Table 2 Statistical summary of 1808 photoinhibition model fits, ordered by increasing mean root mean squared error (RMSE)

From: Parameterization of photoinhibition for phytoplankton

Model

p

All irradiance

Excluding \({{{\rm{I}}}}\) < \({{{{\rm{I}}}}}_{{{{\rm{\alpha }}}}}\)

Median R2adj (%)

Mean RMSE

Mean rRMSE (%)

Median R2adj (%)

Mean RMSE

Mean rRMSE (%)

Tanh-tanh-γ

5

96.5

0.144

−5.860

64.6

0.161

−8.080

Exp-tanh-γ

5

96.4

0.146

−4.620

64.2

0.163

−7.360

Fasham & Platt21

5

96.3

0.148

−3.340

57.7

0.172

−1.590

Amirian

4

96.1

0.151

0.000

59.0

0.175

0.000

Exp−tanh

4

95.9

0.156

3.320

58.5

0.180

2.920

Smith32a

4

95.7

0.161

7.360

52.7

0.194

14.72

Bannister26a

5

95.4

0.161

8.780

50.8

0.193

15.98

Prioul & Chartier25a

5

95.4

0.166

9.250

47.4

0.198

16.06

Exp-exp

4

95.6

0.162

9.170

56.4

0.193

14.67

Neale & Richerson20

4

95.5

0.164

10.62

48.7

0.198

18.52

Platt et al.16

4

95.4

0.169

13.29

47.5

0.204

21.28

Tanh−exp

4

95.4

0.164

10.69

52.1

0.197

17.92

Blackman33a

4

94.6

0.180

27.96

40.1

0.212

33.46

Baly9a

4

94.3

0.186

25.80

44.1

0.228

36.50

Peeters & Eilers28

4

93.5

0.195

34.64

37.8

0.243

49.45

Steele15

3

89.3

0.248

74.03

22.4

0.279

70.25

  1. The number of parameters is p. Statistics are median adjusted R2 (%), mean RMSE, mean relative RMSE (rRMSE) computed over all irradiances and, in the last three columns, excluding data points in the light limited region (\({{{\rm{I}}}}\) < \({{{{\rm{I}}}}}_{{{{\rm{\alpha }}}}}\)). The best model for each number of parameters is highlighted in bold. Positive rRMSE indicates a higher RMSE than the Amirian model, while negative values show a reduction—typically seen in models with additional parameters.
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