**1. Introduction**

Land subsidence (LS) is one of the most challenging catastrophic geohazards due to its potential consequences, including damage to infrastructures, power lines, and buildings, causing sinkholes, floods in coastal areas, and soil degradation [1–3]. Land subsidence is a gradual and slow deformation or sudden collapse of the Earth's surface, which is caused by numerous natural and human-induced factors [4–7]. The ground subsiding movement can be the result of natural causes such as floods, ground lithology, dissolution of carbonated rocks (e.g., limestone), sediment compaction, and tectonic motions of faults [8–11]. Further, anthropogenic activities that alleviate these geological factors, including underground excavations (e.g., mining and tunneling), underground resource withdrawal (gas or oil),

**Citation:** Ranjgar, B.; Razavi-Termeh, S.V.; Foroughnia, F.; Sadeghi-Niaraki, A.; Perissin, D. Land Subsidence Susceptibility Mapping Using Persistent Scatterer SAR Interferometry Technique and Optimized Hybrid Machine Learning Algorithms. *Remote Sens.* **2021**, *13*, 1326. https://doi.org/10.3390/ rs13071326

Academic Editors: Cristiano Tolomei, Paolo Mazzanti and Saverio Romeo

Received: 26 February 2021 Accepted: 29 March 2021 Published: 31 March 2021

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overloading of the land surface through road construction and extending the built environment [12–14], and most importantly, over-exploitation of underground aquifers [15–17].

In the last few decades, the land subsidence phenomenon has widely increased in Iran [18–20], and therefore, growing research interest has focused on studying this geological problem [2,13,17,21–23]. One of the most important causes of the LS in Iran with an arid and semi-arid environment is the excessive groundwater extraction for agricultural usage [13,24]. Therefore, modeling factors affecting land subsidence and land subsidence susceptibility mapping (LSSM) is vital for the environment, safety, economy, and human well-being.

Remote sensing (RS) and geographic information system (GIS) data and tools have been helpful in land subsidence susceptibility studies in terms of acquiring fine resolution data and analyzing various factors affecting this phenomenon [10,11,25]. Many statistical and probabilistic approaches have been applied in the literature to provide susceptibility maps and monitor subsidence. These methods include the frequency ratio (FR) [26], weight of evidence (WOE) [27], logistic regression (LR) [28], evidential belief function (EBF) models [11], artificial neural networks (ANNs) [29,30], analytical hierarchy processes (AHP) [31,32], multi-criteria decision making (MCDM) models [22], as well as fuzzy logic (FL) [27,30] and adaptive neuro-fuzzy inference systems (ANFIS) [33].

However, these methods are mainly based on human assumptions and need expert knowledge. Recently, GIS-based machine learning algorithms (MLAs) have become a favorite in modeling and analyzing environmental hazards, especially LS. They can cope with data peculiarities, reveal complex relationships between data, and produce high accuracy and close-to-real world results [10,23]. Lee and Park [12] conducted a comparative investigation between the decision tree (DT) algorithm and FR model in estimation of LS and its causing factors. Abdollahi et al. [34] applied a support vector machine (SVM) to predict LSS using water table drawdown and other influential factors. Taravatrooy et al. [35] used a hybrid clustering method based on k-means, genetic optimization, and several soft computing algorithms to examine subsided zones. Tien Bui et al. [10] compared four MLAs (Bayesian logistic regression (BLR), SVM, logistic model tree (LMT), and alternate decision tree (ADT)) in assessing LSS near abandoned mining areas in South Korea. In a study in Kerman, Iran, the random forest (RF) algorithm showed superior capability in LSS mapping [36]. Ebrahimy et al. [23] performed a comparative study using three tree-based MLAs, a boosted regression tree (BRT), RF, and classification and regression tree (CART), for studying land susceptibility in Tasuj plane, Iran. Evaluation results revealed that BRT had the best performance. In another study by Rahmati et al. [37], four tree-based MLAs, a rule-based decision tree (RDT), RF, CART, and BRT, were compared for generating LS hazard maps in Hamedan Province, Iran. The results indicated that RF had the best accuracy amongst the employed methods.

Despite the better performance and accuracy of MLAs, all the above-mentioned approaches are dependent on the availability and precision of the subsidence inventory data, which is a serious challenge in developing countries [2,11,37]. On the other hand, interferometric synthetic aperture radar (InSAR) has been utilized in land displacement measurement and demonstrated promising results with millimetric precision [38,39]. SAR is satellite data so there is no need for time-consuming field survey data acquisition; therefore, it is superior to other approaches such as leveling data and is denser than ground positioning system (GPS) station data. Furthermore, radar data are functional in all-time all-weather conditions, making this a cost-efficient method to obtain land subsidence measurements. Recently, InSAR methods were employed in LSS studies as reliable input data along with other data to achieve finer accuracies [6,40]. In this paper, we used the PS-InSAR method to obtain land subsidence inventory data and utilize them among other subsidence triggering factors for land subsidence susceptibility mapping in the study area. As a novel methodology in LSSM, we used ANFIS optimized with two meta-heuristic algorithms: (1) imperialist competitive algorithm (ICA) and (2) gray wolf optimization (GWO). ANFIS uses hybrid learning of ANN in adjusting its membership functions (MF) with output data [41,42]. Further, by taking advantage of meta-heuristic algorithms, the weight parameters of MFs were optimized. The results of the method were compared using the statistical approach of the root mean square error (RMSE) value. Furthermore, the accuracy of LSSMs was evaluated by the area under the receiver operating characteristic (ROC) curve.

#### **2. Materials and Methods**

The methodology applied in this research (summarized in Figure 1) is to generate an updated land subsidence inventory through the PSInSAR technique using a Sentinel-1 SAR dataset spanning the period from 2019 to 2020. Moreover, the aim of this paper is to develop and use an ensemble of ANFIS and meta-heuristic algorithms in modeling land subsidence susceptibility. The main steps of the study are as follows. First, a spatial database was created using generated land subsidence inventory and the layers of the conditioning factors. In the second step, PS-InSAR-derived subsidence inventory data were divided into training (70%) and testing (30%) data. Next, MF parameters were optimized in ANFIS using ICA and GWO meta-heuristic algorithms, and then LSSMs were produced using ANFIS, ANFIS-ICA, and ANFIS-GWO individually. Finally, the produced land susceptibility maps were compared and evaluated using the area under the ROC curves.

**Figure 1.** Flowchart of the overall methodology.

#### *2.1. Study Area*

The region of interest in this paper is Shahryar, the central city of Shahryar County within 35◦35 to 35◦42 latitudes and 50◦59 to 51◦6 longitudes (Figure 2), with the elevation ranging from 1081 to 1222 m. This county is located west of Tehran, the capital of Iran. In recent years, there has been an increase in population migration to cities near Tehran, including Shahryar, for better jobs and income. According to Iran census data in 2016, the county is the 12th largest in the country with a population of more than 700,000 people. This has become a serious problem in urban environment management and food production. Shahryar County is known for its green and beautiful landscape and the major income of the people in the area originates from gardening and agriculture. Owing to population increase, the demand for food has grown dramatically. Therefore, more illegal wells are dug. As a result, the county has suffered from severe land subsidence (250 to 310 mm/year) due to exhaustion of underground water aquifers and water table dropdown.

**Figure 2.** The location of the study area along with the extracted land subsidence inventory.
