1. Study area

The study area is located between the municipalities of Urucará and Parintins in the Amazonas State, Brazil, comprising part of the Amazonas River. It is located between the following coordinates: 22°30′48.84″ and 22°37′59.16″ of south latitude; and 44°31′35.68″ and 44°43′25.94″ of west longitude (fig. 1). The typical climate is classified as Af, that is, tropical rainforest climate without dry season, in the Köppen′s classification system, with average annual precipitation ranging from 1355mm to 2839mm (^{Alvares et al., 2014}). The average annual temperature varies from 25.6°C to 27.6°C. The flooding period occurs mostly between May and July.

2. Remote sensing data sets

This research used three Sentinel-1 SAR images acquired in the VV and VH polarizations during the following flooding periods: 23 June 2017; 18 June 2018; and 7 July 2019. The images were obtained in descending, Interferometric Wide (IW) mode, and processed at Level-1, which includes pre-processing and data calibration (table I).

We also selected Sentinel-2 MultiSpectral Instrument (MSI) images acquired near the Sentinel-1 SAR overpasses (2 July 2017; 22 June 2018; and 29 July 2019). In this study, the Sentinel-2 was used to collect sampling data for training, validation, and testing. The Sentinel-2 MSI images were radiometrically corrected. They have the potential for mapping flooded areas at regional scales, as they are acquired under the spatial resolutions of 10m to 60m and temporal resolution of 10-days (^{Du et al., 2018}) (table II).

3. Methodological approach

Figure 2 shows the main steps of the methodological approach used in this study. We conducted the following pre-processing steps: correction by the orbit file; terrain correction; radiometric calibration; conversion of the data to decibels; and spatial filtering. The images were pre-processed by the image orbit file, containing accurate information on the satellite´s position, trajectory and speed during the image capture process (^{ESA, 2017}). The terrain correction was based on the digital elevation model (DEM) acquired by the Shuttle Radar Topographic Mission (SRTM) at ~3 arc sec^-1. The radiometric calibration was performed using the Sigma Look-Up Table (LUT) file to generate images converted into backscattering coefficients (σ⁰).

SAR images present speckles that originate from destructive or additive interference from the radar return signal for each pixel (^{Lee & Pottier, 2009}). We used Lee filter with a 3×3 window size for processing VV- and VH-polarized images. The Lee filter transforms the multiplicative model into an additive model by expanding the first-order Taylor series around the average. This technique uses local statistics to minimize the mean square error (MSE) through the Wiener filter. In this way, the Lee filter is an adaptive filter that has the characteristics of preserving edges (^{Sant'Anna, 1995}). Lee's filter assumes that the mean and variance of the pixel of interest are equal to the mean and variance of all local pixels, which refer to the inside of the adopted window.

We used the following image processing software: S1-Toolbox available in the Sentinel Application Platform (SNAP) version 7.0.0; ArcGIS version 10.5; and Abilius, which uses the OpenCV library of artificial intelligence algorithms in the C++ programming language.

Sentinel-1 images converted into backscattering coefficients were normalized based on their averages and standard deviations (eq. 1 and 2).

The normalized images were also processed to generate the simple ratio (SR) index and normalized difference (ND) index involving VH and VV polarizations (^{Hird et al., 2017}; ^{Tsyganskaya et al., 2018}) (eq. 3 and 4).

As pointed out by ^{Boateng et al. (2020}), the most widely used nonparametric ML techniques include ensembles of classification trees such as Random Forest (RF) (^{Breiman, 2001}), Artificial Neural Networks (ANNs) (^{Brown et al., 2000}), K-Nearest-Neighbors (KNN) (^{Breiman & Ihaka, 1984}), Support Vector Machines (SVMs) (^{Cortes & Vapnik, 1995}). In this study, we selected two classifiers, the ANN and two KNN (KNN-7 and KNN-11) algorithms to verify the performance of these techniques to classify flooded areas in the region of interest. The widely used RF classifier was not selected because we are interested in only two classes (water and non-water), making it impossible to develop a random forest, ensemble architecture that is the basis of these algorithms. In this ensemble architecture, several classification trees are trained based on subsets of the training data (^{Abdi, 2020}). We did not evaluate SVM either because, together with RF, it has been intensively assessed in literature over several different environmental and terrain conditions.

The ANN adopted in this study was the Multilayer Perceptron (MLP) type with the backpropagation learning algorithm with insertion of the momentum term, which optimizes the network processing with a learning rate of 0.05 and a momentum factor of 0.5. According to ^{Atkinson and Tatnall (1997}), there are several advantages of neural networks, such as the efficient manipulation of large data sets and their use in the classification of remote sensing data without assuming a normal distribution. In the classification by neural networks, we used the Abilius program developed by the University of Brasília, Brazil, which is based on the OpenCV library. We used the logistical activation function in which the output result of the neuron, given a set of input signals, assumes real values between zero and one to facilitate the network training process and to simplify its structure (eq. 5):

where β = real constant associated with a slope level of the logistic function related to its inflection point; and µ = activation potential produced by the difference in value produced between the linear combination and activation threshold.

The KNN classifier is a non-parametric method based on k-training samples closest to the behavior of the analyzed data (^{Cover & Hart, 1967}). The calculation of the nearest neighbor was performed using the Euclidean distance method. In this classification technique, the k-value refers to the number of neighbors to be used in determining the class assigned by the values of most of the nearest pixels that must be assigned. There are several studies in the literature with different values of k (^{Alves et al., 2013}). The unknown sample is assigned to the most common class of the k-training samples that are nearest in the feature space to the unknown sample (^{Maxwell et al., 2018}). In this study, we assigned k-values of seven and eleven. These numbers are a compromise between too-low and too-high k-values. Low k-values will produce complex decision boundaries while high k-values will result in greater generalization (^{Maxwell et al., 2018}).

The training, validation, and testing data set was produced by manual sample collection of 6000 pixels (denoized time signatures) containing two classes (water and non-water), with equal distribution (3000 samples per class), showing well-distributed sampling design (fig. 3). We considered a total of 4200-pixel samples for training (70%), 1200-pixel samples for validation (20%) and 600-pixel samples for testing (10%), according to the methodology defined by ^{Kuhn and Johnson (2013}) and ^{Larose and Larose (2014}). The training of ANNs considered different architectures for VV, VH, SR, and ND images. The number of neurons in the hidden layer was determined by the trial and error methods (^{Hirose et al., 1991}). The selected stopping criterion was the number of learning cycles, defined as 10 000. At the end of the training process, 180 sets of independent samples were collected to validate the classification results. The selection of the best classifier was based on the lowest values of mean squared error (MSE).

The accuracy of the classification was analyzed using the confusion matrix, omission and commission errors, overall accuracy, and Kappa index (^{Congalton & Green, 1993}). Overall accuracy (OA) and the Kappa index were calculated using equations 6 and 7:

where n _ii = diagonal elements of the confusion matrix; n = total number of observations; and m= number of themes mapped.

where n = total number of observations; and x _i and x+i are the sums in row and column.

Kappa is a coefficient that varies from zero to one, representing a general agreement index. Kappa values are associated with the quality of the classification. Cell values were considered for measuring omission and commission errors. The marginal cells in the lines indicate the number of pixels that were not included in a particular category, that is, express the error known by default. Cells on the diagonals represent the pixels that were not included in no category, expressing the error of commission (^{Congalton & Green, 1993}). The omission error (OEi) and the commission error (CEj) were calculated for the thematic classes of the classification (eq. 8 and 9):

where ΣX _ij - X _ii = sum of waste per line; ΣX _ii - X _jj = sum of waste per column; and ΣX _jj = row or column marginal.

We also conducted another validation strategy based on the Sentinel-2 MSI scenes from June and July of 2019 and the McNemar chi-squared test (²). The accuracy analysis used 88 systematic samplings with a 10km diameter in regular grids of 17×17km² (fig. 4). We disregarded the cloud-covered samples in the Sentinel-2 images.

McNemar’s ² test was used considering a statistical level of significance of 0.05 and one degree of freedom to analyze the differences in measured areas between visual interpretation and classified images. According to ^{McNemar (1947)} and ^{Leeuw et al. (2006}), McNemar's analysis is a non-parametric statistical test to analyze pairs and has been widely used in remote detection because it can use the same validation set (Eq. 10):

where f ₁₂ = number of wrong classifications by Method-1, but correctly classified by Method-2; and f ₂₁ = number of correct classifications correct by Method-1, but incorrectly classified by Method-2.

This precision comparison based on related samples is quite popular in the literature (^{Abdi et al., 2020}; ^{Manandhar et al., 2009}; ^{Mayer et al., 2021}; ^{Wang et al., 2018}). The McNemar statistical test was performed at the level of significance of 0.05 and one degree of freedom between the image classifiers to analyze whether the classified images differ statistically.

1. Backscattering values of flooded areas

Table III presents the statistical results for the backscatter coefficients of the three-year images in dual polarization from the Sentinel-1 SAR satellite before and after the data normalization. The results of the normalization showed a slight increase in the mean values compared to the non-normalized images. The value of variance and standard deviation remained identical with the image before adjustment. Decreasing mean values in the fitted images represents a greater concentration of the distribution data, compressing the backscatter values for the image. In other words, the decrease in the mean and standard deviation values indicates a low dispersion of the backscattered data. The characteristics and multi-temporal patterns of the backscatter values were similar to the VH and VV polarizations, as well as to the SR and ND images for the three years.

Figure 5 shows the box plot in a range of grouped multi-temporal backscatter values, measured in all scenes (VH, VV, SR, and ND). In comparison to the backscatter values of water bodies in the time series, there was a considerable increase in the average backscatter values in the following order: VH, VV, SR, and ND. The backscatter of water bodies in the VH image was the lowest among the three scenes, with an average value of -25.8dB in the upper limit and -20.0dB in the lower limit and with backscattering in the value of -24.2dB in the first quartile. In contrast, the VV polarization presented the largest data series between the lower and upper limits, with the upper limit lower value at -23.3dB and the upper limit at -13.3dB, with 75% of its backscatter values being represented by -15.8dB, as shown in quartile-3.

The VH polarization showed the lowest backscatter values for the water body due to the record of the backscattered value of the return signal on the antenna occurring in the horizontal direction. The backscatter values of the indices became more aggregated compared to the scalar values of the polarizations VH and VV, with median, quartiles, and closest limits for the index images.

2. Best ANN model for flooded area detection

The ANN model with the combination of VV and VH polarizations as well as SR and ND presented accurate results in the network learning and training tests, with: 91.3% and 91.9% of overall accuracies for the image acquired in 2017; 90.7% and 90.9% accuracies for 2018; and 90.2% and 90.7% accuracies for 2019. The ANN architecture with the best results was obtained using four neurons in the input layer, two hidden inner layers with eight neurons, and two neurons in the output layer (4-8-8-2 model) (fig. 6).

In the learning phase of the three ANNs, the training errors were slightly higher than the test errors. However, with the increasing number of trainings in some moments, these errors were equalized. The errors stabilized with values of root mean square error (RMSE) in 0.2. The maximum cycles did not exceed 10 000 iterations. These values demonstrate that the maximum learning limit of ANN with 10 000 iterations is sufficient for training, which results in high precision, accuracy, and lower computational processing cost (fig. 7).

3. Classification results

Figure 8 shows the classification of the flooded areas in the Central Amazon region using the ANN, KNN-7, and KNN-11 classifiers in the period of largest flood pulse during the years 2017, 2018, and 2019. The blue-colored areas correspond to areas classified as water bodies. The classifiers delimited precisely the main channel of the Amazon River, as well as the flooded areas adjacent to the river channel. In general, the classification through ANN generated products classified with slightly higher clarity when compared to the KNN classifiers.

The noises classified as upper lands increased from KNN-7 to KNN-11, indicating that the increase in the Euclidean distance from seven to eleven contributes to the increase of confusion between the water body and the upper land. In addition, there was a misclassification of water bodies for all images. These areas are shown as random blue dots mainly after the boundary of the tributaries of the Amazon River, as well as the presence of random pixels scattered in various regions spread in the entire study area.

The largest presence of water bodies was found in the image acquired in 2019, with a total area of 6244km² (ANN), 6268km² (KNN-7), and 6290km² (KNN-11). In other words, the KNN-7 and KNN-11 algorithms presented the largest occurrences of water bodies, as compared with the ANN classification.

4. Accuracy analysis

The image classification by ML showed Kappa coefficient values from 0.77 to 0.91 (table IV). ANN showed higher accuracy for all Sentinel-1 scenes. Second in the classification order, the KNN-7 presented results close to the ANN. The KNN-11, on the other hand, presented the highest differences in the accuracies among the three classifiers, obtaining the lowest Kappa index (0.77) in the image acquired in 2018.

There was no discrepancy between Kappa indexes and the overall accuracies. The classifications by ML showed high overall accuracy values, with ANN presenting the highest values, with 97% in the image from 2019. The lowest value was presented by KNN-11, with 92%, in the image acquired in 2018.

The ANN classification technique obtained the lowest commission error, with 7.0% and omission error of 1.9%, in the image from 2019. The largest commission and omission errors were measured in the image from 2018, classified by KNN-11, with a commission error of 18.9% and an omission of 12.9%. There was more commission error when compared to the omission error in all products generated by the classifiers, proving that the biggest classifier errors occurred in the definition of the drylands as the water body.

The image from 2018 was measured with the lowest presence of water bodies, which was also the image that presented the largest errors and the worst statistical indices analyzed. Thus, it is inferred that due to the smaller grouping and the greater distance between the pixels corresponding to the backscatter values of the water bodies was the determining factor for obtaining the worst results obtained by the KNN classifier with Euclidean distance of eleven.

The classifiers produced an overall good performance in delineating water bodies, especially the ANN and the KNN-7. They showed the lowest levels of noise in the images (fig. 9). The results of the indexes showed that the ANN obtains the best performance in comparison with the other classifiers. ANN and KNN-7 achieved similar levels of precision in two of the three images, these images being classified with greater quantities of water bodies. On the other hand, it was observed that the worst indices occurred in the KNN-11 classification and were obtained in the image with the least amount of water bodies.

Table V shows the results of the McNemar test between the pairs of the three classifications, considering the different combinations of parameters. The ANN showed the best results in the time series, despite obtaining the best values between the methods. The ANN did not differ statistically from the KNN-7 classifier in the time-period. The KNN-11 classifier presented the highest value of χ² with 4.37, in the image from 2018. This result was statistically significant, rejecting the hypothesis of statistical equality between the pairs of classifiers RNA × KNN-11 at the p-value of 0.05, since the calculated χ² is higher than the tabulated χ² (3.84).

In general, the biggest confusion for image classifiers was to distinguish the water class from other non-water targets with similar backscatter values. In this way, the presence of the shadow effects was observed in all images, indicating that this effect was the biggest cause of misclassification, with less interference only in ANN classification (fig. 10).