The primary purpose of this report is to describe an updated process for depicting water-level altitudes and long-term water-level changes in the greater Houston area of Texas. Results from the updated process are compared to the results from traditional, manual contouring methods used to depict water levels in the greater Houston area. Differences between the updated process and the traditional, manual methods used in the annual USGS reports on water-level altitudes and water-level changes include (1) the treatment of the Chicot and Evangeline aquifers as a single hydrogeologic unit as opposed to separate aquifers and (2) the use of geostatistical kriging interpolation methods (Olea, 1975, 2009; Dunlap and Spinazola, 1984) to develop gridded surfaces of water-level altitudes and water-level changes instead of manually drawn contour lines.

The following overview of the geology and hydrogeology of the study area is modified from Kasmarek and Ramage (2017) and Braun and Ramage (2020). The Gulf Coast aquifer system hydrogeologic units include the Chicot aquifer, the Evangeline aquifer, the Burkeville confining unit, the Jasper aquifer, and the Catahoula confining unit (figs. 2, 4, and 5). Baker (1979) used 11 stratigraphic cross sections to describe the Gulf Coast aquifer system hydrogeologic units defined by Turcan and others (1966) from where the hydrogeologic units that contain the aquifer units crop out to the Gulf of Mexico nearshore. Baker (1979) was also among the first reports contributing to an aquifer-wide hydrostratigraphic framework and subsurface delineation of the previously mentioned hydrogeologic units. Carr and others (1985) provided further refinement of the Baker (1979) cross sections in the Houston area and has been much used to describe the stratigraphy of the Gulf Coast aquifer system since publication.

The three primary aquifers in the Gulf Coast aquifer system (the Chicot, Evangeline, and Jasper aquifers) are composed of laterally discontinuous deposits of gravel, sand, silt, and clay (Baker, 1979). The percentage of clay and other fine-grained, clastic material generally increases downdip (Baker, 1979). The uppermost aquifer, the Chicot aquifer, is contained in Holocene- and Pleistocene-age (Quaternary-age) sediments, and the underlying Evangeline aquifer is contained in Pliocene- and Miocene-age (Tertiary-age) sediments (fig. 5). In the companion report on 2021 water-level altitudes and water-level changes in the greater Houston area (Braun and Ramage, 2022), the Chicot and Evangeline aquifers were treated as a single, undifferentiated hydrogeologic unit. The most deeply buried of the three aquifers, the Jasper aquifer, is contained in Miocene-age sediments (fig. 5) (Baker, 1979, 1986). The stratigraphic relations between the hydrogeologic units in the study area are shown on hydrogeologic cross sections A–A´ (figs. 1 and 3) and B–B´ (figs. 2 and 4) of the Gulf Coast aquifer system, which extends through the greater Houston area from northwestern Grimes County southeastward through Waller, Montgomery, Harris, and Brazoria Counties before terminating at the coast in Galveston County.

Young and Draper (2020) updated the Gulf Coast aquifer system geologic stratigraphy and hydrogeologic unit thicknesses; their report featured a coupled chronostratigraphic and lithostratigraphic approach. The approach used by Young and Draper (2020) built on an existing hydrogeologic framework proposed by Young and others (2014), which in turn was based on the work of Young and others (2012) and differs from the hydrogeologic framework in earlier publications (Baker, 1979; Carr and others, 1985; Strom and others, 2003a, b, c) that exclusively used a lithostratigraphic approach. Using information from Young and others (2012) that included sedimentary marker beds and evidence of coastal onlap observed in geophysical logs, Young and Draper (2020) subdivided the Lagarto Clay into upper, middle, and lower parts and depicted the upper part of the Lagarto Clay as one of the formations that contain the Evangeline aquifer (fig. 5). In previous reports (Turcan and others, 1966; Jorgensen, 1975; Baker, 1979; Carr and others, 1985), the Evangeline aquifer was described as being contained in the Goliad Sand and a small section of the uppermost part of the Lagarto Clay. Additionally, in Young and Draper (2020) the Goliad Sand was subdivided into upper and lower parts following Young and others (2012). In the updated hydrogeologic framework, the upper and lower parts of the Goliad Sand collectively contain part of the Chicot and Evangeline aquifers (undifferentiated) (fig. 5). The base of the Chicot aquifer was defined as the base of the Willis Sand in previous reports; however, additional geophysical logs (approximately 650 versus 290 original logs) were used by Young and others (2012) to characterize the contact between the Chicot and Evangeline aquifers. Thus, the thicknesses of the Chicot and Evangeline aquifers in this study differ substantially in some areas compared to previous studies. The implications of this recharacterization of the thicknesses of the Chicot and Evangeline aquifers are discussed in the “Distribution of Groundwater Wells” section of this report. In Baker (1979) and other reports (fig. 5), the Jasper aquifer was depicted as being contained entirely in the Oakville Sandstone. In addition to the Oakville Sandstone, the lower part of the Lagarto Clay was included in the updated definition of the hydrogeologic units that contain the Jasper aquifer, similarly to Turcan and others (1966).

Over the course of geologic time, geologic and hydrologic processes created accretionary sediment wedges (stacked sequences of sediments) more than 7,600 ft thick at the coast (Chowdhury and Turco, 2006); these sediments, which compose the Gulf Coast aquifer system, were deposited by fluvial-deltaic processes and subsequently were eroded and redeposited by worldwide episodic changes in sea level that occurred as a result of oscillations between glacial and interglacial climate conditions (Lambeck and others, 2002). The Gulf Coast aquifer system consists of hydrogeologic units that dip and thicken from northwest to southeast; the hydrogeologic units representing the aquifers and confining units thus crop out in bands inland from and approximately parallel to the coast and become progressively more deeply buried and confined toward the coast (figs. 3 and 4) (Kasmarek and others, 2013; Casarez, 2020). The aquifers receive recharge where the hydrogeologic units composing the aquifers crop out (Kasmarek and Robinson, 2004). The Burkeville confining unit is stratigraphically positioned between the Chicot and Evangeline aquifers (undifferentiated) and Jasper aquifer (figs. 3–5), thereby restricting groundwater flow between the undifferentiated Chicot and Evangeline aquifers and the underlying Jasper aquifer. There is no confining unit between the Chicot and Evangeline aquifers; therefore, these two aquifers have substantial hydraulic connection, which allows groundwater flow between them (Kasmarek and others, 2010; Liu and others, 2019). Because of this hydraulic connection, water-level changes (changes in the depth to water in feet below land surface) that occur in one aquifer can affect water levels in the adjoining aquifer (Kasmarek and others, 2010). Supporting evidence of the interaction of groundwater flow between the Chicot and Evangeline aquifers includes maps of long-term water-level changes that show areas where rises and declines are approximately spatially coincident and colocated wells with different screened-interval depths where rises or declines in water levels are approximately coincident in time (for example, Braun and others, 2019; Braun and Ramage, 2020). Additional evidence of the hydraulic connection between the Chicot and Evangeline aquifers is provided by Borrok and Broussard (2016, p. 330); their geochemical evaluation of the Chicot aquifer system from 1993 to 2015 in Louisiana indicated that in some years (1998, 2008, and 2011) certain wells screened in the Chicot aquifer “appeared to be tapping water with a geochemistry (temperature, salinity, alkalinity, [and so forth]) matching the underlying Evangeline aquifer.” Further evidence for hydraulic connection is provided in Young and others (2014, sec. 3, p. 2), which summarizes the work of previous authors (Hammond, 1969; Sandeen and Wesselman, 1973; Loskot and others, 1982) who documented vertical hydraulic gradients from the Evangeline aquifer to the Chicot aquifer. Lang and others (1950) have also noted similarities in water-level fluctuations between shallower and deeper wells and the absence of extensive clay zones whereby the Chicot and Evangeline aquifers could be considered as a single unit. Hill (1901) hypothesized that prior to large-scale groundwater withdrawals in the region the aquifers of the coastal plain were under sufficient artesian pressure for the groundwater to rise above land surface, which indicates that there was likely unimpeded vertical flow between the Evangeline and Chicot aquifers. Winslow and Wood (1959, p. 1032) stated that although “the principal water-producing zones in the upper Gulf Coast region are more or less distinct locally, they are all in hydraulic connection and regionally may be considered as a unit.” More evidence for hydraulic connection is given in White and others (1944) where patterns of groundwater levels in wells completed at varying depth intervals were documented to be similar across water-production zones in parts of the greater Houston area. 

Hydraulic properties of the Chicot aquifer do not differ appreciably from those of the hydrogeologically similar Evangeline aquifer but can be identified by subtle differences in hydraulic conductivity (Carr and others, 1985, p. 10). From aquifer-test data, Meyer and Carr (1979) estimated that the transmissivity of the Chicot aquifer ranges from 3,000 to 25,000 feet squared per day (ft²/d) and that the transmissivity of the Evangeline aquifer ranges from 3,000 to 15,000 ft²/d; however, despite these slight differences in transmissivities, there is a logical rationale for combining the aquifers for the purposes of providing status updates of water-level altitudes and long-term water-level changes as explained in the “Treatment of the Chicot and Evangeline Aquifers as a Single Hydrogeologic Unit” section of this report. The outcrops and updip limits of the geologic units that contain the Chicot aquifer are shown in figure 1. Proceeding updip and inland of the Quaternary-age sediments containing the Chicot aquifer, the older geologic units (containing the Evangeline aquifer, the Burkeville confining unit, the Jasper aquifer, and the Catahoula confining system) sequentially crop out (figs. 1 and 2). In the updip areas the Jasper aquifer can be differentiated from the Evangeline aquifer on the basis of the depths to water below land-surface datum, which are shallower (closer to land surface) in the Jasper aquifer compared to those in the Evangeline aquifer (Kasmarek and Ramage, 2017). Additionally, in the downdip areas the Jasper aquifer can be differentiated from the Evangeline aquifer on the basis of stratigraphic position relative to the altitude of the Burkeville confining unit (figs. 3 and 4).

Precipitation falling on the land surface overlying the Gulf Coast aquifer system returns to the atmosphere as evapotranspiration, discharges to streams, or infiltrates as groundwater recharge to the unconfined updip sediments composing the different aquifers (Kasmarek and Robinson, 2004). The infiltrating water moves downgradient toward the coast, reaching the intermediate and deep zones of the aquifers southeastward of the outcrop areas, where the water can then be withdrawn and discharged by wells or is naturally discharged by diffuse upward leakage in topographically low areas near the coast. Water in the coastal, deep zones of the aquifers is denser, and this higher density water causes the fresher, lower density water that has not been captured and withdrawn by wells to be redirected as diffuse upward leakage to shallow zones from the confined downdip areas of the aquifer system.

An extensive monitoring-well network was established by the USGS in 1977, and water-level data were collected and used to create the first published maps of water-level altitudes for the Chicot and Evangeline aquifers in the greater Houston area in 1979 (Gabrysch, 1979). In cooperation with the FBSD, which adopted its groundwater management plan in 1990 (Fort Bend Subsidence District, 2013), an increased number of wells were inventoried by the USGS in Fort Bend, Harris, Brazoria, and Waller Counties in 1989 and 1990. A more comprehensive water-level-altitude report for the Chicot and Evangeline aquifers was published by the USGS in 1991 (Barbie and others, 1991) and was revised in 1997 when updated well data became available (Kasmarek, 1997). After the establishment of the LSGCD in 2001, the USGS began publishing water-level-altitude maps for the Jasper aquifer in the greater Houston area (primarily Montgomery County) (Coplin, 2001). In 2004, 2006, and 2007, as additional wells with reliable water-level data were inventoried, revised water-level-altitude maps for the Jasper aquifer were prepared (Kasmarek and Lanning-Rush, 2004; Kasmarek and others, 2006; Kasmarek and Houston, 2007). Since 2007, comprehensive maps for the Jasper aquifer have been included in the annual series of water-level reports for the greater Houston area (Kasmarek and Houston, 2008; Kasmarek and others, 2009, 2010, 2012, 2013, 2014, 2015, 2016; Johnson and others, 2011; Kasmarek and Ramage, 2017; Shah and others, 2018; Braun and others, 2019; Braun and Ramage, 2020).

Several colocated wells exist in the study area, several of which are in Harris County at extensometer sites (figs. 1, 2, and 6–9; table 1). To illustrate the hydrogeologic connection between the Chicot and Evangeline aquifers, water levels at wells screened at differing vertical depth intervals at four sites were analyzed (figs. 6–9). These sites are distributed across Harris County and are considered representative of patterns in water levels across the study area. Patterns in water levels common to the sites in figures 6–9 include (1) minimal changes in water levels over time in wells that are shallower than about 125 ft below land surface (bls) and in which the groundwater is under atmospheric pressure and (2) increasing water levels with substantial degree of similarity over time in wells that are deeper than about 225 ft bls and in which the groundwater is under artesian pressure. A transition zone between atmospheric and artesian pressure exists between about 125 and 250 ft bls, whereby wells screened above this zone are considered not to be a part of the Chicot and Evangeline aquifers (undifferentiated).

At the Pasadena extensometer site (hereinafter referred to as the “Pasadena site”) (fig. 6; table 1), the water levels (represented as depths to water in feet below land surface) in wells C and D were generally stable with less than 12 ft of change and showed little association with water levels in the wells screened at greater depths (wells F through J). Water levels at wells C and D were similarly affected by changes in precipitation; for example, water levels in wells C and D rose during periods of above-mean precipitation and declined during periods of below-mean precipitation (fig. 6C, D). Prior to about 1985, the pattern in water levels over time in well E was similar to the pattern observed in wells C and D. However, after about 1990, the water-level pattern in well E was most similar to the pattern observed in the wells screened at greater depths (wells F through J at the Pasadena site), although the water-level change in well E was less than 55 ft compared to greater water-level changes in the wells screened at greater depths, where water levels ranged from about 70 to 289 ft. The pattern observed in water levels for wells F through J at the Pasadena site was somewhat similar over time; however, the magnitude of the water-level changes in wells F through I was appreciably greater compared to the magnitude of the water-level changes in well J. A likely explanation for the differences in the magnitude of water-level changes in wells F through I compared to well J at the Pasadena site is that well J is screened in the Burkeville confining unit and thus surrounded by a substantial clay layer that decreases the hydraulic connection between well J and the overlying aquifer units. In most cases, drillers’ logs obtained during the installation of wells do not distinguish between clay and silt because the particles are too fine grained to discern in the field and instead record all fine-grained sediment as clay. Fine-grained intervals are therefore referred to as clay intervals in figures 6–9. After about 1990, the pattern of water-level changes in well E was different from the pattern for wells C and D at the Pasadena site, indicating that a transition zone from a shallow zone where groundwater is under atmospheric pressure to a deeper zone where groundwater is under artesian pressure occurs at a depth interval of about 125–200 ft bls.

The similarity of water levels at different depth intervals for wells at the Pasadena site (fig. 6) was observed as far back as 1937. As explained in the “Introduction” section of this report, prior to 1975, the withdrawal of groundwater from the Chicot and Evangeline aquifers was unregulated, and water levels in the aquifers were steadily declining year over year. In 1937, water-level declines in the area where the extensometer at the Pasadena site is installed differed by the depth of the screened intervals, with smaller declines in the more deeply screened wells and larger declines in the more shallowly screened wells (White and others, 1944). However, the pattern of water-level declines in all of the wells was nearly the same even though thick clay beds separated many of the water-production zones (White and others, 1944). Thus, a hydraulic connection among many of the water-production zones at various depth intervals exists (White and others, 1944), which is evident on the basis of water levels measured at the different depth intervals for the wells at the Pasadena site with the exception of the water levels measured in the two shallowest wells (wells C and D) (fig. 6).

Water-level patterns observed in wells at the Pasadena site (fig. 6) were similar to water-level patterns observed in wells at the other three extensometer sites (Baytown, Southwest, and Northeast; figs. 7–9). Unlike the wells at the other extensometer sites, the wells at the Baytown extensometer site (hereinafter referred to as the “Baytown site”) are not screened at regularly spaced intervals representing the full extent of the aquifers in which they are screened (fig. 7). Instead, six wells are screened between 30 and 500 ft bls, and two wells are screened between 1,355 and 1,465 ft bls (fig. 7; table 1). Despite the large differences in screened-interval depths at the Baytown site, the water-level patterns observed at all but the two shallowest wells at the site (wells C and D) were similar. Water levels in the shallowest wells at the Baytown site (wells C and D) increased or decreased in response to changes in precipitation, whereas water levels in well E were similar to those in wells F through J (fig. 7). Therefore, a transition zone likely exists at a depth of about 125–150 ft bls, where the groundwater changes from a shallower zone under atmospheric pressure to a deeper zone under artesian pressure.

At the Southwest extensometer site (hereinafter referred to as the “Southwest site”), water levels were similar throughout nearly 2,350 vertical feet of aquifer sediment (fig. 8; table 1). The shallowest well at the Southwest site (well C; fig. 8) is screened in the deeper zone under artesian pressure, and water levels in this well generally were not responsive to changes in precipitation. The water levels at the Southwest site measured in wells screened in the Chicot and Evangeline aquifers exhibited a high degree of similarity, differing only slightly in the magnitude of the water-level change over time. The shallowest well at the Southwest site is screened between 238 and 248 ft bls (table 1), whereas the Pasadena and Baytown sites each include two shallow wells screened at or above 110 ft bls. The absence of shallow wells at the Southwest site similar to the screened intervals of the two shallowest wells at the Pasadena and Baytown sites (table 1) complicates the estimation of a transition zone. However, on the basis of the available data, it is estimated that the transition zone occurs at a depth of about 125–175 ft bls.

At the Northeast extensometer site (hereinafter referred to as the “Northeast site”), water-level patterns were similar across all colocated wells (fig. 9; table 1), consistent with the patterns in water levels measured at the other three extensometer sites. The shallowest well at the Northeast site (well C) is screened between 283 and 293 ft bls, and water levels in this well are not generally responsive to changes in precipitation (fig. 9C; table 1). The maximum water-level change in the shallowest wells at the Northeast and Southwest sites (each well C) is about 35 ft (figs. 8 and 9) during the 1980–2015 period of record at these sites. Similar to the Southwest site, the absence of shallow wells at the Northeast site complicates the estimation of a transition zone. However, on the basis of the available data, it is estimated that the transition zone at the Northeast site occurs at a depth of about 175–225 ft bls.

Colocated well data at the four extensometer sites indicate that a transition zone from a shallower zone under atmospheric pressure to a deeper zone under artesian pressure exists between about 125 and 225 ft bls. Above the depth interval 125–225 ft bls, water levels have remained relatively stable over time and have not been affected by pressure-head changes within the aquifer that are found when the groundwater is under artesian pressure; any small differences in water levels measured in wells screened above the depth interval 125–225 ft bls are primarily driven by changes in precipitation. The water levels measured in shallow wells (screened at a depth interval from 24 to 110 ft bls) remain largely static over time and are primarily driven by changes in precipitation (figs. 6C, D and 7C, D; table 1). Groundwater from land surface down to a depth of about 125–225 ft bls functions as a “perched” system. This perched system is not indicative of water levels within the Chicot and Evangeline aquifers (White and others, 1939, 1944; Lang and others, 1950; Kasmarek and Strom, 2002). Therefore, wells screened above the transition zone that extends to about 250 ft bls were not classified as wells screened in the Chicot and Evangeline aquifers (undifferentiated). Accordingly, the 2021 annual report on water-level altitudes and water-level changes in the study area (Braun and Ramage, 2022) did not classify wells screened above the transition zone as wells screened in the Chicot and Evangeline aquifers (undifferentiated), and wells screened above the transition zone are not planned to be classified as wells screened in the Chicot and Evangeline aquifers (undifferentiated) henceforth for assessing water-level altitudes and water-level changes in the study area.

At all of the extensometer sites, water levels among all wells screened in the Chicot and Evangeline aquifers below about 125–225 ft bls under artesian pressure were similar on an overall basis during a 40- to 50-year period (figs. 6–9). The extensometer sites were installed between 1973 and 1980, so the period of record varies for each extensometer site depending on the year of installation. The similar water-level patterns among the sites demonstrate a hydraulic connection across a range of depth intervals that has persisted from at least 1980 to 2020 in the Chicot and Evangeline aquifers. This hydraulic connection was also noted in Kasmarek and Ramage (2017); the patterns observed in water-level measurements from Kasmarek and Ramage (2017) support the hypothesis that the Chicot and Evangeline aquifers function as one integrated hydrogeologic unit rather than as distinct aquifers.

Young and Draper (2020) used data from approximately 650 geophysical logs to redefine the contact between the Chicot and Evangeline aquifers and to redefine the top and bottom of the Burkeville confining unit. Teeple and others (2021) compiled data from the same geophysical logs used by Young and Draper (2020) to define the tops and bottoms of the hydrogeologic units of the Gulf Coast aquifer system as gridded surfaces, which were then intersected with the screened intervals associated with wells in the long-term monitoring-well network. As a result of the work by Young and Draper (2020) and Teeple and others (2021), a large number of wells in the study area were reclassified as being screened in a different aquifer (figs. 10–12). Figures 10, 11, and 12 depict the wells in the long-term monitoring-well network at which water-level measurements were made in 2021 that are currently (as defined by hydrogeologic unit extent conceptualization compiled from Teeple and others [2021] and Young and Draper [2020]) or were previously (as defined by hydrogeologic unit extent conceptualization compiled from Strom and others [2003a, b, c] and Kasmarek and Robinson [2004]) screened in the Chicot, Evangeline, or Jasper aquifers, respectively.

As a result of the change in thickness of the hydrogeologic units, a large proportion of wells in the long-term monitoring-well network required reclassification. Specifically, about 125 wells that were classified as Evangeline aquifer wells were reclassified as Chicot aquifer wells, resulting in substantial portions of the Evangeline aquifer (from an areal extent) that no longer had available wells with which to describe water-level changes over time (figs. 10 and 11). Thus, after establishing that the two aquifers have similar hydraulic properties and effectively function as one hydrogeologic unit, combining the Chicot and Evangeline aquifers into a single, undifferentiated hydrogeologic unit was a way to ensure a spatially distributed network of wells with a sufficient distribution of long-term water-level measurements for mapping purposes. Although the water-level-change maps from the previously published reports cannot be directly compared to the maps of the newly combined Chicot and Evangeline aquifers (undifferentiated), comparison at individual wells can reasonably be made, particularly for identification of areas where groundwater demands are greatest and where water-level changes over time are most pronounced.

Semivariograms, which mathematically describe the spatial relation of measured point pairs (Dunlap and Spinazola, 1984) commonly referred to as the “semivariance” (the sum of squared differences of measured point pairs separated by lag distance), were determined using the detrended datasets (residual water-level altitudes after removing the spatial trend) for each of the three aquifers. Dunlap and Spinazola (1984, p. 5) explained, “the most important item in the application of kriging is the semivariogram. The semivariogram is a graph of the variability of the difference of the regionalized data versus the distance between data points * * * the semivariogram is a plot of the squared differences in water-table altitudes at pairs of observation wells that are separated by a certain distance.” The data used in the semivariance analysis are coordinate point data projected in Universal Transverse Mercator zone 15 (measured in meters), a standard map projection used as a “representation of all or part of the surface of a round body, especially the Earth, on a plane” (Snyder, 1987, p. 3). All distance calculations are therefore originally computed in meters. However, the dependent variable of water-level altitude is measured in feet, which means that the native model parameters are all computed in units of feet except for range, which is measured in meters. Range and lag distance is therefore converted from meters to feet to provide a consistent set of units.

The R programming language (ver. 3.6.2) (R Core Team, 2019) was used for all kriging processes. Semivariograms and their associated parameters were developed by using the R package automap version 1.0–14 (Hiemstra, 2013). The autofitVariogram function within the automap package uses the detrended water-level altitudes to estimate the kriging parameters and select the best theoretical model fit (common model types include exponential, Gaussian, spherical, and Matérn [Matérn, 1960; Olea, 2009]) to a given dataset. The kriging parameters are referred to as the “nugget,” “sill” or “partial sill,” “range,” and “kappa value” (Olea, 2009; Sarma, 2009). The nugget describes the small-scale variability of the data over short distances that are less than the smallest distance between measurements and measurement error (Philip and Kitanidis, 1989, p. 857). The sill describes the maximum variability between point pairs (the partial sill is the sill minus the nugget), and the range describes the distance at which point pairs are no longer spatially correlated. The kappa value is a smoothing parameter applied to Matérn class variogram models (Diggle and Ribeiro, 2007; Hiemstra, 2013). A caveat to this process is that autofitVariogram function does not consider anisotropy in the data, which means that any directional trend in the data is not accounted for in the kriging parameters and interpolation. Because in universal kriging it is assumed that the mean of the measured attribute is neither constant nor known (Olea, 2009) and that detrended data using the second-order polynomial equation (eq. 2) are being modeled, it is not necessary to consider the directional trend.

The empirical and theoretical semivariogram for measured water-level altitudes in the Chicot aquifer (Ramage and Braun, 2020) is shown in figure 13. The nugget of 89 square feet (ft²) indicates some small-scale variability in land-surface elevations, measurement error, and other unmeasured variables such as duration and rate of pumping prior to measurement. The empirical semivariogram points were fit with a theoretical Stein model (Stein, 1999), which is a modification of the Matérn model, with a sill of 3,569 ft², range of 267,970 ft, and kappa value of 0.8. The range was fixed as half the maximum distance between point pairs. The theoretical semivariogram has a good closeness of fit with the empirical semivariogram up to a lag distance of about 210,000 ft (about 40 miles [mi]); kriging requires a high degree of autocorrelation in the data in order to work effectively (Olea, 1975), and beyond a lag distance of about 40 mi the degree of autocorrelation in the data begins to decrease markedly.

The empirical and theoretical semivariogram for measured water-level altitudes in the Evangeline aquifer (Ramage and Braun, 2020) is shown in figure 14. The empirical semivariogram points were fit with a theoretical Stein model with a nugget of 71 ft², which indicates that there is good continuity of water-level altitudes within short distances. The computed sill is 11,203 ft²; the range is 235,932 ft (about 45 mi), fixed as half the maximum distance between point pairs; and the kappa value is 0.3.

The empirical and theoretical semivariogram for measured water-level altitudes in the Jasper aquifer (Ramage and Braun, 2020) is shown in figure 15. The relatively large nugget of 117 ft² indicates that there are some small-scale variabilities that are likely caused by measurement or land-surface-elevation errors, or other errors associated with unmeasured variables such as duration and rate of pumping prior to measurement. The empirical semivariogram points were fit with a theoretical Stein model with a sill of 5,991 ft²; a fixed range of 175,539 ft (about 33 mi), or half the maximum distance between point pairs; and a kappa value of 1.6. Measured data for two wells, one in Fort Bend County (site number 294327095445301) and one in Harris County near the southern end of Lake Houston (site number 295449095084101), were excluded from the calculation of maximum distance between point pairs for the semivariogram range owing to their large distance from the rest of the Jasper aquifer monitoring-well network.

After kriging parameters were determined by the autofitVariogram function, selected colocated measurements were removed for instances in which more than one well exists at the same location. This process is necessary because the kriging function requires a single target value at any given measured location in order to calculate semivariance and match the supplied target value (Olea, 2009, p. 114). Multiple wells at the same location and screened in the same aquifer most often are nested piezometers (colocated wells) (figs. 6–9, for example). A processing script written in the R language was used to automatically determine which wells were grouped together within a grid cell and to retain the deepest water level from that group. The reason for retaining the deepest water level within the group is that the deepest water levels at colocated well sites are generally more closely correlated with water levels measured in nearby wells, as shown in the water-level data for the screened wells below the transition zone and above the Burkeville confining unit in the colocated wells in figures 6–9. In most cases, the deepest well in a nested piezometer site will have the deepest water level and is screened at a depth interval that is most similar to nearby production wells, which are often deeper than private wells or monitoring wells and make up the largest proportion of the monitoring-well network. An additional reason for selecting the deepest water level is that it most closely aligns with the underlying assumption of kriging, that data that are spatially close are more similar than data that are spatially farther apart.

As an example of a location where there are multiple wells and a single measurement was selected for use in the kriging process, table 3 lists five wells at a nested piezometer site (indicated by the footnote assigned to selected index wells in the index well column) in Galveston County and three wells within a 9,843-ft (3,000-m) radius of the nested piezometer site. For the purposes of declustering the wells at the nested piezometer site for use in kriging interpolation, the well with an index well number of 46 was the well retained. Index well 46 has the deepest depth to water within the nest and is the deepest (depth of well) of the five nested wells, and when comparing its depth to water to those of the three wells (index wells 36, 40, and 47) most proximal to the five nested wells, their water levels are most similar to index well 46, as are their well depths. In most cases (with the exception of wells completed in the Jasper aquifer in parts of Montgomery County), the well with the deepest well depth has the deepest depth to water among all wells within a given nest or cluster group.

For the Chicot aquifer, 164 of the 173 wells used to measure water levels in the aquifer were retained for kriging purposes. For the Evangeline aquifer, 321 of 326 wells were retained. For the Jasper aquifer, all (112) wells were retained, as there were no nested piezometer wells used in the creation of the original 2020 water-level-altitude map.

After the selected colocated measurements were removed, the kriging interpolation process was performed using the detrended water-level-altitude data in conjunction with the previously determined semivariogram parameters over the established gridded surface. Universal kriging was selected because during the interpolation process it can incorporate the inherent directional trend in the data, which varies by coordinate location (Olea, 2009). Figures 16–18, which show gridded representations of water-level altitudes for 2020 in the Chicot, Evangeline, and Jasper aquifers, respectively, were color shaded in 50-ft increments to match the interval associated with the overlain contours (Braun and Ramage, 2020) for comparison purposes. Kriging interpolation was performed by using R version 3.6.2 (R Core Team, 2019), the R package gstat version 2.0–6 (Pebesma, 2020), the R packages sf version 0.9–8 (Pebesma, 2005) and sp version 1.4–2 (Pebesma, 2005) for spatial point data, the R package raster version 3.3–7 (Hijmans, 2020) for raster data, and the R package automap (Hiemstra, 2013) as discussed in the “Development of the Semivariogram” section of this report.

For the Chicot aquifer in 2020, the universal kriging geostatistical interpolation methods used to develop the estimated gridded surface of water-level altitudes resulted in estimated water-level altitudes that ranged from –169 to greater than (>) 200 ft above the North American Vertical Datum of 1988 (NAVD 88) (fig. 16), and standard error ranged from 10.3 to 97.6 ft with a mean of 21.4 ft. The estimated gridded surface representing 2020 Evangeline aquifer water-level altitudes ranged in estimated water-level altitudes from –285 to >200 ft above NAVD 88 (fig. 17), and standard error ranged from 13.1 to 141.0 ft with a mean of 61.1 ft. The estimated gridded surface representing 2020 Jasper aquifer water-level altitudes ranged in estimated water-level altitudes from –206 to >250 ft above NAVD 88 (fig. 18), and standard error ranged from 11.3 to 84.8 ft with a mean of 23.4 ft.

In a comparison of the outputs from manual contouring and from kriging interpolation for the 2020 Chicot aquifer water-level-altitude map (fig. 16), generally the estimated gridded surface derived from kriging interpolation agrees well with the most recently published manual contours of the Chicot aquifer water-level altitudes (fig. 4 in Braun and Ramage [2020]). Several areas deviate slightly, particularly in the northwestern portion of the mapped area, where the gridded surface extends into areas where available well data are sparse. The gridded area near Beltway 8 and Highway 249 in northwestern Harris County extends slightly beyond the contours to the north and northwest, as well as in an area near the border of Harris and Montgomery Counties, seemingly in response to a single well encircled by the –50-ft contour in south-central Montgomery County. Another slight discrepancy can be seen in the area of northern Fort Bend and Brazoria Counties near the –50-ft contour where the kriging estimates are in the range of –50 to –100.

Much like that of the Chicot aquifer water-level altitudes, the estimated gridded surface of the 2020 Evangeline aquifer water-level altitudes (fig. 17) generally agree favorably with the most recently published manual contours of the Evangeline aquifer water-level altitudes (fig. 6 in Braun and Ramage [2020]). The 50-ft increments of the gridded surface closely follow the contour lines in most cases, only deviating where the lack of control points allows the estimates to extend beyond the contours. Several areas of the gridded surface show this behavior, such as in central Harris County where the –200- to –250-ft shaded region extends beyond the –200-ft contour towards the east and in areas of south-central Montgomery County where steep gradients of water-level altitude are indicated. Also, like those of the Chicot aquifer (fig. 16), as gridded estimates of the Evangeline aquifer water-level altitudes move toward the boundaries of the grid and away from control points, in areas with the largest standard errors, estimates begin to deviate from contours. Kriging uses a weighted average of all measured values to estimate values at unmeasured locations; the weights assigned to measured values are spatially dependent. Hence, transitions in gridded surfaces tend to be more gradual than are often represented with contours. For example, on figure 17, a 50-ft contour bends sharply to “wrap around” a well point, whereas the gridded surface assigns the immediate area at and around the well point with a value approximating the actual measured water-level altitude at that location.

The estimated gridded surface of the 2020 Jasper aquifer water-level altitudes (fig. 18) is also in good agreement with the most recently published manual contours of the Jasper aquifer water-level altitudes (fig. 8 in Braun and Ramage [2020]). Areas where the contours and the gridded surface do not agree are often associated with areas where there is lack of data control, in particular the southern part of the mapped area across much of Harris and Waller Counties where control points are sparse. Another area where the contours and the gridded surface deviate is in the northwestern part of the mapped area, where shaded areas and measured water-level altitudes differ. This area is marked by a less dense well network than is present across the central part of the mapped area and shows that there is variability in the data. The area on the border of Harris and Montgomery Counties also shows some disagreement between the contours and the gridded surface. Within this area there are several wells with measured water-level altitudes that range from –188 to –196 ft (Ramage and Braun, 2020); however, estimates from the gridded surface indicate water-level altitudes up to and less than −200 ft below NAVD 88 and therefore disagree slightly with both measured values at these wells and contours in this area. The outer areas of the mapped area are not as well defined because of a lack of data control, unlike the mapped area associated with the denser network of wells in the central and southern parts of Montgomery County, where there is good data control. Lack of data control can also affect how manual contours are drawn and interpreted, often resulting in approximately equidistant spacing when other control points do not exist to define how the contours should be drawn. In contrast to the shortcomings of developing manual contours when control points are sparse, kriging interpolation includes spatial parameters supplied by the semivariogram to determine how grid cell estimates of water-level altitudes are computed.

Kriging interpolation provides both an estimated value at each grid cell location and an estimation error (variance) that can be used to quantify the uncertainty or quality of the associated estimate (Yamamoto, 2000). Uncertainty is often highest in areas that lack good data control (that is, areas where well points are separated by relatively large distances, as defined by the shape of the theoretical kriging model fit and range of autocorrelation) (Matérn, 1960; Matheron, 1963; Olea, 1975, 2009). In the 2021 annual report on water-level altitudes and water-level changes in the study area (Braun and Ramage, 2022), certain grid cells with high uncertainties were masked out. As explained in the “Introduction” section of this report, grid cells with either extrapolated or interpolated location-specific values representing areas of reduced well density within the well network distribution are masked out herein. For grid cells with high uncertainties, standard errors were calculated from the square root of the variance associated with each grid cell. All grid cells with standard errors exceeding the overall mean standard error were hidden (assigned a value of “NA,” or not applicable). Mean standard error for the 2020 Chicot aquifer water-level altitudes was 21.4 ft. Of the 5,775,728 grid cells in the estimated gridded surface of the Chicot aquifer water-level altitudes, about 27.8 percent (1,608,052) of the grid cells exceeded the mean standard error. Mean standard error for the 2020 Evangeline aquifer water-level altitudes was 61.1 ft. The estimated gridded surface of the Evangeline aquifer water-level altitudes is composed of 5,161,584 cells, and about 43.0 percent (2,219,120) exceeded the mean standard error. The higher mean standard error for the 2020 Evangeline aquifer water-level altitudes is likely the result of a denser network of wells within the center of the Evangeline aquifer grid combined with relatively large distances to wells near the boundaries of the grid that leave large areas with lack of data control. Mean standard error for the 2020 Jasper aquifer water-level altitudes was 23.4 ft. The estimated gridded surface of the Jasper aquifer water-level altitudes is composed of 2,517,048 cells, about 38.3 percent (963,738) of which exceeded the mean standard error. For all three aquifer gridded surfaces, areas of high uncertainty often exist where there is lack of data control or near the boundaries of the interpolated grid where wells are spaced farther apart.