To ensure the applicability of the 3DC, we selected three study areas in Paraguay, Brazil, and Mexico (Figure 2). All three regions have high rates of forest cover and deforestation. Paraguay has a tropical dry forest climate with 54% forest cover. The dominant vegetation type of in Region A is closed deciduous broad-leaved forest. Brazil has 62% forest cover, accounting for one-fifth of the world’s forest area. Region B has a tropical rainforest climate, and the dominant vegetation type is closed evergreen needle-leaved forest. The eastern plain of Mexico has a subtropical humid climate, and open evergreen needle-leaved forest is the dominant vegetation type. The areas of regions A, B, and C are 180 km × 130 km, 150 km × 110 km, and 120 km × 70 km units, respectively.

Based on the separability analysis, we selected the features with the highest separability among the features of each SAR type as the three axes of the 3D feature space. In the feature space, the deforested and non-forested deforested areas are divided into two clusters (Supplementary Figure 1). Then, the pixels in the deforested areas can be extracted using the K-mean clustering algorithm.

The K-mean clustering algorithm is an unsupervised classification method (De Luca et al., 2021; Maurya et al., 2021). Its implementation principle, including the following steps:

Input: dataset D = {x₁, x₂, ⋯, x_n}, the number of class clusters is k, and the maximum number of iterations is υ.

Output: k number of class clusters, C = {C₁, C₂, ⋯, C_n}.

Step 1: Select k sample points from the dataset D randomly as the initial mean vector μ (eq. 4) representing the clusters.

Step 2: Calculate the distance (eq. 5) from each sample x_i to each mean vector μ_j in the dataset D.

Step 3: Divide each sample in dataset D into the closest cluster.

Step 4: Update the class cluster centers (eq. 8) for each category.

where |C_j| represents the sample count in the j th cluster.

Step 5: Repeat Step 2, 3, and 4 until the class cluster centers no longer change or reach the pre-given maximum iterationumber υ.

After completing the above steps, the algorithm terminates. In this study, we set the number of classes for the K-mean clustering algorithm to be 2, and the default ENVI software settings were used for the other parameters.

The overall accuracy (OA) (eq. 9), F1 score (F1) (eq. 10) and intersection over union (IoU) (eq. 13) were employed to evaluate the performance of the 3DC. They are calculated as follows.

where TP, TN, FP, and FN denote the number of true-positive, true-negative, false-positive, and false-negative samples, respectively. IoU_0 and IoU_1 indicate the IoU of the non-deforested and deforested area, respectively (Ma et al., 2022).

Among the BIs (Figure 5), the separation of VV and VH values for the deforested area and forest samples was greater than 1, with M (JM) values of 1.68 (1.50) and 1.75 (1.55), respectively. For the parameters q and tanθ, there was a large overlap between the forest and deforested area samples, indicating that less information was available to help identify deforested areas. In the VIs, the overlap between the RVI and RFDI values for deforested areas and forests was large, while there were large differences in the PRVI and IDPDD, with M (JM) values of 1.10 (1.02) and 1.15 (1.04), respectively. Among the PFs, the C11 and C22 values of the deforested areas and forest samples were highly variable, with M (JM) values of 2.20 (1.81) and 2.15 (1.78), respectively.

Furthermore, the PFs (i.e., C11 and C22) performed better than the BIs (i.e., VV and VH) in separating deforested areas from forests. For parameters with a separation greater than 1, the deforested areas had low values, and the forests had high values except for IDPDD.

Table 3 shows the mapping accuracy of the five strategies (Supplementary Figure 2). It is easy to see that dataset D4 achieved the highest accuracy in all study areas compared to the other four feature combination strategies. The OA, F1, and mIoU of the deforested area extraction results in region A based on dataset D4 were 98.3, 96.4, and 96.5%, respectively. The identification accuracy of study area A was better than that of study areas B and C. The deforested areas in study area A are large and densely distributed, while the deforested areas in study areas B and C are scattered and in small patches. The diversity of distribution patterns and deforested area sizes led to differences in identification accuracy between regions. This is because the degree of landscape fragmentation affects the classification accuracy based on remote sensing images (Xun et al., 2021; Zhang et al., 2022; Zhao and Pan, 2023). To compare the feature space models in more detail and comprehensively, we visualized the extraction results for the three regions (Supplementary Figures 3–5). Overall, the accuracy of the 3D feature space model proposed in this paper is obviously superior to other feature space models.

Table 4 shows the mapping accuracy of the supervised classifiers. Among the four supervised classification methods, SVM had the highest accuracy, and OOC had the lowest accuracy (Table 4). The proposed method outperformed OOC and had similar accuracy to MLC, NN, and SVM classifiers. Specifically, in region B, the OA, F1, and mIoU values of the 3DC were higher than those of the OOC, MLC, NN, and SVM classifiers, indicating that the proposed method performed similarly to supervised classifiers without the use of training samples. In regions A and C, the OA, F1, and mIoU values of the proposed method were all superior to OOC and slightly lower than MLC, NN and SVM classifiers. The results show that (1) the supervised classifier is robust when there are sufficient and high-quality training samples; and (2) when there are no or insufficient training samples, the 3DC is a more appropriate choice.

For a more detailed and comprehensive comparison of the proposed approach with other supervised classifiers, typical deforestation conditions in three regions were selected for further discussion. Supplementary Table 3 describes typical deforestation conditions. Figures 6–8 show the identification results of deforestation areas for the proposed method and the supervised classifiers. In condition 1, the proposed method was highly consistent with the supervised classification method in that both could accurately detect deforested areas. In condition 2, compared to the 3DC, the supervised classification methods suffered from a high omission error. Most of the missing areas correspond to areas of vegetation regeneration on the planet map (for example, natural grass growth or artificial crops after deforestation). In condition 3, the proposed method overestimated the deforestation area compared to the supervised classification method. In condition 4, there were obvious omissions in the supervised classification results, and the deforestation areas detected by the 3DC were highly consistent with the actual map. As shown in Figures 7, 8, there were more speckles in the classification results of region B and region C, which severely affected the accuracy of deforested area identification, which is consistent with the quantitative evaluation results in Table 4. In general, the proposed method is consistent with the four supervised classifiers in the spatial distribution of deforested areas.

Figure 9 shows the 3DC results and GFC maps in the three study areas for a given year. In general, the 3DC results closely matched the GFC maps in all study areas. Moreover, the 3DC results provided more adequate and detailed distribution information. In Region B, for forest loss at two locations on the GFC map, 3DC was able to identify areas as deforested. Furthermore, the 3DC showed the distribution of deforested areas at a higher spatial resolution. For regions A and C, the 3DC and GFC maps were highly consistent in the overall spatial pattern, with differences some areas. For example, the differences occur mainly in some newly deforested areas, as shown by the red circles in Figure 9.

Figure 10 shows the multi-year dynamics of deforestation in Paraguay identified using the 3DC. It is not difficult to see that the identification results of deforestation areas using the 3DC closely match the extent of deforestation areas in the GFC maps (Figure 10). As shown in Figure 10, both maps yield consistent deforestation area extents, but there are differences in the years of deforestation. This is because the 3DC results were derived using single-period image for August, and the deforestation events may occur after August (i.e., between September and December). In conclusion, the comparison with the GFC maps demonstrated the accuracy and robustness of the 3DC in identifying deforestation areas.

Through the above study, we found that the 3DC can accurately and efficiently detect deforestation events in the tropics. We applied the 3DC to the dynamic mapping of deforestation in Paraguay in 2021 (Figure 11). We found that the deforestation events in Paraguay occurred mainly in the latter part of the year (June to January of the following year), which further explains why some deforested areas were missed by the 3DC (Figures 10, 11). Compared to the GFC maps, the 3DC not only accurately identified deforestation events, but also monitored deforestation events at a higher temporal frequency. Specifically, for deforestation events in Paraguay, the reporting time for GFC products is often delayed, by about 6 months or even a year. According to the study (Bárta et al., 2021), the effective management time after forest destruction is 6 weeks. This may need to be a shorter emergency event for deforestation events, which are more damaging and impactful. The 3DC provides a simple and efficient solution for monitoring frequent deforestation events in the tropics, which can better serve emergency response and post-event management.

We explored the separability of forest and deforestation areas in several features of the radar data to inform the selection of feature parameters for radar image-based deforestation identification. In previous studies, BIs (VV and VH) have been widely used to identify deforestation areas (Ballère et al., 2021; Ygorra et al., 2021; Bullock et al., 2022; Tang et al., 2023). In this study, we found that forests returned higher backscatter values in VH and VV, while deforested areas had lower backscatter values (Figure 5). In addition, the VIs are important indicators in forest research (Joshi et al., 2015; Shimabukuro et al., 2019; Stahl et al., 2023). Our experimental results showed that deforested areas and forests can be well separated based on the PRVI and IDPDD, while there is confusion between the two based on the RVI and RFDI (Figure 5). Moreover, PFs are sensitive to the structural information and dielectric behavior of the target (Sugimoto et al., 2022), with surface scattering dominating in deforested areas and double scattering and volume scattering in forested areas. Our experiment confirmed the effectiveness of PFs (C11 and C22) in separating forest and deforested areas (Figure 5), which is consistent with the study by Sun et al. (2022). Furthermore, we also investigated the effectiveness of the radar feature combination strategy in identifying deforested area (Table 3). The results showed that the combination of BI, VI, and PF achieved the best identification precision for deforested areas, but more features were not necessarily better (Supplementary Figures 3–5).

We developed a new method (3DC) based on Sentinel-1 data and tested its accuracy in different regions to extend the forest identification method. First, most previous studies used supervised classification algorithms to map deforestation areas (Magdon et al., 2014; Lee et al., 2020; Ortega Adarme et al., 2022; Slagter et al., 2023). Sample collection requires a lot of manpower and material resources (de Oliveira et al., 2011; Xun et al., 2021; Zhang et al., 2022). Many remote areas are difficult for field investigators to reach, especially in tropical rainforests (de Oliveira et al., 2011). Moreover, existing methods have some lag and delay effect for identifying deforestation area due to limitations of the algorithms or models. The 3DC avoids sample selection work and is suitable for large-scale dynamic monitoring of forests in tropical regions. Second, the GFC maps were updated annually. In contrast, the use of the 3DC method has the potential to achieve higher frequency monitoring of tropical deforestation events. The proposed method achieved accurate identification of deforestation areas on a monthly scale (Figure 11). Finally, the OA, F1, and mIoU in three different test areas were 88.1–98.3%, 90.2–98.5%, and 77.9–96.5%, respectively (Table 4). In conclusion, the 3DC is a simple, efficient, and robust deforestation detection method that can better serve forest management and restoration programs.

Despite the excellent results obtained by the method for the identification of deforested area, there are still some technical details or limitations that can affect the accuracy of the method. First, we used a mask file (VV > −20 dB) to eliminate the effect of water, which is easily confused with deforestation. However, when applying the method to other areas, fine-tuning of the water threshold may be needed. Because water thresholds vary in different regions, a simple threshold may lead to omission or commission information of deforestation area. In addition, other more accurate methods can be used to determine the extent of water bodies, including water identification using radar texture features (Ygorra et al., 2021) or spectral indices (e.g., MNDWI) (Zou et al., 2018; Huang et al., 2023). Second, we found that the accuracy of 3DC varied across the three test areas (Table 3). It has been suggested that differences in geographic conditions, such as terrain slope, may affect the performance of the method (Altarez et al., 2023). The slope of the terrain affects the incidence angle of the radar beam, and the shadows produced by the slope also affect the radar signal. We analyzed the separability of forest and deforested areas at different slopes in regions B and C. As shown in Supplementary Figure 6, at slopes less than 5, the deforested areas and forest are the most separable at all three eigenvalues. When the slope is greater than 5, all three eigenvalues of the deforested area and forest increase, but the increase in the forest is smaller than that of deforested area; therefore, the separability of the deforested area and forest decreases. In the next study, a more accurate terrain correction model should be considered to reduce the effect of terrain on the proposed method. In addition, the application of 3DC to identify deforested areas in areas with large terrain slopes should be carefully considered.

According to the Global Forest Resources Assessment (FRA) data report, an estimated 420 million hectares of forests have been lost to deforestation worldwide between 1990 and 2020 (Arévalo et al., 2020; Smith et al., 2023). Of these, over 90% occurred in the tropics, with an average annual deforestation of 9.28 million hectares in 2015–2020 (Smith et al., 2023). Forest cover and forest loss rates are high in the tropics, but advanced methods for monitoring deforestation events are still lacking. The development of effective forest monitoring methods is the basis for maintaining the stability of tropical forest ecosystems.

The proposal of the Reducing Emissions from Deforestation and Forest Degradation (REDD+) framework has prompted researchers to pay more attention to deforestation events in the tropics (Muthee et al., 2022; Sugimoto et al., 2022; Tang et al., 2023). One of the main challenges in monitoring deforestation events is the use of monitoring methods that are often cumbersome and lack timeliness. One possible way to overcome this challenge is to develop a simple and rapid method for monitoring deforestation events that is easier for farmers and government managers to use.

The 3DC method developed by using Sentinel-1 radar data proved to be an effective method for monitoring deforestation events. That is, 3DC can provide reliable information on forest dynamics for policymakers and planners in the forestry sector. The method is less susceptible to weather conditions and can detect deforestation events in a timely manner, helping to curb illegal logging activities. In future studies, the 3DC approach could be used to monitor forest hotspots, including South America, Africa, Europe, Australia and Canada. In addition, for areas where deforestation has already occurred, a rational ecological restoration plan can be developed based on field conditions. This is essential for the terrestrial carbon cycle and contributes to regional and global sustainable development.