Table 1 Multiple linear regression models are developed to predict the WEs of the Tarbela and Mangla reservoirs.

From: Contribution of changing precipitation and climatic oscillations in explaining variability of water extents of large reservoirs in Pakistan

Reservoirs

Predictors

Numbers of variables

Fitting Model

Criteria

MLR Models

ANOVA

RMSE (km2)

Model Equation

Number of Significant Predictors

Most Influential Predictor

R²

Adj R²

df

Training

Validation

Tarbela

Years, ENSO, NAO, IOD, ERA Tp and ERA Ap

78

Best Model

Stepwise

Forward

Best Adjusted R²

In: P value 0.05 Out: P Value 0.10

P value 0.05

0.56

0.59

0.52

0.53

0.57

0.49

61

63

66

35.0

33.5

35.9

72.9

122.6

60.2

WE = 159.9-0.007×APH Ap-2.57×ERA Tp GB520P+2.48×ERA Tp GL5P-0.039×ERA Ap GL5+0.023×ERA Ap GG20P+0.009×ERA Ap GB520P+0.036×ERA Ap GL5P-0.027×ERA Ap GG20D-0.037×ERA Ap GB520D+0.035×ERA Ap GL5D

WE = 27.4-0.006×APH Ap+0.64×ERA Tp T17+0.74×ERA Tp T21+0.027×ERA Ap T3-0.03×ERA Ap T15+0.027×ERA Ap T17

WE = 160.1-0.66×ERA Tp T15+0.94×ERA Tp T17-0.79×ERA Tp T25+0.043×ERA Ap T3-0.007×ERA Ap GB520P+0.0005×ERA Ap GG20D

10

6

6

ERA Tp GB520P

ERA Ap T3

ERA Ap T3

Years, ENSO, NAO, IOD, ERA Tp, ERA Ap, APH Tp and APH Ap

148

Best Model

Stepwise

Forward

Best Adjusted R²

In: P value 0.05 Out: P Value 0.10

P value 0.05

0.52

0.63

0.56

0.45

0.58

0.53

120

124

124

38.4

33.0

36.4

108.1

69.9

61.1

WE = 207.3-4.46×ERA Tp GB520P+4.42×ERA Tp GL5P+0.16×APH Ap T26-0.032×APH Ap GL5-0.017×APH Ap GG20P-0.047×APH Ap GB520P+0.03×APH Ap GL5P+0.008×APH Ap GG20D+0.07×APH Ap GB520D+0.041×Aph Ap GL5D

WE = 161.5+12.57×ENSO+1.08×ERA Tp T6-3.27×ERA Tp T25-2.73×ERA Tp GB520P+4.12×ERA Tp GL5D+0.035×ERA Ap T3-0.022×ERA Ap T9-0.012×APH Ap T9

WE = 171.5+16.72×ENSO-0.93×ERA Tp T25+0.016×ERA Ap T3-0.02×ERA Ap GG20D+0.0075×ERA Ap GL5D

10

8

5

ERA Tp GB520P

ERA Tp T25

ERA Tp T25

Mangla

Years, ENSO, NAO, IOD, ERA Tp and ERA Ap

22

Best Model

Stepwise

Forward

Best Adjusted R²

In: P value 0.05 Out: P Value 0.10

P value 0.05

0.37

0.23

0.22

0.33

0.22

0.20

60

65

66

55.3

59.3

59.2

78.0

63.0

61.6

WE = 189.6+5.63×ENSO-15.12×NAO-2.03×ERA Tp-0.11×ERA Ap+2.42×ERA Tp GL5P+0.068×ERA Ap M1-2.17×ERA Ap M4+0.055×ERA Ap M5

WE = 184.9-0.96×ERA Tp M1+0.73×ERA Tp

WE = 183.3-16.08×NAO-0.77×ERA Tp M1+0.53×ERA Tp M3

8

2

3

ERA Tp

ERA Tp M1

ERA Tp M1

Years, ENSO, NAO, IOD, ERA Tp, ERA Ap, APH Tp and APH Ap

40

Best Model

Stepwise

Forward

Best Adjusted R²

In: P value 0.05 Out: P Value 0.10

P value 0.05

0.51

0.44

0.39

0.43

0.40

0.36

138

144

143

48.1

47.9

50.1

92.5

88.6

77.0

WE = 172.7-23.3×NAO-1.30×ERA Tp M1+1.11×ERA Tp M3+12.41×APH Tp GL5-11.16×APH Tp GL5D+12.76×APH Ap M4-0.039×APH Ap M5+0.24×APH Ap GL5-0.13×APH Ap GL5P-0.18×APH Ap GL5D

WE = 183.9-0.75×ERA Tp M1+2.81×ERA Tp M3-3.07×ERA Tp GL5P+3.92×APH Tp M4-1.62×APH Tp M5

WE = 182.5-1.05×ERA Tp M1+0.70×ERA Tp M3+3.67×APH Tp M4-1.57×APH Tp M5

10

5

4

APH Ap GL5P

APH Tp M4

ERA Tp M1

  1. Three different regression models’ approaches are employed using different number of predictor variables at monthly scale. Difference in number of predictors for the Tarbela and Mangla is due to different number of sub-basins. Best models are showed in bold (with highest R2 value). Most influential predictor is also identified based on its maximum contribution to model performance and is displayed in bold in extreme column.
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