Table 5 Statistical comparison of calibration (Ca) and validation (Va) estimated Rs (using the locally calibrated of the models coefficients).

From: Calibration and validation of the Angstrom–Prescott model in solar radiation estimation using optimization algorithms

Station

Algorithm

 

A–P model

Model 1

Model 2

Model 3

RMSE

R2

MBE

RMSE

R2

MBE

RMSE

R2

MBE

RMSE

R2

MBE

Bandar Abbas

SCE

Ca

1.13

0.841

0

1.41

0.841

− 0.80

1.13

0.841

0.00

1.17

0.840

0.30

Va

1.60

0.835

− 0.41

2.08

0.840

− 1.25

1.60

0.835

− 0.41

1.55

0.836

− 0.11

HS

Ca

1.16

0.835

0.21

1.16

0.835

− 0.03

1.22

0.816

− 0.01

1.25

0.823

− 0.16

Va

1.53

0.836

− 0.19

1.62

0.827

− 0.43

1.69

0.807

− 0.42

1.63

0.818

− 0.52

IHS

Ca

1.15

0.839

− 0.13

1.17

0.838

− 0.23

1.18

0.833

0.15

1.20

0.821

0.08

Va

1.69

0.832

− 0.55

1.66

0.838

− 0.64

1.56

0.830

− 0.26

1.70

0.809

− 0.34

GHS

Ca

1.16

0.841

− 0.19

1.17

0.841

− 0.16

1.14

0.840

− 0.09

1.35

0.825

0.62

Va

1.61

0.839

− 0.58

1.56

0.841

− 0.54

1.62

0.835

− 0.49

1.73

0.814

0.16

Esfahan

SCE

Ca

0.83

0.970

0.09

0.83

0.970

0.01

0.83

0.970

0.09

0.83

0.969

0.01

Va

1.3

0.941

0.40

1.29

0.940

0.32

1.31

0.940

0.4

1.29

0.946

0.32

HS

Ca

0.84

0.962

− 0.07

0.90

0.966

− 0.19

0.96

0.964

− 0.02

1.13

0.943

0.12

Va

1.26

0.940

0.24

1.29

0.937

0.14

1.40

0.935

0.26

1.53

0.923

0.36

IHS

Ca

0.85

0.966

− 0.04

0.92

0.970

0.04

0.93

0.967

0.06

0.85

0.968

0.07

Va

1.3

0.940

0.27

1.32

0.940

0.36

1.40

0.937

0.37

1.33

0.945

0.38

GHS

Ca

0.84

0.968

− 0.12

0.83

0.970

0.01

0.87

0.970

− 0.28

0.94

0.968

0.26

Va

1.27

0.941

0.19

1.28

0.940

0.32

1.24

0.940

0.03

1.39

0.946

0.58

Kerman

SCE

Ca

1.15

0.923

− 0.82

1.15

0.924

0.01

1.15

0.924

− 0.13

1.14

0.925

− 0.10

Va

1.56

0.909

− 0.27

1.54

0.910

− 0.30

1.58

0.910

− 0.43

1.55

0.911

− 0.41

HS

Ca

1.39

0.908

− 1.34

1.36

0.895

− 0.17

1.74

0.891

1.01

1.71

0.904

− 0.34

Va

1.23

0.895

− 1.62

1.85

0.866

− 0.44

1.79

0.870

0.69

1.72

0.890

− 0.56

IHS

Ca

1.22

0.908

− 1.10

1.24

0.923

0.18

1.30

0.912

0.18

1.29

0.917

− 0.21

Va

1.26

0.923

− 1.35

1.71

0.910

− 0.17

1.74

0.897

− 0.13

1.55

0.901

− 0.50

GHS

Ca

1.29

0.923

− 1.32

1.15

0.924

0.10

1.16

0.923

− 0.08

1.21

0.919

0.25

Va

1.56

0.909

− 1.59

1.55

0.910

− 0.22

1.57

0.908

− 0.38

1.50

0.907

− 0.06

Mashhad

SCE

Ca

0.82

0.981

0.07

0.82

0.981

0.05

0.84

0.981

0.18

0.82

0.981

− 0.10

Va

1.24

0.961

0.07

1.24

0.960

0.08

1.26

0.961

0.17

1.25

0.961

− 0.11

HS

Ca

0.86

0.980

0.12

1.03

0.971

0.12

1.05

0.970

− 0.10

1.02

0.972

− 0.06

Va

1.31

0.960

0.10

1.43

0.951

0.09

1.45

0.948

− 0.10

1.34

0.952

− 0.08

IHS

Ca

0.84

0.981

0.18

0.90

0.977

− 0.05

0.88

0.979

0.14

1.03

0.976

− 0.12

Va

1.26

0.960

0.17

1.30

0.957

− 0.05

1.27

0.959

0.12

1.30

0.957

− 0.12

GHS

Ca

0.83

0.981

− 0.04

0.86

0.979

0.03

0.87

0.981

− 0.15

0.92

0.979

− 0.22

Va

1.22

0.961

− 0.04

1.27

0.959

0.03

1.32

0.960

− 0.17

1.25

0.959

− 0.22

Shiraz

SCE

Ca

1.30

0.923

0.05

1.31

0.921

− 0.18

1.28

0.923

0.05

1.27

0.923

− 0.04

Va

2.61

0.913

− 2.09

2.21

0.913

− 1.5

1.91

0.915

− 1.03

1.95

0.916

− 1.12

HS

Ca

1.35

0.922

− 0.32

2.15

0.918

− 3.9

1.39

0.908

− 0.03

1.48

0.911

0

Va

2.99

0.912

− 2.50

5.38

0.909

− 5.09

2.15

0.899

− 1.27

1.82

0.904

− 0.86

IHS

Ca

1.32

0.922

0.20

1.40

0.917

0.45

1.35

0.917

0.02

1.38

0.913

− 0.11

Va

2.54

0.912

− 1.97

1.90

0.912

− 0.75

1.83

0.909

− 0.91

2.04

0.900

− 1.16

GHS

Ca

1.38

0.923

− 0.33

1.30

0.921

0.15

1.37

0.922

0.06

1.4

0.917

− 0.21

Va

2.85

0.913

− 2.41

1.90

0.913

− 0.98

1.79

0.915

− 0.96

2.28

0.913

− 1.39

Yazd

SCE

Ca

2.67

0.921

− 2.36

2.21

0.921

− 2.65

1.51

0.924

0.04

1.50

0.925

0.02

Va

2.39

0.916

− 2.68

2.11

0.916

− 2.33

1.72

0.919

0.48

1.71

0.920

0.51

HS

Ca

2.03

0.920

− 1.39

1.73

0.913

− 0.30

1.58

0.919

0.15

1.69

0.904

− 0.04

Va

1.75

0.913

0.36

1.99

0.910

0.81

1.78

0.918

0.55

1.86

0.897

0.20

IHS

Ca

1.94

0.921

− 1.25

1.55

0.920

− 0.05

1.70

0.920

− 0.24

1.73

0.905

0.16

Va

1.76

0.914

0.52

1.72

0.914

0.32

1.75

0.915

0.30

1.99

0.899

0.50

GHS

Ca

2.00

0.921

− 1.32

1.56

0.922

− 0.26

1.56

0.924

0.25

1.59

0.920

0.19

Va

1.73

0.915

0.45

1.66

0.917

0.19

1.84

0.919

0.67

1.88

0.915

0.73

  1. RMSE (MJ m−2 day−1), MBE (MJ m−2 day−1).
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