Srikanth Ayyala Somayajula,1,*
Emmanuel Devred,2
Simon Bélanger,3
David Antoine,4,5
V. Vellucci,4
and Marcel Babin1
1Takuvik Joint International Laboratory, Laval University (Canada)—CNRS (France), Département de Biologie et Québec-Océan, Université Laval, Québec City, Québec G1V 0A6, Canada
2DFO-MPO, Fisheries and Oceans Canada, 1 Challenger Drive, Dartmouth, Nova Scotia B2Y 4A2, Canada
3Université du Québec à Rimouski, Département de Biologie, Chimie et Géographie and BORÉAS, 300 allée des Ursulines, Rimouski, Québec G5L 3A1, Canada
4Sorbonne Universités, Université Pierre et Marie Curie, Paris 06, UMR 7093, Laboratoire d’Océanographie de Villefranche, Observatoire Océanologique, Villefranche-sur-Mer 06230, France
5Remote Sensing and Satellite Research Group, Department of Physics and Astronomy, Curtin University, Perth, WA 6845, Australia
Srikanth Ayyala Somayajula, Emmanuel Devred, Simon Bélanger, David Antoine, V. Vellucci, and Marcel Babin, "Evaluation of sea-surface photosynthetically available radiation algorithms under various sky conditions and solar elevations," Appl. Opt. 57, 3088-3105 (2018)
In this study, we report on the performance of satellite-based photosynthetically available radiation (PAR) algorithms used in published oceanic primary production models. The performance of these algorithms was evaluated using buoy observations under clear and cloudy skies, and for the particular case of low sun angles typically encountered at high latitudes or at moderate latitudes in winter. The PAR models consisted of (i) the standard one from the NASA-Ocean Biology Processing Group (OBPG), (ii) the Gregg and Carder (GC) semi-analytical clear-sky model, and (iii) look-up-tables based on the Santa Barbara DISORT atmospheric radiative transfer (SBDART) model. Various combinations of atmospheric inputs, empirical cloud corrections, and semi-analytical irradiance models yielded a total of 13 (11 + 2 developed in this study) different PAR products, which were compared with in situ measurements collected at high frequency (15 min) at a buoy site in the Mediterranean Sea (the “BOUée pour l’acquiSition d’une Série Optique à Long termE,” or, “BOUSSOLE” site). An objective ranking method applied to the algorithm results indicated that seven PAR products out of 13 were well in agreement with the in situ measurements. Specifically, the OBPG method showed the best overall performance with a root mean square difference (RMSD) (bias) of 19.7% (6.6%) and 10% (6.3%) followed by the look-up-table method with a RMSD (bias) of 25.5% (6.8%) and 9.6% (2.6%) at daily and monthly scales, respectively. Among the four methods based on clear-sky PAR empirically corrected for cloud cover, the Dobson and Smith method consistently underestimated daily PAR while the Budyko formulation overestimated daily PAR. Empirically cloud-corrected methods using cloud fraction (CF) performed better under quasi-clear skies () with an RMSD (bias) of 9.7%–14.8% (3.6%–11.3%) than under partially clear to cloudy skies () with 16.1%–21.2% (). Under complete overcast conditions (), however, all methods showed larger RMSD differences (biases) ranging between 32% and 80.6% (). Finally, three methods tested for low sun elevations revealed systematic overestimation, and one method showed a systematic underestimation of daily PAR, with relative RMSDs as large as 50% under all sky conditions. Under partially clear to overcast conditions all the methods underestimated PAR. Model uncertainties predominantly depend on which cloud products were used.
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The acronyms correspond to the following: OBGP, Ocean Biology Processing Group; SB, SBDART radiative transfer model; GC, Greg and Carder model; IS, ISCCP dataset; M, MODIS-Aqua dataset; DS, Dobson and Smith cloud attenuation formulation; B, Budyko cloud attenuation formulation as modified by Morel and Andre [39]; NC, new cloud attenuation formulation (this study).
Table 2.
Meteorological and Sun Variables Represented in the Gregg and Carder Model
Parameter
Value
Pressure (), Pa
101325
Air-mass type (AM)
1 (maritime aerosol)
Relative humidity (RH), %
80
Precipitable water (WV), cm
1
Mean wind speed (WM),
4
Instantaneous wind speed (WS)
6
Visibility (), km
23
Total ozone (), DU
300
Sun zenith angle ()
20°–89°
Table 3.
Input Parameters Used in SBDART Model to Generate LUT
Parameter
Values
Sun zenith angle ()
0° to 90° at every 5°
Ozone column ()
100–550, at every 50 Dobson units (DU)
Cloud optical thickness ()
0, 1, 2, 4, 8, 16, 32 and 64
Marine aerosol
optical thickness equal to 0.1 at 550 nm
Mid-latitude summer atmosphere
defining standard vertical profiles of pressure, temperature and water vapor (McClatchey et al.) [49]
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Estimated Between Each Method Estimate and In situ for Daily and Monthly PAR Valuesa
Model
Daily
Monthly
(%)
(%)
(%)
(%)
OBPG
0.96
4.91 (19.7%)
4.79
1.17 (6.6%)
0.98
1.71
0.98
3.61 (9.9%)
3.04
1.94 (6.3%)
0.98
2.49
SB_M
0.93
5.73 (25.5%)
6.73
0.16 (6.8%)
1.02
−0.67
0.98
3.28 (9.6%)
3.22
0.63 (2.6%)
1
0.29
SB_IS
0.93
5.96 (27.3%)
5.96
0.61 (11.9%)
1
0.35
0.98
3.63 (9.8%)
3.37
1.34 (3.9%)
1
0.88
SB_DS_M
0.92
8.1 (35.4%)
8.1
−4.29 (−3.7%)
0.82
1.13
0.98
5.02 (14.4%)
3.3
−3.78 (−10.3%)
086
0.68
SB_DS_IS
0.92
8.9 (40%)
8.9
−5.43 (−3.6%)
0.72
3.03
0.97
6.49 (16.6%)
0.19
−4.96 (−13%)
0.79
1.73
SB_B_M
0.92
6.23 (30.8%)
6.83
0.95 (10.7%)
0.96
0.05
0.98
2.89 (9%)
2.87
0.32 (0%)
0.98
0.088
SB_B_IS
0.93
6.44 (35.9%)
6.44
0.56 (19.3%)
0.89
2.82
0.97
3.21 (9.9%)
3.21
0.034 (2.7%)
0.94
1.76
GC_DS_M
0.91
8.02 (36.7%)
7.14
−3.64 (−8.7%)
0.78
2.92
0.98
6.2 (13.4%)
4.22
−4.54 (−6.9%)
0.77
2.48
GC_DS_IS
0.92
8.93 (41.3%)
7.6
−4.69 (−8.9%)
0.68
5
0.97
6.88 (16.1%)
4.95
−4.78 (−9.1%)
0.73
3.67
GC_B_M
0.92
6.36 (32.5%)
6.85
0.25 (15.9%)
0.92
1.95
0.98
3.29 (8.9%)
2.62
2 (3.7%)
0.97
2.75
GC_B_IS
0.92
6.78 (36.8%)
6.77
0.28 (24.8%)
0.84
5.11
0.97
3.75 (12.1%)
3.26
1.81 (6.7%)
0.91
4.34
SB_NC_M
0.95
5.87 (36.8%)
5.87
1.66 (27.3%)
0.97
2.4
0.98
3.87 (11.4%)
2.93
2.53 (9.9%)
1
1.31
SB_NC_IS
0.94
6.28 (43.1%)
6.28
2.25 (35.1%)
0.92
4.61
0.98
4.41 (14.5%)
3.1
3.13 (13.1%)
1
2.67
RMSD, CMRSD and Bias are in units of mol photons . The % values refer to relative RMSD and Bias.
Table 5.
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Computed between Each Method Estimate and in situ towards the Study of Impact of Clouds and Cloud Products on PAR Values Under Different Sky Conditionsa
Model
Sky Conditions
(%)
(%)
(%)
(%)
(%)
(%)
OBPG
0.97
4.32 (9.7%)
4.25
0.77 (3.6%)
0.95
2.64
0.94
5.72 (16.1%)
5.18
2.43 (9.2%)
0.96
3.08
0.94
5.67 (32%)
5.62
0.77 (8.7%)
1
0.47
SB_M
0.95
6.02 (13%)
5.44
2.58 (7.2%)
1
0.34
0.91
6.42 (16.3%)
6.35
−0.9 (−1.5%)
0.94
0.73
0.88
7.54 (42.7%)
7.29
−1.9 (−10.1%)
0.86
1.24
SB_IS
0.97
5.4 (14%)
4.75
2.56 (8.5%)
1
0.14
0.94
5.6 (20.1%)
5.51
1.03 (8.5%)
0.98
1.58
0.91
6.79 (47.9%)
6.55
−1.8 (−18.7%)
0.84
1.82
SB_B_M
0.97
5.17 (11.5%)
4.5
2.54 (7.8%)
1
0.42
0.94
5.18 (13.9%)
4.98
−1.5 (−2.2%)
0.88
3.03
0.9
8.73 (57.3%)
7.52
−4.4 (−20.5%)
0.6
4.45
SB_B_IS
0.96
5.06 (13.7%)
4.69
1.89 (7.4%)
1
0.69
0.94
5.59 (20.1%)
5.5
1 (4.64%)
0.86
3.55
0.9
8.23 (74.1%)
7.78
−2.7 (−45%)
0.6
6.51
GC_B_M
0.96
5.39 (12.4%)
4.38
3.13 (9.9%)
1
2.53
0.94
5.38 (14.1%)
5.27
1.08 (2.1%)
0.81
4.6
0.9
9.05 (61.6%)
8.2
−3.83 (−28.3%)
0.51
6.24
GC_B_IS
0.96
5.02 (14.8%)
4.38
2.44 (11.3%)
0.97
3.24
0.94
6.76 (21.2%)
6.75
0.47 (8.8%)
0.76
7.21
0.9
8.69 80.6%)
8.59
−21.35 (−54.5%)
0.51
8.4
RMSD, CMRSD and Bias are in units of in mol photons . The % values refer to the relative RMSD and Bias.
Table 6.
Comparison of Mean Differences of Daily Integrated PAR Modeled and Estimated Under Different Spatial and Temporal Binning for MODIS (; 24 h) and ISCCP (; 3 h)a
PAR
Mean Absolute Difference (%) (Mean Difference (%))
Difference Due to Spatial Mismatch
1 deg ()
()
()
280 Km
()
()
()
Difference Due to Temporal Mismatch
24 h
3 h
The values are given in relative units.
Table 7.
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Computed between Each Method Estimate and In Situ Data Under All Sky Conditions for Low Sun Elevationsa
Model
(%)
(%)
SB_IS
0.88
92.5 (55.1%)
91.91
11 (23.2%)
0.97
17.03
SB_DS_IS
0.86
92.4 (50.7%)
89.15
−24 (−6.4%)
0.82
16.07
SB_B_IS
0.87
94.7 (55.4%)
94.51
6 (21.5%)
0.95
17.33
SB_NC_IS
0.88
94.8 (57.2%)
93.7
14 (27%)
0.97
20.6
RMSD, CMRSD and Bias are in units of in μmol photons . The % values refer to the relative RMSD and Bias.
Table 8.
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Computed Between Each Method Estimate and In Situ Data Under Different Sky Conditions for Low Sun Elevationsa
Model
Sky Conditions
(%)
(%)
(%)
(%)
(%)
(%)
SB_IS
0.89
100.19 (44.5%)
94.37
33.64 (21.8%)
1
21.5
0.86
84.46 (64.8%)
83.86
−9.32 (−9.3%)
0.83
26.14
0.77
85.46 (65.3%)
84.61
−11.98 (−18.2%)
0.72
29.89
SB_DS_IS
0.89
86.75 (39%)
86.69
−3.21 (−6.8%)
0.9
22.02
0.85
100.61 (59.8%)
86.41
−51.53 (−40.3%)
0.64
25.93
0.74
93.01 (63.9%)
86.53
34.1 (−8.1%)
0.53
37.4
SB_B_IS
0.99
53.23 (44.9%)
34.57
40.48 (22.4%)
0.88
−1.31
0.89
59.9 (65.3%)
40.26
−44.35 (−29.2%)
0.77
7.55
0.86
34.57 (64.8%)
40.43
−16.19 (−9.6%)
0.76
19.94
SB_NC_IS
0.89
103.28 (45.2%)
95.8
38.29 (24.3%)
1
29.5
0.86
87.98 (68.9%)
87.9
−2.91 (−8.2%)
0.85
35.15
0.77
81.31 (65.4%)
81.3
−21.7 (−18%)
0.63
34.5
RMSD, CMRSD and Bias are in units of in μ mol photons . The % values refer to the relative RMSD and Bias.
Tables (8)
Table 1.
Description of PAR Estimation Methods from Different Sources and Inputs Under All Sky Conditionsa
#
PAR Model
Cloud-Correction Scheme
Input Data
Method Name
Parameters Used
CF
1
OBPG Frouin et al.
N/A
MODIS-A
OBPG
✓
2
SB Ricchiazzi et al.
None, as in Bélanger et al. [18]; Laliberté et al. [24]
The acronyms correspond to the following: OBGP, Ocean Biology Processing Group; SB, SBDART radiative transfer model; GC, Greg and Carder model; IS, ISCCP dataset; M, MODIS-Aqua dataset; DS, Dobson and Smith cloud attenuation formulation; B, Budyko cloud attenuation formulation as modified by Morel and Andre [39]; NC, new cloud attenuation formulation (this study).
Table 2.
Meteorological and Sun Variables Represented in the Gregg and Carder Model
Parameter
Value
Pressure (), Pa
101325
Air-mass type (AM)
1 (maritime aerosol)
Relative humidity (RH), %
80
Precipitable water (WV), cm
1
Mean wind speed (WM),
4
Instantaneous wind speed (WS)
6
Visibility (), km
23
Total ozone (), DU
300
Sun zenith angle ()
20°–89°
Table 3.
Input Parameters Used in SBDART Model to Generate LUT
Parameter
Values
Sun zenith angle ()
0° to 90° at every 5°
Ozone column ()
100–550, at every 50 Dobson units (DU)
Cloud optical thickness ()
0, 1, 2, 4, 8, 16, 32 and 64
Marine aerosol
optical thickness equal to 0.1 at 550 nm
Mid-latitude summer atmosphere
defining standard vertical profiles of pressure, temperature and water vapor (McClatchey et al.) [49]
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Estimated Between Each Method Estimate and In situ for Daily and Monthly PAR Valuesa
Model
Daily
Monthly
(%)
(%)
(%)
(%)
OBPG
0.96
4.91 (19.7%)
4.79
1.17 (6.6%)
0.98
1.71
0.98
3.61 (9.9%)
3.04
1.94 (6.3%)
0.98
2.49
SB_M
0.93
5.73 (25.5%)
6.73
0.16 (6.8%)
1.02
−0.67
0.98
3.28 (9.6%)
3.22
0.63 (2.6%)
1
0.29
SB_IS
0.93
5.96 (27.3%)
5.96
0.61 (11.9%)
1
0.35
0.98
3.63 (9.8%)
3.37
1.34 (3.9%)
1
0.88
SB_DS_M
0.92
8.1 (35.4%)
8.1
−4.29 (−3.7%)
0.82
1.13
0.98
5.02 (14.4%)
3.3
−3.78 (−10.3%)
086
0.68
SB_DS_IS
0.92
8.9 (40%)
8.9
−5.43 (−3.6%)
0.72
3.03
0.97
6.49 (16.6%)
0.19
−4.96 (−13%)
0.79
1.73
SB_B_M
0.92
6.23 (30.8%)
6.83
0.95 (10.7%)
0.96
0.05
0.98
2.89 (9%)
2.87
0.32 (0%)
0.98
0.088
SB_B_IS
0.93
6.44 (35.9%)
6.44
0.56 (19.3%)
0.89
2.82
0.97
3.21 (9.9%)
3.21
0.034 (2.7%)
0.94
1.76
GC_DS_M
0.91
8.02 (36.7%)
7.14
−3.64 (−8.7%)
0.78
2.92
0.98
6.2 (13.4%)
4.22
−4.54 (−6.9%)
0.77
2.48
GC_DS_IS
0.92
8.93 (41.3%)
7.6
−4.69 (−8.9%)
0.68
5
0.97
6.88 (16.1%)
4.95
−4.78 (−9.1%)
0.73
3.67
GC_B_M
0.92
6.36 (32.5%)
6.85
0.25 (15.9%)
0.92
1.95
0.98
3.29 (8.9%)
2.62
2 (3.7%)
0.97
2.75
GC_B_IS
0.92
6.78 (36.8%)
6.77
0.28 (24.8%)
0.84
5.11
0.97
3.75 (12.1%)
3.26
1.81 (6.7%)
0.91
4.34
SB_NC_M
0.95
5.87 (36.8%)
5.87
1.66 (27.3%)
0.97
2.4
0.98
3.87 (11.4%)
2.93
2.53 (9.9%)
1
1.31
SB_NC_IS
0.94
6.28 (43.1%)
6.28
2.25 (35.1%)
0.92
4.61
0.98
4.41 (14.5%)
3.1
3.13 (13.1%)
1
2.67
RMSD, CMRSD and Bias are in units of mol photons . The % values refer to relative RMSD and Bias.
Table 5.
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Computed between Each Method Estimate and in situ towards the Study of Impact of Clouds and Cloud Products on PAR Values Under Different Sky Conditionsa
Model
Sky Conditions
(%)
(%)
(%)
(%)
(%)
(%)
OBPG
0.97
4.32 (9.7%)
4.25
0.77 (3.6%)
0.95
2.64
0.94
5.72 (16.1%)
5.18
2.43 (9.2%)
0.96
3.08
0.94
5.67 (32%)
5.62
0.77 (8.7%)
1
0.47
SB_M
0.95
6.02 (13%)
5.44
2.58 (7.2%)
1
0.34
0.91
6.42 (16.3%)
6.35
−0.9 (−1.5%)
0.94
0.73
0.88
7.54 (42.7%)
7.29
−1.9 (−10.1%)
0.86
1.24
SB_IS
0.97
5.4 (14%)
4.75
2.56 (8.5%)
1
0.14
0.94
5.6 (20.1%)
5.51
1.03 (8.5%)
0.98
1.58
0.91
6.79 (47.9%)
6.55
−1.8 (−18.7%)
0.84
1.82
SB_B_M
0.97
5.17 (11.5%)
4.5
2.54 (7.8%)
1
0.42
0.94
5.18 (13.9%)
4.98
−1.5 (−2.2%)
0.88
3.03
0.9
8.73 (57.3%)
7.52
−4.4 (−20.5%)
0.6
4.45
SB_B_IS
0.96
5.06 (13.7%)
4.69
1.89 (7.4%)
1
0.69
0.94
5.59 (20.1%)
5.5
1 (4.64%)
0.86
3.55
0.9
8.23 (74.1%)
7.78
−2.7 (−45%)
0.6
6.51
GC_B_M
0.96
5.39 (12.4%)
4.38
3.13 (9.9%)
1
2.53
0.94
5.38 (14.1%)
5.27
1.08 (2.1%)
0.81
4.6
0.9
9.05 (61.6%)
8.2
−3.83 (−28.3%)
0.51
6.24
GC_B_IS
0.96
5.02 (14.8%)
4.38
2.44 (11.3%)
0.97
3.24
0.94
6.76 (21.2%)
6.75
0.47 (8.8%)
0.76
7.21
0.9
8.69 80.6%)
8.59
−21.35 (−54.5%)
0.51
8.4
RMSD, CMRSD and Bias are in units of in mol photons . The % values refer to the relative RMSD and Bias.
Table 6.
Comparison of Mean Differences of Daily Integrated PAR Modeled and Estimated Under Different Spatial and Temporal Binning for MODIS (; 24 h) and ISCCP (; 3 h)a
PAR
Mean Absolute Difference (%) (Mean Difference (%))
Difference Due to Spatial Mismatch
1 deg ()
()
()
280 Km
()
()
()
Difference Due to Temporal Mismatch
24 h
3 h
The values are given in relative units.
Table 7.
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Computed between Each Method Estimate and In Situ Data Under All Sky Conditions for Low Sun Elevationsa
Model
(%)
(%)
SB_IS
0.88
92.5 (55.1%)
91.91
11 (23.2%)
0.97
17.03
SB_DS_IS
0.86
92.4 (50.7%)
89.15
−24 (−6.4%)
0.82
16.07
SB_B_IS
0.87
94.7 (55.4%)
94.51
6 (21.5%)
0.95
17.33
SB_NC_IS
0.88
94.8 (57.2%)
93.7
14 (27%)
0.97
20.6
RMSD, CMRSD and Bias are in units of in μmol photons . The % values refer to the relative RMSD and Bias.
Table 8.
Pearson’s Correlation Coefficient (), RMSD (), CMRSD (), Bias (), Slope (), and Intercept () Computed Between Each Method Estimate and In Situ Data Under Different Sky Conditions for Low Sun Elevationsa
Model
Sky Conditions
(%)
(%)
(%)
(%)
(%)
(%)
SB_IS
0.89
100.19 (44.5%)
94.37
33.64 (21.8%)
1
21.5
0.86
84.46 (64.8%)
83.86
−9.32 (−9.3%)
0.83
26.14
0.77
85.46 (65.3%)
84.61
−11.98 (−18.2%)
0.72
29.89
SB_DS_IS
0.89
86.75 (39%)
86.69
−3.21 (−6.8%)
0.9
22.02
0.85
100.61 (59.8%)
86.41
−51.53 (−40.3%)
0.64
25.93
0.74
93.01 (63.9%)
86.53
34.1 (−8.1%)
0.53
37.4
SB_B_IS
0.99
53.23 (44.9%)
34.57
40.48 (22.4%)
0.88
−1.31
0.89
59.9 (65.3%)
40.26
−44.35 (−29.2%)
0.77
7.55
0.86
34.57 (64.8%)
40.43
−16.19 (−9.6%)
0.76
19.94
SB_NC_IS
0.89
103.28 (45.2%)
95.8
38.29 (24.3%)
1
29.5
0.86
87.98 (68.9%)
87.9
−2.91 (−8.2%)
0.85
35.15
0.77
81.31 (65.4%)
81.3
−21.7 (−18%)
0.63
34.5
RMSD, CMRSD and Bias are in units of in μ mol photons . The % values refer to the relative RMSD and Bias.