# 6 Results of empirical models

## 6.1 Ag

Regionality test
Characteristic Beta (95% CI)1 p-value
log10(Rrs_665/Rrs_560) 1.4 (1.3 to 1.5) <0.001
Region
EGSL
JB 0.00 (-0.05 to 0.05) 0.93
log10(Rrs_665/Rrs_560) * Region
log10(Rrs_665/Rrs_560) * JB -0.23 (-0.43 to -0.03) 0.026

1 CI = Confidence Interval

The Region parameter is not significant here, in fact, no real difference of trend are observed between the two regions.

Figure 6.1: Ag regionality

### 6.1.1 Ag(440)

Several band ratio model are presented hereafter.

The first one is fitted with a blue / red ratio. The blue part of the visible spectrum is the most influenced by CDOM absorption and it is expected to better grasp the variability according to the theory. In fact the distribution of $$a_g(440)$$ with $$B(blue)/B(red)$$ ratio is very sharp. It show a steep slope, likely induced by the saturation of light absorbed by CDOM as succinctly observed in 4.3 (see Figure 4.6) . There is a small constant offset between the measured and fitted value, the addition of a constant offset could then improve the model.

Figure 6.2: power law model for Ag, red over blue

Characteristic Beta (95% CI)1 p-value
a 3.4 (3.2 to 3.5) <0.001
b 1.4 (1.3 to 1.5) <0.001

1 CI = Confidence Interval

MeanAE MedAE bias
0.443 0.281 0.0883
Region rho
EGSL -0.091
JB 0.170

The last one take advantage of of a green / red ratio, less affected by blue(ish) atmospheric correction errors and which give fairly good results. The slope of this distribution is less steep, confirming the saturation of light absorption by CDOM in the blue.

As this model present the least independents parameters and the best performance metrics it is chosen to be applied on Sensor images.

Figure 6.3: power law model for Ag, Red over Green

Characteristic Beta (95% CI)1 p-value
a 20 (17 to 24) <0.001
b 1.8 (1.6 to 1.9) <0.001

1 CI = Confidence Interval

MeanAE MedAE bias
0.344 0.233 0.0391
Region rho
EGSL -0.01700
JB 0.00057

### 6.1.2 Houskeeper style

Figure 6.4: power law model for Ag, Red over Green

Characteristic Beta (95% CI)1 p-value
a 1.9 (1.8 to 2.1) <0.001
b -0.45 (-0.49 to -0.41) <0.001

1 CI = Confidence Interval

MeanAE MedAE bias
0.695 0.621 0.181

Figure 6.5: power law model for Ag, Red over Green

## [[1]]
MeanAE MedAE bias
0.494 0.377 0.212

### 6.1.3 Ag(295, 275)

## [[1]]
MeanAE MedAE bias
3.49 2.28 0.0159
## [[1]]
MeanAE MedAE bias
4.76 3.42 0.152

## 6.2 SPM

We try to see if the ‘Region’ variable created earlier is of any importance in the determination of $$C_{spm}$$ from $$R_{rs}$$ to do that we can use a generalized linear model, glm function in R. The formula that we used take the form $$SPM \sim Rrs(\lambda) + Region + Rrs(\lambda) * Region$$ the last part of the formula express the interaction effect.

Characteristic Beta (95% CI)1 p-value
log10(Rrs_665) 0.29 (0.11 to 0.48) 0.002
Region
EGSL
JB 1.3 (0.69 to 2.0) <0.001
month(DateTime) -0.05 (-0.08 to -0.03) <0.001
log10(Rrs_665) * Region
log10(Rrs_665) * JB 0.63 (0.40 to 0.86) <0.001

1 CI = Confidence Interval

As we see, $$R_{rs}$$ and $$Region$$ are significant variable to determine $$C_{spm}$$, $$C_{spm}$$ varies both across $$R_{rs}$$ and $$Region$$. The interaction factor is also significant, meaning that $$C_{spm}$$ relation with $$R_{rs}$$ also varies with $$Region$$.

What could be misleading here, is that $$C_{spm}$$ varying across $$Region$$ is also a matter of $$C_{spm}$$ range. This one is wider for JB than for EGSL, hence it may affect the significance of $$Region$$.

Considering the results presented above, models have been fitted specifically for those region.

Grouped under the Estuary and Gulf of Saint-Lawrence (EGSL) and James Bay (JB) region, distribution of $$C_{spm}$$ vs $$R_{rs}$$ show two clear and different pattern.

### 6.2.1 SPM from Rrs

Characteristic EGSL JB
Beta (95% CI)1 p-value Beta (95% CI)1 p-value
a 3.6 (2.0 to 6.5) <0.001 13 (8.7 to 19) <0.001
b 0.21 (0.13 to 0.30) <0.001 0.52 (0.44 to 0.60) <0.001

1 CI = Confidence Interval

Region MeanAE MedAE bias
EGSL 3.42 1.790 0.518
JB 3.47 0.829 0.296