Zeeshanktk1992@yahoo.com;
Thomas J. Burbey;
Virginia Polytechnic Institute and State University
tjburbey@vt.edu
Correspondence: Hone-Jay Chu;
honejaychu@geomatics.ncku.edu.tw;
No.1, University Road, Tainan City 701, Taiwan; National Cheng Kung
University
Tel.: +886-937923481
Development of a groundwater-drawdown function to estimate spatially
varying land subsidence: a case study of the Choshui River basin, Taiwan
Abstract
Land subsidence caused by groundwater overexploitation is a critical
global problem. Spatial distribution of land subsidence is crucial for
environmental management and land planning due to the sensitive nature
of land-surface gradients. Given the nonlinear relationship of
subsidence and long-term drawdown
from groundwater exploitation, and the heterogeneity of the aquifer in
the Choshui River alluvial fan, a developed spatial regression model can
effectively estimate nonlinear and spatially varying subsidence. That
is, the root-mean-square-errors
(RMSEs) of annual subsidences are less or equal to 0.8 cm. Considering
various data inputs in the Choshui River alluvial fan, the spatial
regression model offers a robust method for estimating the spatial
patterns of subsidence using drawdown as
observations. Results show that
the largest water-level cone of depression occurs in the distal fan
area. Nonetheless, the calculated subsidence bowl closely approximates
the observed one located much farther inland.
Without requiring extensive calibration or an elaborate numerical
groundwater flow and subsidence model, the model provides reasonable and
detailed patterns using a spatially varying relationship between
drawdown and resulting land subsidence. Results indicate that the
spatial regression model reasonably estimates the spatial distribution
of the skeletal storage coefficient in the aquifer system. The large
coefficient that represents inelastic compaction occurs in the inland
areas, whereas the small coefficient that represents elastic compaction
occurs along the coastal area. Furthermore, this model is relevant for
water policy or land subsidence regulation.
Keywords: subsidence; spatial regression; drawdown; groundwater
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