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Table 3 Sunshine duration-based annual regression results and their statistical evaluation

From: Global solar radiation estimation from commonly available meteorological data for Bangladesh

Model no.

Model type

Equations

\(R^{2}\)

MBE

MPE

RMSE

MARE

t stat

1

Linear

\(H{/}H_0 = 0.4256 (S{/}S_0) + 0.2199\)

0.8888

0.0183

0.3446

0.2404

0.3446

0.2538

2

Quad.

\(H{/}H_0 = 0.749(S{/}S_0)^2 - 0.3752(S{/}S_0) + 0.417\)

0.8920

0.0216

0.3276

0.2369

0.0440

0.3049

3

Cubic

\(H{/}H_0 = 3.1987(S{/}S_0)^3 - 4.4223(S{/}S_0)^2 + 2.3158(S{/}S_0) - 0.0306\)

0.8899

0.0231

0.3246

0.2393

0.0471

0.3226

4

Expo.

\(H{/}H_0 = 0.2673 \exp [0.9422(S/S_0)]\)

0.8913

0.0261

0.1707

0.2376

0.0494

0.3673

5

Log.

\(H{/}H_0 = 0.2152\,\hbox {ln}(S{/}S_0) + 0.5916\)

0.8729

0.0153

0.3850

0.2570

0.0560

0.1981

6

Power

\(H{/}H_0 = 0.6093(S{/}S_0)^{0.478}\)

0.8804

0.0233

0.1998

0.2493

0.0537

0.3125