PLSRSGDR SVR (linear)
Figure 5.5:Absolute values of the PLSR, SGDR, and SVR (linear) coefficients as a function of the different input parameters:θ0,θ,∆φand 81 wavelength bands noted with the wavelength number.
High values indicate that the input parameter is important for the prediction. The numbers in the x-axis represent the differentλvalues in (Lrac). Savgol filter was applied to the input radiance spectra for SGDR, which is highlighted in the upper right corner of the orange plot, whereWl, Poly, and Der are window length, polynomial degree and derivative as described in 4.3.3.
Case 1 and Case 2 Validation and Discussion
The AC approach was intended to work on both Case 1 and Case 2 waters. The results presented so far were validated on a combination of data classified as both Case 1 and Case 2 water. It would therefore be interesting to see how the AC algorithms would perform on the data classified as Case 1 and Case 2 waters, separately, by classifying spectra with Rrs(665)< 0.0005 to Case 1 and the rest to Case 2, as done in [33]. The ML models trained on the same training data as discussed so far, but the validation data would be split into Case 1 and Case 2 water data and validated thereafter.
The results are shown in Tab. 5.4 and show that the ML models predicted significantly better for the data classified as Case 1 water compared to the Case 2 data. It turned out that about 65%of the data was classified as Case 2 water data and the rest was Case 1 data.
This could be the reason why the ML models performed better on the Case 2 validation data. To test if this was the reason, the data was separated into Case 1 and Case 2 data, and each ML model was then trained and validated separately on the two classes of data.
Table 5.4:Results when validating Case 1 and Case 2 data separately when predictingRrs(λ) fromLrac(λ)with NN, PLSR, SGDR, and SVR.
Metrics NN PLSR SGDR SVR
Case 1 Case 2 Case 1 Case 2 Case 1 Case 2 Case 1 Case 2
R2 0.940 0.997 0.672 0.974 0.843 0.987 0.792 0.967
APD[%] 15.1 10.1 45.4 32.0 44.1 32.0 31.0 24.1
Bias[%] 5.00 5.3 29.5 5.41 11.3 12.15 8.71 4.27
NRMSD 0.148 0.0640 0.423 0.189 0.333 0.127 0.30 0.22
The results when of predictingRrs(λ)fromLrac(λ)when training the models on Case 1 and Case 2 data, separately is shown in Tab. 5.5. The same hyperparameters and Savgol filters were used as before. Improvement was observed for both cases compared to train them together, which makes sense as the ML models would train on datasets with smaller variations. Therefore, a solution for improved performance could be to train multiple ML models on several smaller datasets representing different types of atmospheric and marine conditions, like Case 1 and Case 2 waters. However, the challenge to find a way to select the useful ML model fitting the atmospheric and marine conditions. This could be done by choosing the useful ML models based on geographical locations. Consider Case 1 and Case 2 waters which more or less can be separated into inland/coastal and open ocean waters. Also, as discussed by Fanet al(2017) [33], a data analysis technique could be introduced to help select the ML model that would best match the atmospheric and marine condition based on the TOA satellite measurements. Realistically, it can be difficult to divide the ML models based on atmospheric and marine conditions. To avoid this, one should increase the number of training data points. However, increasing the sample number would also increase the training time.
5.1 Atmospheric Correction Validation and Discussion Table 5.5:Results when of predictingRrs(λ)fromLrac(λ)when training the models on Case 1 and Case 2 data, separately.
Metrics NN PLSR SGDR SVR
Case 1 Case 2 Case 1 Case 2 Case 1 Case 2 Case 1 Case 2
R2 0.980 0.997 0.927 0.974 0.900 0.962 0.842 0.952
APD[%] 6.56 7.05 13.5 17.9 14.8 15.34 24.2 41.0
Bias[%] -1.45 -2.84 3.71 2.60 3.71 2.45 -4.82 -20.1
NRMSD 0.070 0.068 0.123 0.150 0.148 0.180 0.225 0.237
Ntrain 37971 53731 37971 53731 37971 53731 14250 14250
Summary of Atmospheric Correction ofLractoRrs
The NN showed the best results of the ML models based on the metrics. SVR also pro-vided good results, but both training time and predicting time was higher than for the other models. PLSR and SGDR performed almost equally, where PLSR performed best with re-spect toR2andNRMSDand SGDR forBiasandAPD. However, the results show that PLSR was more than 100 faster than SVR(rbf) and SGDR with respect to Tpred, and 10 times faster than NN. Also, PLSR did not need a lot of hyperparameter tuning, especially compared to SVR and SGDR. PLSR was more or less independent of the Savgol filters used, which is positive as less pre-processing would have to be done. Without Savgol fil-ters, the PLS coefficients would be based directly on the measured spectrum. Interpretation can be easier for coefficients based on the original spectrum, rather than some derivative of a filter. Both NN and SGDR should use Savgol filters as they significantly improved their results. The predicted spectra from SGDR and SVR became spiky, perhaps due to lack of enough training data. This could be problematic if one would use different band ratios to predict IOPs like done with the OCx algorithm. The PLSR model, therefore, stands out as the preferred linear model, when choosing between SGDR and SVR(lin).
In conclusion, the NN network was the overall best ML model as the metric values were significantly better than the other models. An equivalent plot as shown in Fig. 5.2, but for NN only, is shown in Fig. 5.6. It shows scatterplots of NN predicted and simulatedRrs(λ) for each 25-th wavelength band from 400 to775 nm. The scatterplots show good corre-lations between the predicted and simulated remote sensing reflectance. A very similar study done by Fanet al.(2017) [33] on AC of multispectralLracwith MLNN produced R2 > 0.993 for 7 bands in VIS (412, 443, 488, 531, 547, 667 and678 nm) andAPD= 3.1 %. The NN trained on hyperspectral data done in my study showed comparable results withR2> 0.992 for all 81 bands andAPD=4.4 %. In fact, R2calculated with NN in my study was 0.999, which was higher than 0.996 reported by Fanet al.(2017) [33]. These results imply that both models have been able to predict the spectral relationship between LracandRrs.
The validation done in this thesis is based on data generated with AccuRT. The data gen-erated do not include whitecap, strong sun glint, and polarization effects, which are effects present inin situ measurements. However, these effects are often very small and sen-sors can also avoid these effects to some extend [13]. So far, it is not possible to know whether the models actually could work on real measured satellite data. Therefore, the models should be tested against in situmeasurements from turbid, coastal areas with strong aerosol properties. Besides, other standard AC algorithms should also be validated on the same data to compare them with the models produced in this study. However, it can be stated from the results that the ML models, especially NN, can learn the RTM very accurately, and find the spectral relationship betweenLracandRrs. The spectral shape ofin situmeasurements should be very similar to what has been generated in this study, and the promising results indicate that it could work onin situmeasurements. Fanet al.
(2017) [33] validated their MLNN againstin situmeasurements and compared them with standard AC algorithms which were a part of the SeaDAS framework. They reduced the APD for blue bands inLwby more than60 %and25 %for highly absorbing waters and highly scattering coastal waters, respectively, compared to the standard SeaDAS NIR al-gorithm [33]. This showed that a method build on data generated with RT models actually could perform better onin situmeasurements than standard AC algorithms, even though this was on multispectral data.
5.1 Atmospheric Correction Validation and Discussion
Figure 5.6:Scatterplots of NN predicted and simulatedRrs(λ)fromLrac(λ)for each 25-th wavelength band from 400 to775 nm. The orange line represents where the predicted and simulated data are exactly the same and would indicate a R2equal to 1. The wavelength is described in the labels and the metrics R2, NRMSD and APD are given in the top left corners of the plots.