Case Study

This methodology is applied to twenty eight stations which are already shown in Fig. 6.4 for Turkey. Also for interpretations three stations (Adana, Ankara and Istanbul) are considered in detail. Parameter estimation according to restricted and UMs are given in Table 6.2 for all considered sites.

Through the UM, it has been observed that in the classical regression tech­nique, requirements of normality in the frequency distribution function and of lin­earity and the use of the cross-correlation coefficient are imbedded unnecessarily in the parameter estimations. Assumptions in the restrictive (Angstrom) model cause

Table 6.2 Estimated Angstrom parameters with restricted and UMs

Station Name

Restricted (Angstrom Equation

Unrestricted Methodology (UM)

a

b

a

b’

Adana

0.33

0.29

0.20

0.50

Adiyaman

0.30

0.22

0.25

0.28

Afyon

0.40

0.28

0.36

0.34

Amasya

0.30

0.38

0.26

0.41

Anamur

0.36

0.25

0.26

0.40

Ankara

0.31

0.32

0.28

0.38

Antalya

0.33

0.38

0.22

0.55

Aydin

0.32

0.42

0.25

0.53

Balikesir

0.23

0.37

0.20

0.41

Bursa

0.27

0.33

0.21

0.46

Canakkale

0.31

0.33

0.27

0.41

Cankiri

0.35

0.32

0.32

0.40

Diyarbakir

0.23

0.48

0.16

0.61

Erzincan

0.44

0.15

0.34

0.33

Eskijehir

0.39

0.26

0.33

0.39

Istanbul

0.30

0.35

0.27

0.41

Isparta

0.36

0.16

0.30

0.26

Izmir

0.33

0.33

0.25

0.45

Kars

0.50

0.12

0.34

0.45

Kastamonu

0.32

0.24

0.29

0.29

Kayseri

0.36

0.23

0.30

0.36

Kirsehir

0.43

0.20

0.36

0.30

Konya

0.38

0.27

0.30

0.40

Malatya

0.31

0.37

0.26

0.45

Mersin

0.33

0.40

0.36

0.45

Trabzon

0.28

0.38

0.23

0.51

Van

0.51

0.14

0.38

0.34

over-estimations in the solar irradiance amounts as suggested by Angstrom for small (smaller than the arithmetic average) sunshine duration and under-estimations for large sunshine duration values. Around the average values solar irradiation and sunshine duration values are close to each other for both models, however, the UM approach alleviates these biased-estimation situations. Additionally, the UM includes some features of non-linearity in the solar energy data scatter diagram by ignoring consideration of cross-correlation coefficient. Finally, in Fig. 6.7 straight­lines obtained separately from the classical regression and UM approaches are pre­sented for Ankara, Adana and Istanbul stations. Especially, at Adana, Fig. 6.7b, UM and classical approach deviates significantly. This means that at Adana all points are scattered more randomly than others. In the CD accompanying this book the reader will find details of Fig. 6.7.

0. 2

S/So

(c)

—I__________ I__

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

S/So

Fig. 6.7 Restricted and unrestricted methodologies (a) Ankara; (b) Adana; (c) Istanbul

Updated: August 3, 2015 — 4:30 am