

21.20

Kayseri

0.36

0.23

0.31

0.30

2.87

4.02

13.73

24.10

Kirsehir

0.43

0.20

0.18

0.25

1.31

2.15

57.30

21.81

Konya

0.38

0.27

0.31

0.39

1.79

3.80

20.00

32.20

Malatya

0.31

0.37

0.24

0.47

2.04

0.47

23.45

21.80

Mersin

0.33

0.40

0.27

0.48

0.87

1.25

16.60

17.30

Samsun

0.34

0.31

0.22

0.40

2.78

6.23

33.70

22.40

Trabzon

0.28

0.38

0.26

0.46

6.82

23.69

6.27

17.86

Van

0.51

0.14

0.40

0.23

34.07

41.92

21.76

36.60

for Adana, Ankara and Istanbul stations separately during 129 months. In addition, the CD-ROM includes relation between average a’ and b’ values for mentioned three stations.

It is possible to obtain empirical frequency distribution functions or any other time variation features of the parameters from estimations, where Angstrom ap­proach by the classical regression technique application does not give such an op­portunity at a fixed point. Figures 6.5a and 6.5b present the empirical and theoretical histograms of a’i and b’t for Adana, respectively. The theoretical histograms appear as normal distribution functions.

Figure 6.6 presents the monthly average regional relationships between and bi for Adana and Ankara stations. These two figures can be arranged as the

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 6.6b Relationship between a’ and b’ at Ankara temporal variation graph between a’ and b’. It is seen that high (low) values of a’ follow low (high) values of b’. Additionally, SSM provides sequences of coefficient estimations at any station that constitutes the basis of temporal histogram and this is useful in setting up the confidence limits in future global irradiation estimations.

Updated: August 3, 2015 — 12:57 am