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Table 4 Sunshine duration-based seasonal regression models and their statistical evaluation

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

Model no.

Model type

Seasons

Equations

\(R^{2}\)

MBE

MPE

RMSE

MARE

t stat

7

Linear

Summer (February–September)

\(H/H_0 = 0.5077(S/S_0) + 0.1915\)

0.96833

0.00131

0.09172

0.12833

0.02795

0.03394

Winter (October–January)

\(H/H_0 = 0.8805(S/S_0) - 0.1174\)

8

Quadratic

Summer (February–September)

\(H/H_0 = 0.5469(S/S_0)^2 - 0.0692(S/S_0) + 0.3315\)

0.97693

0.0023

0.05783

0.10953

0.02242

0.06984

Winter (October–January)

\(H/H_0 = 9.3987(S/S_0)^2 - 11.518(S/S_0) + 3.9476\)

9

Third degree

Summer (February–September)

\(H/H_0 = -1.6819(S/S_0)^3 + 3.2167(S/S_0)^2 - 1.4324(S/S_0) + 0.5545\)

0.98538

−0.00178

0.09116

0.08719

0.01302

0.06798

Winter (October–January)

\(H/H_0 = 1290(S/S_0)^3 - 2585.5(S/S_0)^2 + 1723.8(S/S_0) - 381.77\)

10

Exponential

Summer (February–September)

\(H/H_0 = 0.2523\exp [1.1088(S/S_0)]\)

0.97284

0.00425

0.04336

0.11886

0.02535

0.11858

Winter (October–January)

\(H/H_0 = 0.1341\exp [1.8733(S/S_0)]\)

11

Logarithmic

Summer (February–September)

\(H/H_0 = 0.254\hbox {ln}(S/S_0) + 0.6323\)

0.95165

−0.00049

0.1278

0.1586

0.03468

0.01023

Winter (October–January)

\(H/H_0 = 0.5763\hbox {ln}(S/S_0) + 0.705\)

12

Power

Summer (February–September)

\(H/H_0 = 0.6617(S/S_0)^{0.5567}\)

0.96336

0.00293

0.05992

0.13805

0.029

0.07044

Winter (October–January)

\(H/H_0 = 0.7715(S/S_0)^{1.227}\)