Table 4 Maximum residual errors of the convolved radiances assuming sub-band-averaged extraterrestrial solar irradiance and a filter response function. Residual errors lager than the expected residual values are underlined

(a) 936 nm

Type 1

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

221

0.451

0.205

0.063

145

0.165

0.022

0.140

110

0.173

0.117

0.193

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

12.7

0.016

0.053

0.024

8.13

0.005

0.019

0.062

7.00

0.002

0.014

0.071

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

221

0.451

0.331

0.063

145

0.375

0.071

0.140

110

0.421

0.169

0.193

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

23.2

0.057

0.126

0.024

21.2

0.216

0.074

0.183

18.2

0.249

0.055

0.265

Type 2

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

127

1.038

0.437

0.123

107

0.624

0.441

0.239

86.8

0.573

0.436

0.296

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

23.3

0.019

0.013

0.032

17.4

0.002

0.038

0.054

14.0

0.026

0.045

0.042

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

194

1.038

0.619

0.123

136

0.624

0.550

0.239

105

0.573

0.525

0.296

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

67.1

0.397

0.183

0.046

28.8

0.265

0.109

0.065

18.0

0.169

0.089

0.105

Type 3

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

93.2

1.470

0.512

0.214

7.58

1.213

0.311

0.218

17.9

1.000

0.249

0.178

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

14.4

0.005

0.035

0.002

11.9

0.043

0.048

0.037

8.19

0.067

0.065

0.052

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

93.2

1.470

0.541

0.214

43.2

1.213

0.405

0.218

41.8

1.006

0.329

0.178

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

86.7

0.177

0.035

0.084

38.9

0.075

0.094

0.085

24.0

0.067

0.080

0.052

Type 4

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

144

0.996

0.520

0.205

114

0.611

0.501

0.254

91.3

0.573

0.465

0.293

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

14.4

0.020

0.011

0.023

11.7

0.006

0.028

0.037

10.1

0.015

0.033

0.033

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

176

0.996

0.578

0.205

128

0.611

0.557

0.254

98.7

0.573

0.517

0.293

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

32.5

0.180

0.058

0.026

13.4

0.139

0.056

0.037

10.1

0.094

0.052

0.043

Expected residual error (\(\times 10^{ - 3}\))

\(D{\Phi }\left( {\varepsilon_{E}^{2} } \right)^{1/2}\)

2.0

1.4

1.1

(b) 940 nm

Type 1

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

72.8

0.018

0.261

0.646

136

0.166

0.099

0.199

128

0.169

0.028

0.097

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

1.66

0.007

0.046

0.060

3.71

0.005

0.029

0.051

4.77

0.006

0.018

0.051

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

72.8

0.329

0.260

0.719

136

0.391

0.099

0.407

128

0.416

0.037

0.217

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

24.0

0.347

0.112

0.073

28.2

0.230

0.052

0.208

25.6

0.253

0.047

0.263

Type 2

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

80.0

0.472

0.228

0.185

127

0.631

0.275

0.157

116

0.573

0.324

0.236

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

11.5

0.033

0.044

0.039

14.8

0.019

0.024

0.029

15.3

0.002

0.028

0.033

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

85.3

0.472

0.506

0.185

140

0.631

0.378

0.216

130

0.573

0.356

0.235

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

11.5

0.295

0.278

0.283

14.8

0.203

0.103

0.088

15.3

0.159

0.033

0.033

Type 3

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

26.7

1.639

0.335

0.087

44.2

1.486

0.407

0.169

35.7

1.136

0.342

0.101

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

11.0

0.011

0.053

0.018

12.5

0.007

0.040

0.022

11.6

0.026

0.045

0.040

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

47.0

1.639

0.455

0.087

75.6

1.486

0.445

0.169

65.5

1.136

0.389

0.101

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

20.3

0.170

0.119

0.018

31.4

0.104

0.040

0.022

29.8

0.039

0.048

0.040

Type 4

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

80.3

0.465

0.374

0.013

130

0.638

0.331

0.277

119

0.573

0.346

0.296

(ALM)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

7.72

0.033

0.030

0.021

9.73

0.020

0.016

0.016

10.3

0.006

0.018

0.022

\(\left| {\varepsilon_{{\hat{I}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

81.9

0.465

0.497

0.121

136

0.638

0.382

0.300

126

0.573

0.369

0.296

(PPL)

\(\left| {\varepsilon_{{\hat{R}{\text{max}}}} } \right|\)(\(\times 10^{ - 3}\))

7.72

0.150

0.123

0.129

9.73

0.102

0.051

0.039

10.3

0.083

0.024

0.022

Expected residual error (\(\times 10^{ - 3}\))

\(D{\Phi }\left( {\varepsilon_{E}^{2} } \right)^{1/2}\)

2.0

1.4

1.1