Observations at the Lake Houston site
In general, GPS-derived subsidence represents the total compaction of unconsolidated and semi-consolidated sediments below the land surface. The compaction within a specific aquifer is often challenging to ascertain using GPS data alone. Combining GPS and long-term borehole extensometer (compaction recorder) datasets may provide compaction information within specific aquifers (e.g., Yu et al. 2014; Liu et al. 2019a, b). Unfortunately, there are no extensometers in Montgomery County. As of 2020, USGS and HGSD operate 14 borehole extensometers within the greater Houston region. The closest extensometer to Montgomery County is located at Lake Houston, Harris County, approximately 17 km to the south boundary of Montgomery County (Fig. 1). The extensometer measurements (1980–2020) are provided by USGS (Ramage and Shah 2019). Land surface elevation at this site is approximately 16 m above mean sea level.
The extensometer borehole at Lake Houston was terminated at the top of the Burkeville confining unit, 591 m below the land surface (Fig. 10a). Six groundwater observation wells were also installed adjacent to the extensometer site (Fig. 10b). Two wells were terminated in the Chicot aquifer; three wells were completed at different depths of the Evangeline aquifer, and one deep well was terminated within the top portion of the Jasper aquifer. The borehole of the extensometer was screened at the bottom. The screen allows groundwater to flow in and out. Thus, the extensometer borehole (out case) also works as a deep groundwater well measuring the groundwater hydraulic head within the top portion of the Burkeville confining unit. HGSD installed a GPS (LKHU) antenna on the top of the inner pole in 1993 with the purpose of providing a stable reference for regional land subsidence monitoring. The inner pole was anchored on the top of the Burkeville confining unit 591 m below the land surface (Fig. 10b). A permanent GPS (P009) was installed adjacent to Lake Houston in 1999 (see Fig. 1 for the location). The linear distance between P009 and LKHU is 15 km.
Evangeline compaction
Figure 11a depicts the Lake Houston extensometer and GPS (LKHU) measurements during the past 4 decades. The extensometer measured the total compaction of sediments from the land surface to the bottom of the Evangeline aquifer. The average compaction rate was 11.8 mm/year during the 1980s, reduced to 3.8 mm/year during the 1990s, and further reduced to approximately 1.3 mm/year during the 2000s. The GPS measurements (LKHU) on the top of the inner pole indicate no considerable vertical movements during the entire history from 1993 to 2020. That is, no groundwater-withdrawal-induced aquifer compaction occurred within the Burkeville confining unit and the Jasper aquifer at this site.
GPS-derived subsidence time series at P009 indicates that the ongoing land subsidence (total compaction) rate in this area has been about 1.8 mm/year since the 2000s. There are tall trees around P009; therefore, the scatters of the subsidence time series at P009 are remarkably larger than the scatters at other GPS sites. According to the empirical formula (Eq. 1) for estimating the accuracy (95% CI) of GPS-derived vertical site velocities, the two-decadal observations (1999–2020) would be long enough to secure submillimeter-per-year accuracy for estimating an overall linear trend (subsidence rate) (Wang 2021). The extensometer data indicates that the average subsidence rate during this period (1999–2020) is approximately 1.3 mm/year. According to an analysis of co-located and closely-spaced daily-GPS and monthly-extensometer measurements at Addicks in northwestern Houston (Wang et al. 2014), the root-mean-square (RMS) accuracy of the monthly-extensometer measurements is a few millimeters. The accuracy (95% CI) of the compaction rate derived from the 20-year monthly-extensometer data (1999–2020) is certainly below 1 mm/year. Considering the uncertainty of both datasets, the subsidence rates derived from GPS and extensometer datasets agree reasonably well (− 1.3 mm/year vs. − 1.8 mm/year), which also suggests no considerable compaction below the Evangeline aquifer.
Figure 11b illustrates the groundwater levels recorded at these seven groundwater-level observation wells. The deep Chicot well (USGS ID: 295451095083901, 165 m below land surface) shows a consistent groundwater-level change pattern with these Evangeline groundwater levels. It is likely that the groundwater level in this well was dominated by the groundwater-level change in the Evangeline aquifer. This implies that the interface between the Chicot and the Evangeline aquifers at this site is close to 165 m below the land surface. The units that make up the Chicot and Evangeline aquifers are similar in lithology and are difficult to differentiate (Baker 1979). The Chicot and Evangeline aquifers are hydraulically connected, which allows groundwater to flow between them. The shallow Chicot well (USGS ID: 295449095083401, 60 m below land surface) shows a slight rise (0.2 m/year) of the Chicot groundwater level from approximately − 18 m in 1980 to − 10 m in 2020. The Chicot groundwater level has been above the pre-consolidation head since the 1990s. It is unlikely that the Chicot aquifer could considerably contribute to the land surface subsidence since the 1990s. Thus, the total aquifer compaction recorded by the extensometer during the past 3 decades is solely contributed by the compaction of the Evangeline aquifer.
Pre-consolidation head
The correlation between the primary aquifer compaction and groundwater-level changes can be explained by the Principle of Effective Stress (Terzaghi 1925):
$$p^{\prime} = p - u_{w} ,$$
(2)
where \(p^{\prime}\) represents effective stress at the grain-to-grain contact points within the sediments; \(p\) represents total stress due to the weight of the overlying water and sediments; \(u_{w}\) represents pore-fluid stress, which is corresponding to the hydraulic head within local sediments. \(u_{w}\) can be divided into two parts: a static or equilibrium head (\(u_{s} )\) in the pore water and a transient pore-water stress (\(u\)) in excess of the equilibrium pore-water stress. That is, \(u_{w} = u_{s} + u\). Within aquitards, \(u\) decays to zero slowly as water drains from an aquitard and stress equilibrium is approached. The total stress (\(p\)) is also called geostatic stress, often regarded as unchanged during multi-decadal to century time scales. The total stress (\(p\)) is balanced by the changes of pore-fluid pressure (\(u_{w}\)) and effective stress (\(p^{\prime}\)) exerted on clay particles. Pumping causes the reduction of pore-water stress (\(u_{w}\)) in response to the declining of the hydraulic head. The reduced stress will be taken over by the solid grains. The maximum effective stress that a lay of sediments had sustained for a long period (century-scale) during its history is called pre-consolidation stress. When the effective stress exceeds the pre-consolidation stress, the clay grains will undergo significant, permanent rearrangement, resulting in inelastic (irreversible) compaction. The groundwater level corresponding to the pre-consolidation stress is called the pre-consolidation hydraulic head, simply the pre-consolidation head. In the Greater Houston region, the pre-consolidation head in each aquifer is approximate to the groundwater level before the 1940s when no excessive groundwater pumping occurred.
The Evangeline wells indicate that the groundwater hydraulic head remained constant during the 1980s, approximately at − 50 m (Fig. 11b). According to groundwater data in the long history illustrated in Fig. 7, regional-scale groundwater decline began in the 1970s. The Evangeline groundwater level started to rise in the early 1990s and reached approximately − 35 m at the end of 2008. Extensometer measurements indicate that the compaction of Evangeline was about 1 mm/year from 2000 to 2008. The minor subsidence rate suggests that the groundwater level was approaching the pre-consolidation head. A slight aquifer elastic expansion (or land surface rebound) is expected if the groundwater level had recovered to the pre-consolidation head (e.g., Galloway and Burbey 2011; Liu et al. 2019a; Zhou et al. 2021). Since no rebound was recorded around this period by the extensometer, it is most likely that the Evangeline groundwater level (− 35 m) as of 2008 is still below the pre-consolidation head.
According to the investigations of USGS (e.g., Kasmarek and Robinson 2004; Kasmarek 2012) and UH (Kearns et al. 2015, 2019), the pre-consolidation heads of the Chicot and Evangeline aquifers are approximately − 20 to − 30 m in southern Harris County. Since the land elevation in the Lake Houston area is about 10 m higher than the land elevation in southern Harris County, a slight hydraulic gradient would occur over the long distance from the north to the south. Combining the observations at this site and the pre-consolidation head in southern Harris County, we deduce that the Evangeline pre-consolidation head in Lake Houston area is approximately at − 15 to − 25 m, 5 m higher than the pre-consolidation head in southern Harris County. Determination of the pre-consolidation head will be further discussed in the following sections. The long-term static groundwater hydraulic heads in the two aquifers are approaching the same level since the groundwater in the Chicot and the Evangeline aquifers are hydraulically connected. The pre-consolidation head in the Chicot aquifer would be the same as the pre-consolidation head in the Evangeline aquifer.
The groundwater level in the extensometer borehole (USGS ID: 295449095084105, completed at 591 m below land surface) was relatively stable during the past 4 decades, ranging from − 25 to − 35 m (Fig. 11b). Since the borehole is terminated within the top of the Burkeville confining unit, the groundwater level represents the groundwater hydraulic head in the Burkeville confining unit. The thickness of the Burkeville confining unit is approximately 100 m in this area. The GPS antenna (LKHU) on the inner pole of the extensometer was stable over the past 2 decades, indicating no considerable compaction within the confining unit.
The groundwater level in the Jasper well (USGS ID: 295449095084101, 790 m below land surface) shows a gentle decline from 1980 to 2000 with an average decline rate of 0.5 m/year. A rapid groundwater-level drop of 10 m occurred within 2 years from 2002 to 2003, which did not induce any significant subsidence at the land surface. The Jasper groundwater continued to decline from 2004 to 2014 with an average rate of − 2.5 m/year. The decline rate slowed down since 2016 with an average rate of − 0.6 m/year (2016–2020). The Japer groundwater-level altitude declined to − 10 m at the beginning of 2020. Since there is no groundwater-withdrawal-induced compaction within the Jasper aquifer as verified by GPS data (LKHU), the Jasper pre-consolidation head in this area would be lower than the current groundwater level (− 10 m).
Virgin-compaction/head-decline ratio
The aquifer compaction that occurred when the groundwater level is below the pre-consolidation head is also referred to as virgin compaction in the hydrology literature (e.g., Helm 1975; Galloway and Burbey 2011). The increased effective stress that exceeds the maximum historic stress (pre-consolidation stress) during the virgin compaction phase is called virgin stress. In this article, the virgin compaction is specifically referred to as the compaction that occurred when the groundwater level was continuously declining and below the pre-consolidation head, distinguishing it from the compaction that occurred when the groundwater level was stable or rising (see Fig. 11a).
The Evangeline wells completed at different depths indicate a rapid Evangeline groundwater-level drop of 5 m from mid-2008.5 to 2013 (Fig. 11b), which resulted in a compaction of 2 cm within the Evangeline aquifer during the period from mid-2009 to 2014 (Fig. 11a). Compaction occurs primarily due to the change in pore pressure in the clay beds in an aquifer. It takes time for the pressure change in the sand to propagate into the clay, for the compaction of clay to occur, and for the deep compaction to propagate to the land surface ultimately. The time lag between groundwater level drop and land subsidence occurring at this site is about 1 year. The 5-m groundwater-level decline in the Evangeline aquifer led to a 2-cm virgin-compaction at this site. The ratio of virgin-compaction to head-decline is approximately 1:250. This ratio is a direct measure of the virgin compressibility of the Evangeline aquifer in this area. The compressibility is related to the geologic age, burial depth, and content (thickness) of clay layers within the aquifer. The Lake Houston site is only 17 km away from Montgomery County. According to USGS investigations (e.g., Kasmarek and Robinson 2004), the clay layers within the top aquifers (Chicot, Evangeline, upper Jasper) are similar on both sides of the boundary between Harris and Montgomery counties.
In practice, it is a challenge to estimate the virgin compressibility of an aquifer. On the one hand, it is often difficult to measure the compaction within a specific aquifer; on the other hand, it is difficult to get the groundwater and compaction measurements during the virgin-compaction phase. The groundwater levels have been rising while the land surface is continuously subsiding in the majority part of northern Harris and Montgomery counties since the mid-2010s. So, most GPS data are collected during the non-virgin-compaction phase. Fortunately, the datasets at Lake Houston provide valuable information to delineate the virgin-compaction/head-decline ratio in the Evangeline aquifer in this region.
In summary, the long-history of groundwater, extensometer, and GPS datasets at the Lake Houston site have contributed to essential conclusions: (1) groundwater pumping has not induced considerable compactions in the Burkeville confining unit and the Jasper aquifer in this area; (2) the pre-consolidation head in the Evangeline aquifers would be slightly higher than − 30 m, and the pre-consolidation head in the Jasper aquifer would be deeper than − 10 m; (3) the virgin-compaction/head-decline ratio in the Evangeline aquifer is approximately 1:250 in the Lake Houston area.
Observations in The Woodlands
The Woodlands is located in southern Montgomery County, 45 km north of Houston. The terrain is essentially flat, ranging from 40 to 60 m above sea level. The Woodlands is one of the fastest-growing suburban areas in Texas. Groundwater pumping has increased significantly since the 2000s.
Evangeline virgin-compaction/head-decline ratio
Figure 12a shows the locations of six GPS stations and three sets of closely-spaced Evangeline and Jasper groundwater wells in The Woodlands area. Figure 12b, c show site views at GPS stations P013 and WHCR. P013 is a typical PAM station installed on the free field. WHCR is a typical UH GPS station installed on school buildings. GSEC, PWES, and WHCR are installed on single-story school buildings in Galatas Elementary School, Powell Elementary School, and The Woodlands High School. Figure 13a depicts the GPS-derived land subsidence time series at these GPS sites. GPS-derived subsidence time series at these six sites consistently suggest that the average rate of ongoing subsidence (2016–2020) in this area is approximately 7–8 mm/year. P013 has a history of 2 decades (2000–2020) and shows the occurrence of an acceleration of subsidence in the middle of 2004. The subsidence rate changed from 11 mm/year (2001–2004.5) to 16 mm/year (2005–2015). There has been a deceleration of subsidence since 2016. The Woodlands area began receiving surface water from Lake Conroe in 2015. Subsequently, land subsidence reduced from 16 mm/year (2005–2015) to 8 mm/year (2016–2020).
Figure 13b depicts the history of groundwater-level changes in The Woodland area. Measurements at three Evangeline wells indicate that the Evangeline groundwater-level altitude was below the pre-consolidation head and declined with a steady rate of 2.4 m/year from 2001 to 2014. The groundwater level began to rise after the surface water was available for municipal use since approximately 2015. The observations at the Lake Houston site have suggested that the Evangeline virgin-compaction/head-decline ratio in this area is about 1:250 (Fig. 11). The groundwater-level decline of 2.4 m/year in the Evangeline aquifer would result in a compaction approximately 10 mm/year. GPS measurements at P013 indicate that the total compaction rate was 16 mm/year from 2004 to 2015. The compactions of the Chicot aquifer and the Burkeville confining unit are ignorable, as previously discussed. That means the compaction of the Jasper aquifer resulted in the remaining 6 mm/year. The measurements at three Jasper wells closely-spaced with these three Evangeline wells indicate that the Jasper groundwater-level decline rate was approximately 4.8 m/year from 2004 to 2014. Accordingly, the virgin-compaction/head-decline ratio in the Jasper aquifer in this area is approximately 1:800. That is, the Jasper Aquifer is three to four times less susceptible to compaction than the overlying Evangeline aquifer in this area.
The groundwater level and GPS datasets also suggest that the Jasper aquifer contributed approximately one-third of the total compaction (6 of 16 mm/year) from 2005 to 2015. Unfortunately, it is difficult to distinguish the contribution of the Jasper aquifer from the land subsidence (total compaction) since 2016. Groundwater levels in both the Jasper and Evangeline aquifers have been rising since 2016. The ongoing compactions since 2016 are in a none-virgin-compaction phase. The compressibility of each aquifer during the non-virgin-compaction phase could be differ from the compressibility during the virgin-compaction phase.
Jasper pre-consolidation head
GPS-derived subsidence at P013 shows a reduction of the subsidence rate in the middle of 2004. The subsidence rate was 11 mm/year from 2001 to 2003, which is comparable to the rate that could be produced by the compaction of the Evangeline aquifer alone (~ 10 mm/year) with the groundwater hydraulic head decline rate of 2.4 m/year. There were no substantial groundwater-level changes in the Evangeline aquifer around 2004. So, the increased subsidence rate (from 11 to 16 mm/year) might be primarily contributed by the additional compaction of the Jasper aquifer. In other words, the compaction of the Jasper aquifer likely began in 2004. The Jasper groundwater level in 2004 would be close to the pre-consolidation head of the Jasper aquifer. Figure 13b indicates that the Jasper groundwater-level altitude in 2004 was approximately − 25 m. The observations at the Lake Houston site already concluded that the pre-consolidation head in the Jasper aquifer must be below − 10 m. It is very likely that the pre-consolidation head in the Jasper aquifer is between − 15 and − 25 m, which is similar to the pre-consolidation heads in the Chicot and Evangeline aquifers in this area. The land elevation at P013 is approximately 50 m above sea level. The Jasper pre-consolidation head in this area would be 65–75 m below the land surface.
In summary, the observations at The Woodlands suggest: (1) the compaction in the Jasper aquifer began in the mid-2000s in The Woodlands area and contributed to approximately one-third of the land subsidence from the mid-2000s to mid-2010s; (2) the pre-consolidation head of the Jasper aquifer is approximately at − 15 to − 25 m; (3) the virgin-compaction/head-decline ratio in the Jasper aquifer is approximately 1:800 in Montgomery County.
Observations in the City of Conroe
The City of Conroe is the county seat, the economic and geographic center of Montgomery County (Fig. 5). Figure 14a depicts four permanent GPS stations, three Chicot wells, one Evangeline well, and six Jasper wells in the Conroe area. Figure 14b shows a site photo at the GPS antenna TXCN, mounted on the roof of the office building of TxDOT at Conroe. Figure 15 illustrates GPS-derived subsidence and groundwater level changes during the past 2 decades. TXCN (2004–2020) recorded steady subsidence from 2007 to 2015 with an average rate of − 14 mm/year. The subsidence rate has been reduced to 6 mm/year since 2016. Observations at other three GPS stations (UH02, P070, P071) also suggest that the ongoing subsidence rate is approximately 6 mm/year in this area (Fig. 15a). There is only one Evangeline well (USGS ID: 301614095284201, terminated 216 m below land surface) in the Conroe area, which indicates a groundwater level decline rate of 2.7 m/year (2004–2013) (Fig. 15b). The Jasper groundwater level declined with a rate of 3.2 m/year during the same period. The 2.7 m/year groundwater-level decline in the Evangeline aquifer would lead to subsidence of approximately 11 mm/year based on the virgin-compress/head-decline ratio of 1:250; the 3.2 m/year groundwater-level drop in the Jasper aquifer will lead to subsidence of approximately 4 mm/year based on the virgin-compress/head-decline ratio of 1:800. The total subsidence rate would be about 15 mm/year. GPS station TXCN did record land surface subsidence of 14 mm/year during this period (2007–2015). The analytical solution (15 mm/year) and the direct measurement (14 mm/year) agree with each other, which further verifies that the estimated virgin-compaction/head-decline ratios are reasonable.
The groundwater level in the Jasper aquifer declined to below − 25 m in the early 2006. GPS-derived subsidence time series at TXCN indicated a rapid drop of the land surface at the end of 2006 (Fig. 15a). The additional compaction of the Jasper aquifer possibly caused the increased subsidence rate. So, − 25 m is a reasonable estimate of the lower bound of the pre-consolidation head in the Jasper aquifer. According to the declining trend of the Evangeline groundwater, the Evangeline groundwater level in the Conroe area was above the pre-consolidation before 2000. In other words, land subsidence in the Conroe area would be minor before 2000 since the groundwater levels in all aquifers (Chicot, Evangeline, Jasper) were above their pre-consolidation heads (− 15 to − 25 m).
In summary, the compaction of the Evangeline aquifer began in the early 2000s in the Conroe area, and the compaction of the Jasper aquifer began in the mid-2000s. The Jasper compaction contributed approximately one-third of the total compaction (subsidence) from 2007 to 2015. The observations in the Conroe area confirmed that the estimates of pre-consolidation heads and virgin-compaction/head-decline ratios in the Evangeline and Jasper aquifers are reasonable.
Observations in the Southeast area
Figure 16 depicts land subsidence and groundwater-level changes in southeastern Montgomery County and adjacent areas. Locations of groundwater-level observation wells and GPS are marked in Fig. 5. GPS station P072 is in the New Caney area. P012 is next to the southeast border of Montgomery County, adjacent to Kingwood, the largest master-planned residential community in northern Harris County and southern Montgomery County. COH6 and P065 are two GPS stations in Harris County, approximately 5 km from Montgomery County. GPS-derived subsidence at these four sites indicates that the ongoing subsidence since the 2010s in southeastern Montgomery County is about 5–8 mm/year (Fig. 16a). The Evangeline groundwater level was stable and close to the pre-consolidation head during past 3 decades (Fig. 16b).
The Jasper well at the eastern border (USGS ID: 301911095092901), near Cleveland, indicates that the Jasper groundwater level has been declining over its entire history since the 1990s and is still above the pre-consolidation head as of 2020 (Fig. 16c). The Jasper well near Splendora (USGS ID: 301443095091801) indicates that the Jasper groundwater has been approaching the pre-consolidation head since the mid-2010s. The Jasper well (USGS ID: 301016095165501) close to P012 shows that the Jasper groundwater level declined to the pre-consolidation head in 2006 and reached the lowest level in 2014. The Jasper groundwater level began to rise in 2015 following the reduction of groundwater pumping. The average decline rate of the Jasper groundwater level was approximately 5.0 m/year (2004–2014), which would produce approximately 6 mm/year compaction according to the virgin-compaction/head-decline ratio of 1:800. The analytical compaction rate of 6 mm/year within the Jasper aquifer is comparable with the total compaction rates (5–8 mm/year) recorded by GPS in this area. That is, the ongoing land subsidence in this area is dominated by the compaction of the Jasper aquifer. This result is consistent with the fact that the Chicot and Evangeline groundwater levels were above their pre-consolidation head during the past 2 decades (Fig. 16b).
In summary, the observations in southeastern Montgomery County indicate that land subsidence in this area is dominated by the compaction of the Jasper aquifer since the late 2000s. The observations further confirm that the estimates of regional pre-consolidation heads and the virgin-compaction/head-decline ratios are reasonable.
Observations in the Southwest area
Figure 17 illustrates GPS-derived subsidence and groundwater-level changes in southwestern Montgomery County. Locations of these GPS stations and groundwater wells are marked in Fig. 5. GPS stations P017 and ROD1 are located in northern Harris County, approximately 5 km to Montgomery County. GPS measurements at P017 indicate that the subsidence rate was up to 2 cm/year during the 2000s and slowed down since the mid-2010s. The ongoing subsidence in this area is about 7–12 mm/year (2015–2020) (Fig. 17a). The Chicot groundwater level was stable and above the pre-consolidation during the past 3 decades. The Evangeline groundwater level declined to below the pre-consolidation head in the late 1990s and retained stable during the 2010s (Fig. 17b). The Jasper groundwater level declined to the pre-consolidation head in the mid-2000s and retained stable during the 2010s (Fig. 17c). The Jasper groundwater level declined with a rate of 5 m/year during the virgin-compaction phase (2005–2010). According to the virgin-compaction/head-decline ratio of 1:800, the 5 m/year head-decline would result in approximately 6 mm/year of compaction. The contribution of the Jasper compaction was also approximately one-third of the land subsidence (6 mm/year vs. 15–20 mm/year) during the virgin compaction phase. Both the Evangeline and Jasper groundwater-level altitudes are approximately 30 m below their pre-consolidation heads as of 2020. Land subsidence will continue until groundwater levels in both the Evangeline and Jasper aquifers recover to their pre-consolidation heads.