Generalized Composite Mangrove Index for Mapping Mangroves Using Sentinel-2 Time Series Data

Monitoring mangroves is critical to protect the coastal ecosystems. Some studies resorted to remote sensing for constructing mangrove indices (MIs). However, there are still some drawbacks in existing MIs. On the one hand, difficulty still persists in distinguishing mangroves from nonmangrove vegetation and nonvegetated areas at the same time. On the other hand, the existing MIs have not fully utilized the phenological trajectories, which can greatly help to distinguish mangroves from other land covers. To overcome these issues, we built a novel mangrove index, namely generalized composite mangrove index (GCMI) by compositing vegetation indices (VIs) and water indices (WIs) based on Sentinel-2 time series data. Firstly, to determine the optimal indices, a similarity trend distance (ST distance) measure was proposed based on Pearson correlation coefficient and dynamic time warping (DTW). Secondly, in order to optimize the weights of selected indices, a population reconstruction genetic algorithm (PRGA) was designed. Finally, mangroves were mapped by feeding the time series of GCMI into random forest classifier. Experiments conducted over three areas along the southern coast of China demonstrate that: 1) GCMI enhances the separability between mangroves and other land covers compared to the existing VIs, WIs, and MIs, with an averaged overall accuracy of 91.45%; 2) ST distance outperforms Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW in optimizing the weights of GCMI; 3) PRGA greatly improves the probability of attaining global optimal result. The innovation lies in the presented GCMI considering both the vegetation trajectory information and water inundation using time series.

hard to rehabilitation due to its poor self-recovery ability [1]- [5]. Therefore, proper utilization and protection of mangrove ecosystem has become the focus of the worldwide attention.
Reliable and accurate mangrove mapping is the basis and prerequisite for protection and restoration. However, mangroves are usually distributed in harsh coastal conditions, making it difficult to survey in large-scale. Remote sensing has the advantages of surveying in large and inaccessible areas, analyzing in time, and acquiring the information without disturbing the environment, which has become an important tool of mangrove mapping [6]- [9]. Among various remote sensing data, Sentinel-2 multispectral instrument (MSI) has been widely used in mangrove mapping due to its high spatial and temporal resolution [10]- [13]. However, mapping mangroves by using remote sensing has two difficulties: 1) mangroves are highly similar to terrestrial vegetation, and there is no natural isolation in geographical space between them, leading to misclassification and omission; 2) mangroves are submerged by periodic tides, resulting in extracting mangroves periodically flooded a tough task. In order to solve the above two-sided difficulties, existing studies mainly focused on: 1) exploring appropriate classification models; 2) extracting more discriminating features; and 3) constructing novel MIs.
Exploring classification models is an effective way since it can make up the limitations of previous proposed classifiers. Various related studies mainly used ensemble learning [14]- [16], support vector machine (SVM) [17]- [19], decision tree (DT) [20], [21], and deep learning [22]- [24]. 1) Ensemble learning uses multiple learning algorithms to obtain better results. For example, Li and Hughes [14] applied bagging, boosting, and stacking to map wetland distribution in Manning River Estuary. Moreover, random forest (RF) is now commonly applied in remote sensing, such as Navarro et al. [15] used RF to map mangroves in South-Eastern Australia from 1991 to 2015. Further on, considering an ensemble of machine learning methods is more accurate than a single model, Liu et al. [16] ensembled RF, gradient boosting machine, and neural network (NN) to map mangrove at high accuracies. 2) SVM is also widely used because it can get great classification results from complex and noisy data. Nwobi et al. [17] mapped mangroves using maximum likelihood (ML) and SVM methods, which found that SVM performed better than ML. Likewise, Quang et al. [18] investigated the performance of NN, DT, RF, and SVM to classify mangroves, This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ which also concluded that SVM was the most accurate classifier. 3) DT is easy to be implemented, and it has high interpretability. Zhang et al. [20] developed DT based on multitidal Landsat 5 thematic mapper (TM) data and a digital elevation model to map mangrove forests. Furthermore, by using DT, McCarthy et al. [21] not only mapped the extent of mangroves, but also distinguished between healthy and degraded mangroves. 4) Deep learning is gaining widespread popularity in the remote sensing community recently since it can extract high-level features directly from the raw input data. For example, Iovan et al. [22] designed a model based on deep convolutional neural network (CNN) using WorldView-2 and Sentinel-2 images. Guo et al. [23] also utilized CNN, but the difference is that they embedded three modules to improve performance. To conclude, utilizing a proper classification method is highly important to distinguish mangroves. Besides considering classification methods, extracting more discriminating features can help to enhance the difference between mangroves and other land covers, because diverse features can provide complementary information.
1) On the one side, extracting features from single-source optical data is effective to get distinguishing features.
Since time series can demonstrate phenological information of different land covers, Lymburner et al. [25] used Landsat dense time series as features to quantify the mangrove extent in Australia. With the development of remote sensing satellite technology, the increased spatial resolution is expected to obtain a more detailed mangrove mapping. Therefore, Wang et al. [26] selected features from Landsat 8, Sentinel-2, and Pliades-1 based on RF to map mangroves in a higher spatial resolution. Due to more spectral details are provided from hyperspectral data, Li et al. [27] mapped multilayered mangrove by using airborne hyperspectral images. 2) On the other side, as optical data are easily influenced by weather and illumination conditions, using multisource data can resolve the problem to some extent. For example, Bunting et al. [28] used features from Advanced Land Observing Satellite (ALOS) Phased Array-type L-band Synthetic Aperture Radar (SAR) (PALSAR) to distinguish mangroves from coastal areas firstly, then used features from Landsat to differentiate between mangroves and adjoining terrestrial forests. 3) In addition, some studies used multitemporal features from multisource data with a view to the special phenology of mangroves [29]. For example, Hu et al. [30] used Sentinel-1 SAR and Sentinel-2 MSI time series imagery as input features of RF to classify mangroves in China. Instead of directly regarding time series as features, Chen et al. [31] proposed a new classification algorithm which mapped mangroves by identifying the greenness, canopy coverage, and tidal inundation from time series of Landsat data and Sentinel-1 A. What is more, Zhao and Qin [32] used the temporal profiles derived from a multisource and multitemporal satellite to enhance the discrimination between mangroves and other land covers. Ghorbanian et al. [33] also generated seasonal features from Sentinel-1 and Sentinel-2 satellite images to obtain a more reliable mangrove ecosystem map. To sum up, the abundant features can be extracted from multisource and multitemporal data, assisting in masking mangroves from other vegetation and tide more easily. What is more, many indices are designed to get specific information, e.g., normalized difference vegetation index (NDVI) [34] can estimate the density of green, and leaf area index [35] can highlight the leaf greenness. Therefore, constructing MIs is also feasible to take full advantage of mangrove characteristics.
1) In the aspect of distinguishing mangroves from terrestrial vegetation, Gupta et al. [36] utilized the correlation between NDVI and normalized difference water index (NDWI) to develop a new index, namely combined mangrove recognition index (CMRI). Rather than constructing index based on the existing indices, Baloloy et al. [37] used Sentinel-2 data to design the mangrove vegetation index (MVI) specifically for mangrove mapping. 2) In the aspect of differentiating between mangroves and tides, many scholars used multitide data to relieve this issue. For example, Jia et al. [38] established the inundated mangrove forest index (IMFI) based on high tide and low tide lines, which successfully extracted the mangroves submerged by seawater. Furthermore, Xia et al. [39] utilized the near-infrared band, which is more likely to reflect spectral differences in high tide and low tide periods, to construct submerged mangrove recognition index (SMRI). Particularly, Li et al. [40] proved the robustness of SMRI as an effective indicator to detect submerged mangroves in both high and medium spatial resolution satellite images. Likewise, Xu et al. [41] proposed normalized intertidal mangrove index (NIMI) by comparing and analyzing the spectral characteristics of exposed mangroves, submerged mangroves, and seawater bodies. 3) In the aspect of extracting mangroves from nonmangrove vegetation and tides simultaneously, Kumar et al. [42] designed mangrove probability vegetation index (MPVI), normalized difference wetland vegetation index, and shortwave infrared absorption depth based on EO-1 Hyperion data. Consequently, it is useful to construct an effective index in order to precisely map mangroves. However, there are still some deficiencies in the existing MIs. For one side, although MIs can distinguish mangroves form nonmangrove vegetation and tidal, it is still difficult to distinguish mangroves from other vegetation and nonvegetated simultaneously. For another side, the existing MIs have not fully utilized the phenological trajectories from the multitemporal data.
In this article, we constructed a novel and effective generalized composite mangrove index (GCMI) composited by VIs and WIs with Sentinel-2 time series. Firstly, in order to determine the optimal indices, we proposed an similarity trend distance (ST) measure based on Pearson correlation coefficient and dynamic time warping (DTW), which was used to select indices to construct the GCMI. Secondly, since the weights of the selected indices were undetermined, population reconstruction genetic algorithm (PRGA) was designed to get the optimal weights. Finally, the time series of GCMI were used as the inputs of RF to get mangrove maps of Maowei Sea, Dongzhai Port, and Quanzhou Bay at 10-m spatial resolution in 2020.
This rest of this article is organized as follows. Section II presents the study area and data. The methodologies are illustrated in Section III. The experimental results are presented and analyzed in Section IV. The discussion is drawn in Section V. Finally, Section VI concludes this article.

A. Study Area
The study area is located in the south coastal regions of mainland China, including Maowei Sea in Guangxi Province [see  Fig. 1(c)]. The climates in these areas vary from tropical monsoon to subtropical monsoon climate with high temperature and rainfall in summer, whereas low temperature and little rainfall in winter. Port development, rapid economic growth as well as abundant habitats of microbial communities have made mangrove ecosystems the priorities of the coastal management programs [38], [43].
Owing to its north-limit distribution, the mangrove forests in China are dominated by low-temperature tolerant species such as Kandelia obovata, Aegiceras corniculatum, and Avicennia marina. The majority of mangrove forests in China are distributed in estuaries, and characterized by abundant inputs of freshwater and nutrients [44].
Maowei Sea is the largest and most typical mangrove forest area in China, which is the ideal place for mangrove introduction, cultivation experiment and development. The representative mangrove growth types in this area is Bruguiera gymnorhiza, Kandelia candel, Rhizophora stylosa, Acanthus ilicifolius, etc., accounting for 43.2% of mangrove species in China. Dongzhai Port is the largest coastal mudflat forest in China with abundant species genes and resources. The reserve is rich in mangrove species and accounts for 97% of mangrove species in China, including Nypa fruticans, Sonneratiaovata, Xylocarpus granatum, etc. Quanzhou Bay has a piece of native mangrove where it is rich in wetland resources. The representative mangrove growth types in this area are Kandelia candel, Aegiceras Gaertn, Avicennia marina, etc. The above three nature mangrove reserves have different representative mangrove growth types and various ecological environments. Therefore, we conducted our research based on the above three study areas.

B. Remote Sensing Data
In this article, Sentinel-2 MSI data during 2019 to 2020 was obtained, and the numbers of images in each region are listed in Table I. The data preprocessing was implemented on Google Earth Engine (GEE) platform, where Sentinel-2 data  have been radiometric corrected and there is no geometric distortion. Therefore, radiometric calibration, atmospheric correction, and geometric correction were not required. In order to get highquality time series, we made the following preprocess. Firstly, a band logic operation was used to remove cloud according to the quality evaluation information of the dataset. Secondly, a linear interpolation was used to fill gaps in time series after removing cloud. Thirdly, to unify the time interval of data and weaken the influence of cloudy, the maximum synthesis method was used to construct a seven-day time series. Finally, an S-G filter was used to smooth the time series, aiming to eliminate outliers in time series.

C. Reference Data
Reference data was randomly sampled as evenly as possible throughout the research sites covering mangroves (hereafter named "Mangrove"), nonmangrove vegetation (hereinafter named "Vegetation"), and the regions without vegetation (hereafter named "Nonvegetated"). Among them, the mangrove samples were selected referring to the Global Mangrove Classification products (with 10-m resolution and overall accuracy of 91.62%) released by [45] and Zhao's sample set [46].The above two datasets were acquired on Science Data Bank 1 . And the other two types were selected by visual interpretation based on Google Earth images. Further on, in order to avoid mixed samples, we tried to select samples from the center of the area. The number of samples for each study area is reported in Table II, and the distribution maps of samples are shown in Fig. 2.

III. METHODOLOGY
A flowchart of the presented methodology is illustrated in Fig. 3. Firstly, Sentinel-2 dataset after preprocessing was used to construct time series for each index. Secondly, the optimal indices were selected according to ST distance. Thirdly, by using PRGA, the weights of the GCMI were optimized. Finally, RF was adopted to classify mangroves with the time series of GCMI as the inputs.
A. Generalized Composite Mangrove Index 1) Indices Calculation: Since the mangroves and other land covers, especially nonmangrove vegetation, have same trend in most wavelengths (see Fig. 4), we constructed GCMI based on the existing indices rather than based on bands. Considering that mangroves are evergreen broad-leaved forests and their growth environment is influenced by tides, mangroves have special vegetation information and tidal inundation information. In order to make full use of the above information, we considered both vegetation indices (VIs) and water indices (WIs) to map mangroves (Table III). Among them, VIs not only can distinguish mangroves from nonvegetated area, but also from other deciduous vegetation to a certain extent. What is more, mangroves are submerged by tides periodically, thus the WIs are added to distinguish mangroves from nonmangrove vegetation.
2) GCMI Construction: Since the information of mangroves described by single index is limited, we considered compositing different indices to increase the separability between mangroves and other land covers. Considering too much of the indices may lead to information redundancy, we only selected two VIs and WIs to construct GCMI, which is given in where V I A and V I B are the two optimal VI, and W I A and W I B are the two optimal WI. The numerator of the equation (V I A + V I B ) enhanced the differences of vegetation greenness between mangrove forests and nonvegetated area. Whereas the denominator of the equation (W I A + W I B ) expressed the special moisture information of mangroves, which is quite different from other vegetation. GCMI measured the probability of mangrove pixels by utilizing both the VIs and WIs to highlight mangroves' greenness and moisture, respectively. Therefore, GCMI can separate mangroves from other land covers simultaneously. Besides, there are also some salt marsh plants (like spartina alterniflora) distributed in the tidal flats, which might be similar to mangroves in WIs. However, this type of vegetation has an obvious seasonal characteristic that can be distinguished by VIs easily.

B. Similarity Trend Distance
To construct GCMI, it is necessary to select the optimal indices with large discrimination. Therefore, a suitable measure is required to describe the difference between time series. Some commonly used distances measures are Cosine distance, Euclidean distance, Pearson correlation coefficient, and dynamic time warping (DTW) [54], etc. Since the input time series was the average values of a land cover, the distance measure should focus more on the trend rather than the value. Therefore, the above metrics are not quite suitable. For example, Euclidean distance only focuses on the difference between two values whereas Cosine distance only considers the angle difference. Pearson correlation coefficient does not fully consider the trend of time series and DTW distance needs to unify scales of the input before comparing. Furthermore, the above metrics use a single criterion to determine the difference, which may lead to one-sided effects. Therefore, in this study we intend to define a novel distance measure, namely ST distance, which can consider both similarity and trend of time series.
ST distance was composed of two parts: 1) one part aiming to measure similarity of time series; 2) the other part aiming to determine trend differences of time series. In the first part, we chose the Pearson correlation to describe the similarity between time series since it has been standardized, which pays less attention to the value differences. In the second part, we constructed the trend subsequence of time series firstly, then used DTW to calculate distance between the subsequences since the dimension of subsequences are variant.
Given a time series X n [(2)], the trend subsequence of time series can be constructed as follows (see Fig. 5): where i is the length of the input time series and x n i is the value in X n . 1) Using a sliding window to calculate the difference between two adjacent x n i , which is given in 2) Judging the state of each x d i , where x d j greater than 0 (the rising state) is 1, x d j less than 0 (the falling state) is −1, and x d j equal to 0 (the invariable state) is 0 as where x s j represents the state of x d j . 3) Merging the adjacent x s j that are in the same state as   where m p is the length of adjacent x s j in the same state and X t is the trend subsequence of X n . In this context, ST distance can be formulated as where X n and X n are the pair of time series to be compared correspondingly, X t and X t are the trend subsequence of the X n and X n , respectively. Besides, in order to make the dissimilar pair of time series has the higher value of ST distance, we used one minus the absolute value of Pearson correlation as the first part of ST distance. Consequently, when ST is larger, then the difference between the two time series would be greater. According to ST distance, the VIs and WIs with greater differentiation will be selected to construct GCMI.

C. Population Reconstruction GA
Intuitively, genetic algorithm (GA) [55] can be used to optimize the undetermined weights of the GCMI. GA is a heuristic search algorithm based on Darwin's theory of evolution, which searches for the optimal value by imitating the genetics and evolution in biology [56]. But the classical GA still has some limitations. For example, it probably cannot get the optimal solution because of the premature convergence. In addition, the optimization results greatly depend on the initial value and the effectiveness of fitness function [57]. To overcome the above problems, we improved the classical GA by reconstructing population, i.e, PRGA. PRGA can get optimal value more probably in the same condition. The flow chart of PRGA is shown in Fig. 6.
Firstly, the given information would be encoded in a particular bit string. Encoding schemes play an important role in most of computational problems since it can directly affect overall calculation speed of the algorithm and whether optimal result can be found. Considering the simplicity of GCMI, the search range of the undetermined weights was specified as (0,5] with an interval of 0.1. Therefore, we adopted an efficient and simple coding method which is based on permutation (Table IV ). After encoding, genes were selected randomly according to initial population size. So far, the population had been initialized.
Secondly, genes need to be evaluated by a fitness function. We chose ST distance as the fitness function, which can better evaluate the differences between time series due to jointly considering both similarity and trend. The fitness function used in  PRGA is formulated as where ST mv is the ST distance between time series of mangrove and vegetation, and ST mn is the ST distance between time series of mangrove and nonvegetated. Thirdly, the population needed to be evolved according to f . We chose roulette wheel as selection techniques, simulated  binary crossover [58] as crossover operator, and random permutation as mutation operator.
Finally, in order to overcome the problem of premature convergence, we proposed PRGA by adding a module named population reconstruction. If it reaches the maximum accumulative time of invalid iteration, PRGA will reconstruct the population. The concrete operations of population reconstruction are as follows: 1) PRGA evaluates genes by dividing genes into the inferior and the superior. In this article, the average fitness of current population is regarded as evaluation criteria, which means that the genes greater than average are the superior and the genes lower than average are the inferior. 2) PRGA keeps superior genes and deletes inferior genes. Besides, inferior genes are stored in the inferior gene bank. 3) PRGA adds new random genes into population. Especially, new random genes are not in the inferior gene bank to prevent repeated searches. After population reconstruction, new population is used to perform the above steps again.
Compared with classical GA, PRGA added the module of population reconstruction. Since one of the reasons of causing local optimization is the unicity in population, this module deletes the inferior genes and adds new random genes to maintain the diversity in population, which can avoid suffering from local optima problem to some extent.

D. Classification and Accuracy Assessment
After selecting indices according to ST distance and determining weights by using PRGA, the time series of GCMI were adopted for classification using RF. RF not only has high classification accuracy and less training time, but also has low sensitivity to training sample quantity, quality, and sample imbalance, which have been widely used for remote sensing image classification [59]. The study area contains three land cover types, where 60% labeled samples are randomly selected for training and the rest of 40% samples are used for test. Consumer accuracy (CA), overall accuracy (OA), and Kappa coefficient were calculated by confusion matrix as the evaluation indices.

B. Determination of GCMI 1) Time Series Separability Analysis:
For the purpose of selecting optimal indices to construct GCMI, we analyzed the separability of time series. Fig. 7 shows the time series of different land covers. On one hand, the time series of VIs between mangrove and vegetation are highly similar, which is difficult to distinguish mangrove from other vegetation by only using time series of VIs. Therefore, time series of VIs were mainly used to distinguish between mangrove and nonvegetated. On the other hand, the time series of WIs are quite different from other vegetation since mangroves are inundated by periodic tides. Therefore, time series of WIs are used to distinguish between mangrove and vegetation.    In each study area, one hundred training data for each mangrove, vegetation, and nonvegetated classes were independently selected to determine GCMI, which can avoid losing information of samples and increase the generalization performance of GCMI. The ST distances between the time series of different land covers were calculated according to (6), and the results are given in Table V. For WIs, the ST distances of LSWI and RNDWI are larger than the other two indices. As for VIs, the ST distances of EVI and gNDVI are larger than the other two indices. Therefore, the above four indices were selected to construct GCMI as 2) Optimization of Undetermined Weights: Since the weights of the selected indices are unknown, we used PRGA to optimize weights, whose parameters were used in the algorithm given in Table VI. The optimal weights were obtained by PRGA, A = 3.4, B = 2.9, C = 4.3, and D = 1.1 (Table VII). Finally, GCMI was determined as We show the time series of GCMI in Fig. 8, where GCMI increases the separability between mangroves and other land covers significantly compared to that illustrated in Fig. 7. Besides, the trends of different land covers are quite different, which is quite useful for accurate classification.

C. Effectiveness of PRGA
In order to verify the effectiveness of PRGA, we compared the results with classical GA. Since GA is a heuristic algorithm, the result just running once is randomness. Therefore, the results of classical GA and PRGA after running ten times respectively are listed in Table VII. According to the table, PRGA reaches the optimal result nine times out of ten runs, whereas classical GA only reaches the optimal result three times. Moreover, PRGA can get the optimal result in average around the 34th iteration. Therefore, PRGA can avoid trapping in local optimum and get the global optimal to some extent. However, the running time of PRGA increased by about 10% due to population reconstruction.

D. Effectiveness of ST Distance
To prove the effectiveness of ST distance, we compared Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW. The results of using different fitness functions in PRGA are reported in the Table VIII. In order to further verify the effectiveness of ST distance, the results of using the suboptimal parameters were also compared (Table IX). According to the results, ST distance yields the highest Kappa and OA. The OA is higher than Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW with 1%, 1.61%, 0.5% and 1% improvements, respectively. Comparing with the other suboptimal results, Kappa and OA are improved by about 0.014 and 1%, respectively, which clearly demonstrates the effectiveness of ST distance. Since GCMI does not consider the difference between vegetation and nonvegetated, the CA of vegetation and nonvegetated do not yield the highest, whereas the CA of mangrove is the highest. To sum up, regarding ST distance as fitness function can get the optimal result. Compared with Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW, ST distance can better measure the difference between time series.

E. Effectiveness of GCMI
To verify the effectiveness of GCMI, we compare the classification accuracies with the existing VIs, WIs, and MIs. The accuracies using time series of different indices are listed in the Table X. It is obvious that GCMI has the highest Kappa, OA, and the CA of mangrove, which demonstrated the effectiveness of GCMI. In VIs, NDVI obtained the highest Kappa and OA, which are around 0.0091 and 0.61% lower than GCMI, respectively. Besides, the CA of mangrove improved about 7.15% compared with that of VIs. In WIs, NDWI yielded the highest Kappa and OA, which are around 0.0304 and 2.03% lower than GCMI, respectively. Moreover, the CA of mangrove improved about 6.62% compared with WIs. As for MIs, the CA of mangrove improved 6, 0.74, 7.3 and 7.48%. Therefore, using the time series of GCMI to map mangroves could get the best classification result.  The classification results of different indices are shown in Fig. 9. It is obvious that GCMI can make full use of vegetation information and tidal inundation information of mangroves to get a better classification result. On the whole, for VIs and CMRI, we can see that nonmangrove vegetation is misclassified as mangroves in certain areas. For WIs, IMFI, and NIMI, we can see that nonvegetated is easily misclassified as mangroves in some regions. As for MVI, the mangroves adjoining to sea are easily misclassified.
For a clearer comparison, we chose two sites (A and B in Fig. 10) in Maowei Sea to show the clearer classification results of mangrove. Fig. 11 shows the local area (A) where there is no mangrove distribution. It is obvious that excepting for GCMI and MVI, the other existing indices cannot distinguish vegetation and mangroves satisfactorily. Fig. 12 shows the mangrove classification result in local area (B) where there is mangrove distribution. By contrast, we can see VIs and MVI have omission errors in the boundary between sea and mangroves, which is due to the fact that mangroves are inundated by tidal periodically in this place where there have sparse vegetation information. What is more, since WIs, CMRI, IMFI, and NIMI did not consider the vegetation information, thus the water and some salt marsh plants are easily misclassified as mangroves.

A. Advantages of the GCMI
This article presented a novel mangrove index GCMI based on VIs and WIs. Using the time series of GCMI to map mangroves, the obtained Kappa and OA can reach to 0.8758 and 91.72%, respectively. GCMI is the first mangrove index that considers both vegetation information and tidal inundation of mangroves based on time series. The advantages of GCMI are as follows: 1) Using phenology trajectory of mangrove. Mangrove is easily confused with terrestrial vegetation, but mangrove has phenological information of evergreen and tide    inundation, which can be used to distinguish it from other land covers.
2) Regarding ST distance as the criterion to measure the separability of time series. ST distance refers to the multicriteria judgment, which evaluates the similarity and trend of time series at the same time. In this article, ST distance helps to confirm the indices and weights in GCMI. The precision of using ST distance is the highest compared with Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW, which proves the reliability of ST distance. 3) Using PRGA to optimize weights involved in GCMI. Depending on the module of reconstructing population, the probability of getting the global optimum can be increased by about 55%. However, the running time of PRGA is about 10% higher than classical GA, because population would be reconstructed when reach the number of max invalid iteration. Different from the existing normalized index, the weights of GCMI are more interpretable and can be more useful to distinguish mangroves from other land covers.

B. Application to Other Study Areas
GCMI was utilized to test the performance of mapping mangroves in other study areas, i.e., Dongzhai Port and Quanzhou Bay. Firstly, the indices with higher difference of time series were selected. Table XI reports ST distance between different  indices, where LSWI, NDWI, EVI, and gNDVI were selected for Dongzhai Port, whereas EWI, RNDWI, NDVI, and gNDVI were selected for Quanzhou Bay. Secondly, PRGA was used to optimize the undetermined weights and the parameters used in PRGA are listed in Table XII. Similarly, we compared the optimization results of classical GA and PRGA (see Table XIII). From Table XIII, it can be seen that PRGA has a more robust ability to get the global optimal result. Finally, GCMI in Dongzhai Port and Quanzhou Bay were defined as (10) After constructing the index, accuracies are reported in Tables XIV and XV. From Table XIV, it can be seen that ST distance yields the highest Kappa, OA, and CA of mangrove. In DongZhai Port, the OA of ST distance is higher than that of Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW, with 0.25%, 0.48%, 1.41%, and 2.62% improvements, respectively. In QuanZhou Bay, the OA of ST distance is higher than that of Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW with 2.18%, 2.55%, 1.35%, and 2.8% improvements, respectively. According to Table XV, GCMI has the highest Kappa, OA and CA of mangrove, which demonstrated the effectiveness of GCMI. In DongZhai Port, the OA of GCMI improved 3.63%, 1.97%, and 2.69% comparing with VIs, WIs, and MIs, respectively. In QuanZhou Bay, the OA of GCMI improved 3.23%, 3.03%, and 1.23% comparing with VIs, WIs, and MIs, respectively. What's more, the classification results in DongZhai Port and QuanZhou Bay are shown in Fig. 13. Since spartina alterniflora was introduced in Quanzhou Bay in 1982, and it has had a great negative impact on the ecosystem, affecting the growth of mangroves seriously. Therefore, mangrove in Quanzhou Bay is sparsely distributed, as shown in Fig. 13(b). The results in DongZhai Port and QuanZhou Bay demonstrate the effectiveness of ST distance, validity of PRGA, and universality of GCMI.

C. Prospects
In this article, we demonstrate that GCMI time series can be efficiently used for mangrove mapping in South China coastal region. GCMI enhances the separability between mangrove and other land covers by taking full advantage of its vegetation information and tide inundation information. However, GCMI still requires further study and improvement in the future work. Currently, the phenological information contained in time series has not been fully explored since they are directly used as features for classification. Therefore, mining the phenological information from time series may achieve better classification results.

VI. CONCLUSION
In this article, we proposed a new mangrove index, namely GCMI based on Sentinel-2 data. Firstly, GCMI was built by compositing indices selected by using ST distance. Then, the weights of GCMI were optimized by PRGA. Finally, the time series of GCMI were regarded as features to map mangroves by using RF. Taking south China coastal regions as study areas, the mainly results are given as follows: 1) The classification results show that GCMI enhances the separability between mangroves and other land covers compared to existing VIs, WIs, and MIs. Using the GCMI time series to map mangrove in Maowei Sea, the kappa and OA are 0.8758 and 91.72%, respectively. 2) ST distance jointly evaluates the similarity and trend of time series, which is more suitable for measuring the differences between time series. ST distance produces about 1, 1.61, 0.5, and 1% improvements in terms of OA compared to Euclidean distance, Cosine distance, Pearson correlation coefficient, and DTW, respectively. 3) PRGA has greater capability to obtain the optimal result since it can maintain the diversity in population. The average probability of getting the global optimum within ten times is 70%, whereas the average probability is only 16% when using classical GA. This article develops GCMI based on existing indices, and GCMI time series show superior performance in mapping mangroves. The method is novel and propagable, which can be used for mangroves mapping in other sites. What is more, the 10-m mangrove map can provide support for coastal management and decision basis to protect mangrove.
The innovative contributions of this study are as follows. 1) We proposed GCMI by compositing existing VIs and WIs based on time series. Compared with other MIs, GCMI cannot only fully make use of the information from phenological trajectories, but also distinguish mangroves from other vegetation and nonvegetated simultaneously. 2) We designed ST distance to measure the time series differences. Different from the other distance measures, ST distance can consider both similarity and trend of time series. 3) We improved the classical GA by reconstructing population to optimize the parameters in GCMI. PRGA has more robust ability to get the optimal result in contrast to the classical method. Currently, the phenological information contained in time series has not been fully explored since they are directly used as features for classification. Therefore, in our future work, we will exploit the phenological information from time series, which may achieve better classification results.