Introduction
Land subsidence caused by excessive groundwater exploitation is a severe problem in numerous cities and regions, including Shanghai (Shen and Xu, 2011; Xu et al., 2016), Mexico City (Kirwan and Megonigal, 2013), Bangkok (Phien-Wej et al., 2006), Iran (Amiraslani and Dragovich, 2011; Rahmati et al., 2019), Las Vegas (Bell et al., 2008; Hoffmann et al., 2001) and the San Joaquin Valley in California (Faunt et al., 2016; Poland, 1972). These areas with problematic subsidence have long been monitored; their distribution and extent of subsidence and water-level decline are well established as the result of the compaction of fine-grained aquitards and interbeds due to aquifer overexploitation (Bonì et al., 2016). The removal of water from storage in fine-grained silts and clays, interbedded within the aquifer system, causes these highly compressible sediments to compact and cause land subsidence. Furthermore, large-scale groundwater utilization from human activities causes environmental problems (Rahmati et al., 2019), such as land degradation, soil salinization and desertification.
Land subsidence is correlated with variations of the aquifer system pore pressures or water-level response to pumping (Burbey, 2001). The drawdown of water levels leads to land subsidence from over-extraction of groundwater (Bell et al., 2008; Galloway and Burbey, 2011). However, generating the subsidence–drawdown relation is critical to better understand and predict the spatial distribution of land subsidence. Accurate modeling requires observations of land deformation and water levels over months to years of time (Faunt et al., 2016; Kim, 2000; Yan and Burbey, 2008). To model the subsidence–drawdown relation, traditional numerical groundwater flow models such as MODFLOW (Mahmoudpour et al., 2016; Shearer, 1998; Zhou et al., 2003) combined with a post-processing software package such as GMS (Parhizkar et al., 2015) can provide water-level and flow distributions of the system under observation. Thus, land subsidence can be simulated from changes in water pressure within the aquifer system coupled with the SUB Package (Hoffmann et al., 2003b). A coupled numerical model that incorporates the concepts of three dimensional poroelasticity based on Biot’s consolidation theory (Biot, 1941, 1955) is developed for simulating three dimensional displacement of solids within unconsolidated aquifers in response to induced changes in water pressure (Burbey, 2006; Burbey and Helm, 1999). Elastic (recoverable) and inelastic (permanent) compaction from stress–strain diagrams (Epstein, 1987; Hanson, 1989; Riley, 1969) can be identified. Fine-grained sediments tend to compact inelastically if the effective stress exceeds the preconsolidation stress. Decreasing hydraulic heads, such as by increasing effective stresses, causes a small amount of elastic compaction if the effective stress remains less than the preconsolidation stress (Galloway and Burbey, 2011). However, uncertainty still exists in traditional numerical models because heterogeneous geological conditions cannot be described in the same detail that occurs in nature.
Reasonable estimates of the subsidence–drawdown relation can be obtained from regression models using land subsidence and drawdown data, provided sufficient subsidence data and water-level records are available for the area of investigation (Yan and Burbey, 2008). However, drawdown and subsequent compaction of compressible hydrogeologic layers can result in spatially non-uniform and heterogeneous land subsidence of the hydrogeological system (Galloway et al., 1998a; Hoffmann et al., 2003a; Teatini et al., 2006). The subsidence–drawdown relation is rarely well correlated and therefore seldom readily applied in multi-linear regression analyses (Jiang et al., 2015). Moreover, the subsidence–drawdown function is found to be far more heterogenous than most previous studies suggest (Sundell et al., 2019). Spatial regression (SR), i.e. geographically weighted regression (GWR), is a local form of linear regression used to model spatially varying relationships (Fotheringham, et al., 2003). Such methods are powerful for capturing the effects of spatially heterogeneous processes and can identify spatial nonstationarity in the subsidence–drawdown relation by allowing regression coefficients to vary spatially. However, previous studies on SR merely consider the relationship between subsidence and groundwater level variation at starting and ending times without considering any compaction processes (Shang et al., 2011).
The present study aims to estimate the spatially variable land subsidence distribution based on accumulated drawdown between ground-based observations and to improve the limitations of linear regression methods, which typically fail in spatial hydrogeologic settings. The SR-based method developed in this study provides a reliable model of the spatial relationship between accumulated drawdown and the resulting land subsidence. The model coefficients are expected to provide the spatial patterns of elastic and inelastic storage coefficients of the aquifer. In addition, a spatial subsidence map is proposed based on only the groundwater drawdown distributions in the aquifer system.
Study area and data