Geology and Hydrostratigraphy

The following Cretaceous-age geologic units (listed from oldest to youngest) are exposed at the land surface in the study area (fig. 2): the lower and upper members of the Glen Rose Limestone of the Trinity Group (Rose, 1972; Clark and others, 2020); the Kainer/Fort Terrett and Person/Segovia Formations of the Edwards Group (Rose, 1972; Clark and others, 2020); the Georgetown Formation, Del Rio Clay, and Buda Limestone Formation of the Washita Group; and the Eagle Ford, Austin, and Taylor Groups. The rocks that compose the Washita Group, Eagle Ford Group, Austin Group, and Taylor Group (Clark and others, 2020) form the upper confining unit to the Edwards aquifer and will not be discussed further in this report. The Edwards aquifer is contained in the rocks that compose the Edwards Group (or in the stratigraphically equivalent Devils River Limestone), and the Trinity aquifer is contained in the rocks that compose the Trinity Group; the upper zone of the Trinity aquifer is contained in the upper member of the Glen Rose Limestone (fig. 2). The Edwards and Trinity aquifers have been identified as major aquifers by the Texas Water Development Board (TWDB) (George and others, 2011). The carbonate rocks (limestone and dolomite) that contain both aquifers are part of a karst system characterized by sinkholes, vugs, fractures, and conduits (Clark and others, 2020, 2023). Base flow in Medina River is supported by groundwater inflows from the hydraulically connected Edwards and Trinity aquifers. Groundwater recharge occurs through the surficial rocks that contain the Edwards and Trinity aquifers. The rocks that contain these aquifers are characterized by solution enhanced porosity and permeability that has developed along faults and fractures. Porosity is the percentage of interstices (void space) in a rock unit and is determined by dividing the volume of interstices by the total rock volume. The degree to which the pore spaces are connected determines the permeability of the rock unit (Lohman, 1972). The Edwards and Trinity aquifers are characterized by porosity and permeability that vary spatially in the rock units underlying the Medina and Diversion Lake system, providing a pathway for seepage losses of surface water stored in the lakes to enter the groundwater system (Clark and others, 2020, 2023). Previous studies established that recharge occurs as seepage losses from the lake system into the subsurface and can be related to the altitude of the water surface of Medina Lake in feet above NGVD 29 (hereinafter referred to as “Medina Lake stage”) (Lambert and others, 2000; Slattery and Miller, 2017). Within the Medina and Diversion Lake system, seepage losses enter the Edwards aquifer and the upper zone of the Trinity aquifer as recharge. The Edwards aquifer is absent upgradient from Medina Lake. Recharge in the Medina Lake drainage area upgradient from the Medina and Diversion Lake system consists of a large degree of precipitation that enters the upper and middle zones of the Trinity aquifer. Further information on the geology and hydrostratigraphy of the area is provided in Clark and others (2020, 2023).

Previous Studies

The mean annual recharge to the entire Edwards aquifer in south-central Texas has been estimated as approximately 689,000 acre-feet per year (acre-ft/yr) (1934–2022) (Slattery and Choi, 2023). Seepage losses from Medina and Diversion Lakes have been estimated to contribute a mean annual recharge amount of 61,300 acre-ft (1934–2022), or about 9 percent of the total mean annual recharge to the Edwards aquifer (Slattery and Choi, 2023). Recent studies indicated that the upper 120 ft of the upper zone of the Trinity aquifer is hydraulically connected to the Edwards aquifer in some locations (Clark, 2003; Johnson and others, 2010; Gary and others, 2011; Hunt and others, 2016; Saribudak, 2016). It is unknown how much of the 9 percent of the total estimated recharge to the Edwards aquifer ultimately recharges the upper zone of the Trinity aquifer (Lambert and others, 2000; Clark and Journey, 2006).

The amount of seepage losses entering the Edwards aquifer and the upper zone of the Trinity aquifer as recharge varies depending on the Medina Lake stage and the characteristics of the rocks underlying the lakes (fig. 2) (Puente, 1978; Lambert and others, 2000). Seepage losses from Medina and Diversion Lakes enter the aquifers through the porous and permeable outcrops of rocks containing the Edwards aquifer and the upper zone of the Trinity aquifer. Lohman (1972, p. 4) wrote, “Transmissivity is the rate at which water of the prevailing kinematic viscosity is transmitted through a unit width of the aquifer under a unit hydraulic gradient,” and explained that transmissivity indicates how readily groundwater can flow through a rock unit. Transmissivity is measured in cubic feet per day per square foot times the aquifer thickness in feet ([ft³/d/ft²])×ft), which can be simplified to feet squared per day (ft²/d) (Lohman, 1972). Because the porosity and permeability of the rocks that contain the Edwards and Trinity aquifers (and the resulting transmissivity) have been enhanced by secondary porosity along faulting and fracturing associated with the Balcones fault zone (figs. 1 and 2), the transmissivity in the Edwards aquifer and the upper zone of the Trinity aquifer can be quite large. Lohman (1972, p. 4) explains “Solution of carbonate rocks such as limestone or dolomite by water containing dissolved carbon dioxide takes place mainly along joints and bedding planes and may greatly increase the secondary porosity. Similarly, solution of gypsum or anhydrite by water alone may greatly increase the secondary porosity.” Within the Edwards aquifer, transmissivity in areas of faulting ranges from 10,000 to as much as about 5,000,000 ft²/d, whereas within the Trinity aquifer, transmissivity ranges from 100 to 58,000 ft²/d (Lambert and others, 2000).

Whereas groundwater recharge in the form of seepage losses from the Medina and Diversion Lake system can occur in all hydrostratigraphic units underlying the lakes, certain units are more permeable based on their lithology and the resulting effective porosities (Clark and others, 2020). The rock units that contain the Edwards aquifer and the upper zone of the Trinity aquifer are in contact with Medina Lake in the southern part of Medina Lake. Because faulting has displaced the rock units that contain the Edwards aquifer and the upper zone of the Trinity aquifer, contacts between the lake and the rock units have been identified at altitudes of 1,045, 970, 960, and 945 ft above NGVD 29 (Clark and others, 2020). In Diversion Lake, most of the recharge in the form of seepage losses enters the upper zone of the Trinity aquifer, and the only location where seepage losses directly recharge the Edwards aquifer in Diversion Lake occurs in an area near Medina Diversion Lake Dam where faulting has placed the contact of the Edwards aquifer and the upper zone of the Trinity aquifer below the base of the lake (Small and Lambert, 1998; Lambert and others, 2000; Clark and others, 2020, 2024).

The amount of groundwater recharge entering the Edwards aquifer and the upper zone of the Trinity aquifer as seepage losses from Medina Lake can be related to the Medina Lake stage, as documented in previous studies (Lambert and others, 2000; Slattery and Miller, 2017). The relation between seepage losses from Medina Lake and the Medina Lake stage varies depending on the lake stage and depending on which hydrostratigraphic units are in contact with water impounded by Medina Lake Dam (Small and Lambert, 1998). The variation in the amount of recharge is a result of variations in the porosity and permeability of the hydrostratigraphic units underlying the lake (Small and Lambert, 1998). The amount of recharge entering the Edwards and Trinity aquifers in the form of seepage losses may increase as the Medina Lake stage increases, which increases the hydraulic head and thus creates a high-pressure gradient (Winter and others, 1998). Also, recharge in the form of seepage losses from Medina Lake is likely halted when the surficial hydrostratigraphic units that contain the Edwards and Trinity aquifers become saturated by large amounts of precipitation recharge. Once the hydrostratigraphic units that contain the aquifers are saturated, any additional water that infiltrates to the water table discharges from the aquifer because the aquifer is full and cannot accept it, resulting in rejected recharge (Lohman, 1972).

Incorporating engineering work done by others, Puente (1978) published two graphs depicting the correlation between reservoir stage and seepage into the aquifer, which he referred to as “correlation curves.” These curves relate the storage (and therefore, stage) in Medina Lake to monthly seepage losses from the Medina and Diversion Lake system. The first correlation curve represents seepage losses with a rising stage, and the second correlation curve represents seepage losses with a falling stage. Puente (1978, p. 23) noted, “the [correlation] curves are substantially different and apparently reflect the influence of bank storage.” Puente (1978) noted that the correlation curves were originally intended only as a tool for evaluating the design of a proposed reservoir in the lower part of the Medina River drainage area. Puente (1978) adapted the correlation curves to estimate annual recharge to the Edwards aquifer in that drainage area, assuming all seepage losses from Medina Lake entered the Edwards aquifer as recharge (hereinafter referred to as the “Puente method”). The Puente method is described in detail in the “Puente Method of Estimating Annual Groundwater Recharge From Medina Lake” section of this report. Small and Lambert (1998) and Clark and others (2020) describe how seepage from Medina Lake enters both the Edwards and Trinity aquifers as recharge, owing to their hydrological connection through faults and other karst features in some locations in and near Medina Lake (Clark, 2003; Johnson and others, 2010; Hunt and others, 2016; Saribudak, 2016).

During October 1995–September 1996, the USGS conducted a study (Lambert and others, 2000) with the objectives of better defining short-term rates of recharge from seepage losses and reducing the error and uncertainty associated with estimates of monthly seepage losses from the Medina and Diversion Lake system. As part of that study, the USGS developed water budgets for Medina Lake, Diversion Lake, and the Medina and Diversion Lake system to derive the amount of groundwater recharge attributable to seepage from the two individual lakes and from the Medina and Diversion Lake system. During that period of study, the Medina Lake stage ranged from 1,018 to 1,046 ft above NGVD 29. Consequently, the recharge estimates derived by the 1995–96 study (Lambert and others, 2000, p. 12) are considered “* * * valid only for a range in Medina Lake stage between about 1,018 and 1,046 ft above [NGVD 29].”

During a subsequent 2001–02 study, the USGS collected additional data to refine and, if possible, extend the previously derived (1995–96) relations between the Medina Lake stage and recharge to the Edwards aquifer and the upper zone of the Trinity aquifer to include the effects of reservoir stages less than 1,018 ft and greater than 1,046 ft above NGVD 29. The results of the 2001–02 study were originally published in 2004 featuring three different linear regression equations to estimate groundwater recharge from Medina Lake, Diversion Lake, and the Medina and Diversion Lake system. These equations were derived from the computation of water budgets, representing steady-state conditions over a range of stages for Medina and Diversion Lakes individually, and for the Medina and Diversion Lake system. The study found that seepage losses from Medina Lake increase with increases in the Medina Lake stage. Specifically, as the Medina Lake stage increased from 1,020 to 1,064 ft above NGVD 29, an increasing portion of the seepage losses from Medina Lake (as much as 40 percent) returned to Diversion Lake; and when the Medina Lake stage was greater than about 1,040 ft above NGVD 29, Diversion Lake gained more water than it lost to the groundwater system. This movement of water into and out of the groundwater system was also observed in the downstream reach between USGS streamgaging station 08180010 Diversion Lake near Riomedina, Tex. (site 9), and the downstream site USGS streamgaging station 08180500 Medina River near Riomedina, Tex. (site 10) (fig. 1; table 1). During periods when there was no flow past site 9, the Medina River gained between 32 and 94 acre-feet per day (acre-ft/d), the gains increasing with increases in the Diversion Lake stage (Slattery and Miller, 2017).

Using the linear regression equation developed during the 2001–02 study for the Medina and Diversion Lake system, seepage losses during October1995–September 2002 were computed and found to be about 44 percent less than the seepage losses estimated by using the Puente method. The study also indicated that seepage losses from Medina and Diversion Lakes could not be independently estimated based on the stage of the lakes because of the variable nature of seepage losses from Medina Lake that return as inflows to Diversion Lake or discharge to the Medina River downstream from Diversion Lake (Slattery and Miller, 2017).

A revised version of the report documenting the 2001–02 study was subsequently published in 2017, featuring three new regression equations resulting from a 2016 study (Slattery and Miller, 2017). The three new regression equations described in Slattery and Miller (2017) were the result of a detailed statistical reanalysis of the relation between the Medina Lake stage and the seepage losses from the Medina and Diversion Lake system completed in 2016 to improve upon the linear regression equations resulting from the previous 2001–02 study. The data for the 2016 study were published in a USGS data release (Asquith and Slattery, 2016) and as an appendix to Slattery and Miller (2017). The statistical reanalysis of the Medina Lake stage and the seepage losses culminated in a “preferred” log-log weighted least-squares (WLS) regression equation. This equation provided prediction intervals with the least amount of variability and a better relation between Medina Lake stage and groundwater recharge compared to the two other types of regression equations explored in 2016 and compared to the original linear regression equation. The coefficient of determination (R²) of the 2016 preferred regression equation was 0.88, and the probability (p-value) was less than 0.05, indicating that the regression model provided a reasonably good estimate of recharge to the Edwards aquifer and the upper zone of the Trinity aquifer with a high degree of confidence (Helsel and others, 2020). However, findings of the 2016 study also identified periods where the relation between Medina Lake stage and groundwater recharge estimates were not well defined and where additional data were needed to address data gaps. Therefore, between 2017 and 2022, the USGS—in cooperation with the San Antonio Water System and the Edwards Aquifer Authority— collected data as part of a new study to refine the previously derived relations between Medina Lake stage and recharge to the Edwards aquifer and the upper zone of the Trinity aquifer in the form of seepage losses from the Medina and Diversion Lake system. Between 2017 and 2022, additional water-budget data were collected at various data-collection sites in the upper Medina River drainage area (fig. 1) to refine previously published regression equations used to model the relation between the Medina Lake stage and the seepage losses from the lake system that provides recharge to the Edwards aquifer and the upper zone of the Trinity aquifer. The additional water-budget data collected during 2017–22 and the historical data from March 1955 through June 2002 were published in a companion USGS data release (Slattery and Choi, 2024).

Purpose and Scope

The purpose of this report is to quantitatively relate groundwater recharge to the Edwards aquifer and the upper zone of the Trinity aquifer (derived from the Medina and Diversion Lake system seepage losses) to the Medina Lake stage. Groundwater recharge was estimated using a water-budget approach for Medina and Diversion Lakes that included precipitation, evaporation, and surface-water data collected during March 1955–October 2022. The water-budget incorporated data collected by the USGS and various agencies during four different periods: March 1955–August 1964 (Slattery and Miller, 2017); October 1995–September 1996 (Lambert and others, 2000); March 2001–June 2002 (Slattery and Miller, 2017); and March 2017–October 2022. Water-budget data from the previous studies (March 1955–June 2002) were updated with the water-budget data collected during 2017–22 to develop a new log-log WLS regression equation to relate the Medina Lake stage to estimates of groundwater recharge. Recharge calculated from monthly and annual water budgets (method 1) were compared to recharge obtained from the new WLS regression equation (method 2) and to recharge obtained from a mass-balance (inflow minus outflow) approach published by Puente (1978) (method 3).

Precipitation

Precipitation data were collected at the USGS streamgaging station 293355098560601 Medina Lake meteorological station near Riomedina, Texas (hereinafter referred to as the “Medina Lake meteorological station”) (site 6) (fig. 1; table 1) (Slattery and Choi, 2024). These data were used to estimate precipitation (P) falling on the Medina and Diversion Lake system. Precipitation was measured with an 8-inch tipping bucket rain gage (Xylem, 2024) mounted 5 ft above the land surface. Measurements were recorded every 15 minutes and transmitted hourly by the Geostationary Operational Environmental Satellites to the USGS National Water Information System (NWIS) database (U.S. Geological Survey, 2023). To maintain the accuracy of the rain gage, the instrument was periodically inspected and cleaned, and calibration checks were performed as described by the manufacturer and USGS protocols (U.S. Geological Survey, 2005; Xylem, 2024). When an instrument was determined not meeting calibration standards (if calibration values differed from expected values by more than 6 percent), it was replaced. Precipitation data were also reviewed by comparing data from sites 2, 3, and 5 (fig. 1; table 1) to better identify periods when the rain gage might have been clogged and, therefore, under-recorded precipitation. Affected data were removed from the USGS NWIS database (U.S. Geological Survey, 2023).

Daily precipitation totals were calculated from the sum of the 15-minute values for each day. Totals were not reported for days with more than 20 percent of the 15-minute values missing. Aside from removing anomalous values caused by instrumentation noise (anomalous values not corroborated by preceding and subsequent values), no further corrections were made to the precipitation data. For the nearly 6 years of data that were collected, about 16 days of precipitation data were missing. For days when measured precipitation data were not available, daily precipitation onto the Medina and Diversion Lake system was obtained from the TWDB (TWDB, 2023) and included data from 31 days before the operation of site 6 (fig. 1; table 1).

To calculate the precipitation (P) that fell on the Medina and Diversion Lake system for use in the water-budget equation, the total daily precipitation was converted from inches into feet, then multiplied by the sum of the daily mean surface areas (acres) of Medina and Diversion Lakes. The lake surface area for Medina and Diversion Lakes was computed by the TWDB stage-volume-area tables for Medina and Diversion Lakes (Sullivan and others, 2003). Daily precipitation totals and the daily mean surface areas (acres) collected during 2017–22 and used in the calculation of P are published in the USGS NWIS database (U.S. Geological Survey, 2023). Daily precipitation totals, daily mean surface areas (acres), and the calculated P terms are provided in the companion USGS data release (Slattery and Choi, 2024).

Evaporation

Evapotranspiration is the process by which water is transferred from the Earth’s surface to the atmosphere by evaporation of water from wet surfaces, soils, and open water bodies, and by transpiration from plants (Brutsaert, 1982). The evaporation component of evapotranspiration is the focus for this study, and refers in this report to the process and measurement of evaporation from the lake surface of Medina and Diversion Lakes although the actual measurements may include some evaporation from land surfaces and transpiration from plants. Evaporation from the Medina and Diversion Lake system was measured at site 6 (fig. 1; table 1) using the eddy covariance (EC) method (Swinbank, 1951; Brutsaert, 1982). The EC method measures evaporation directly by simultaneously measuring the moisture content of the atmosphere and the speed and direction of the atmosphere transporting the moisture (Baldocchi, 2003; Foken, 2008; Stannard and others, 2013). All measured values are reported in the English or metric units in which they were collected to avoid introducing errors and because the native units are needed for all calculations.

Measurement of evaporation from lakes made by using the EC method will often also include measurements of available energy to determine net radiation over the lake surface, and energy stored or released from the lake during warming or cooling, which allows for an assessment of the complete energy budget at the lake surface, commonly referred to as the “energy budget closure” (Moreo and Swancar, 2013). The instrumentation used for this study did not facilitate measuring all energy-budget components. Hence, it was not possible to compute an energy budget closure as an additional check on the measured evaporation values reported herein.

Instrumentation

To obtain the atmospheric data necessary for calculating evaporation, site 6 (fig. 1; table 1) was instrumented with the Campbell Scientific IRGASON system, consisting of an integrated infrared gas analyzer with a three-dimensional sonic anemometer (IRGASON) equipped with an interface to process atmospheric water concentrations, three-dimensional wind speed and direction, and air temperature (Campbell Scientific, Inc., 2021). These measurements were recorded by using a Campbell Scientific micrologger at a rate of 10 measurements per second (10-hertz [Hz] flux data). The micrologger was programmed (Online Corrections Flux Program version 1.1, 2015) to process the 10-Hz flux data into 30-minute means. The selected means were then output to a Sutron SatLink data logger (Veralto, 2024) to transmit hourly to the USGS NWIS database. At the end of each day, the 30-minute means processed by the Campbell Scientific Flux program, and the raw 10-Hz flux data for the previous 24 hours, were compiled and compressed to a Campbell Scientific CR3000 secure digital memory card.

On April 4, 2017, the Medina Lake meteorological station, where a full suite of meteorological data, including EC evaporation data, was collected, was installed by mounting the Campbell Scientific IRGASON system on a 3-meter (m) tower at 3 m above the water surface on the shore of Medina Lake at site 6 (figs. 1 and 3A; table 1). The site was visited periodically to retrieve the data from the Campbell Scientific CR3000 secure digital memory card and to do routine maintenance and repairs. During site visits, the lenses of the gas analyzers were inspected, cleaned, and rinsed with deionized water. At least annually, the Campbell Scientific IRGASON system was returned to Campbell Scientific for recalibration of the gas analyzer. To prevent any data loss during this process, a spare Campbell Scientific IRGASON system was installed while the system was being recalibrated.

Source Area of Measurements

The land-surface area surrounding the Medina Lake meteorological station that affects evaporation is referred to as the “flux footprint” of the site. Fetch is the distance that wind blows over open water or land within the flux footprint (Burba, 2013). Burba (2013, p. 122 and 136) explains the terms of flux footprint and fetch as follows:

In simplest terms, the flux footprint is the area “seen” by the instrument on the tower. In other words, it is an area upwind from the tower, such that fluxes generated in this area are registered by the tower instruments. Another frequently used term, “fetch,” usually refers to the distance from the tower when describing the footprint. *** Flux footprint describes a contributing area upwind from the tower. This is the area that the instruments can “see.” Flux footprint mainly depends on measurement height, surface roughness, and atmospheric thermal stability. The size of the footprint increases with increased measurement height, with decreased surface roughness, and with changes in thermal stability from unstable to stable. The area near the tower may contribute a lot to the flux footprint, if the measurement height is low, surface roughness is high, or if conditions are very unstable.

Thus, the fetch footprint is the area “seen” by the instruments on the tower of the site, and the evaporation generated in this area is measured by the EC instruments installed at the Medina Lake meteorological station. Because Medina Lake is relatively small, the fetch footprint—especially when the lake is not full—may incorporate land features such as terrain, ground cover, vegetation types, water bodies, and structures that affect airflow patterns of the wind and moisture content of the atmosphere, thereby affecting the measured evaporation (Burba, 2013).

The distance that the fetch footprint extends from the EC instruments at the Medina Lake meteorological station for wind directions from 40 to 260 degrees from true north at the instrument tower was estimated using the EasyFlux software. This software includes two models: the Kljun model (Kljun and others, 2004) and the Kormann-Meixner model (Kormann and Meixner, 2001). When the wind direction was from 40 to 260 degrees from true north, the fetch footprint best represented open water at the site. By default, the Kljun model is used to estimate fetch distance with the EasyFlux software. When meteorological values pertaining to the measurement of evaporation are outside of predefined ranges of atmospheric conditions of stability and turbulence, the Kormann-Meixner model is used. Both models depend on the height of the instrument, the height of the vegetation canopy, surface roughness, and the stability of the atmosphere to calculate the fetch. For each processing period (about 40 days), the mean height of the Campbell Scientific IRGASON instrument above the water surface was entered into the EasyFlux software for calculating the fetch distance.

The EasyFlux software was used to estimate five fetch distances from the instrument tower, expressed as a percentage (10, 30, 50, 70, and 90 percent) of the cumulative evaporation contributions measured at the site. The percentages of the cumulative evaporation contributions by fetch distance from the instrument tower are provided in figure 4.

The location of the Medina Lake meteorological station, installed by the USGS on Medina Lake, was selected to provide the EC instruments with good exposure to the open water and prevailing winds (figs. 1 and 3A). Based on the location of the site, when the wind was from the directions between 260 and 360 and 0 and 40 degrees from true north, the footprint was considered to be from a land source, and when the wind was from the directions between 40 and 260 degrees from true north, the footprint is considered to be from an open-water source. For the period of record (April 5, 2017–October 6, 2022), 33 percent of the EC measurements were made when wind directions were from the direction of land and accounted for 18 percent of the total measured evaporation. Sixty-seven percent of the EC measurements were made when the wind direction was from the direction of open water and accounted for 82 percent of the total measured evaporation. Measurements made when the wind was from the direction of land were qualified as estimated evaporation in NWIS. The greater percentage of measured evaporation coming from the direction of open water is because these directions coincide with the prevailing winds during the summer months, when evaporation rates are generally the highest. When the winds are more often from the direction of land, these wind directions most often occur in the winter months, when evaporation rates are generally the lowest.

Evaporation measured at the Medina Lake meteorological station varied with fetch distance, and increases in fetch distance corresponded to decreases in annual mean Medina Lake stage (fig. 4). During the first 4 years of the study (2017–20), it was determined by using the two models built into the EasyFlux software that an estimated 90 percent of the measured evaporation at the Medina Lake meteorological station originated from within about 900 m (about 2,953 ft) of the instrument tower, representing a fetch footprint of mostly open water. However, the Medina Lake stage declined substantially after 2020, and by 2021, the fetch footprint began to greatly expand. By 2021, 90 percent of the measured evaporation originated from an area within 1,250 m (about 4,101 ft) of the fetch distance, and by 2022, the fetch distance increased to a distance of 1,690 m (about 5,545 ft) from the EC instruments (fig. 4). For fetch distances greater than 800 m (about 2,625 ft), the expected fetch footprint includes not only the open water of Medina Lake but also the land surface on the opposite shore of the lake. When the land surface on the opposite shore of the lake is part of the fetch distance, bias is introduced into the measured evaporation within the fetch footprint because evaporation from land sources and evapotranspiration from vegetation are included in the computation of evaporation (fig. 4). Additionally, as lake levels declined, the fetch footprint included exposed lakebed near the evaporation site, potentially biasing the measured evaporation (fig. 3B). Consequently, the measured evaporation from the latter period was not used, and an alternate source of evaporation data was used, as described in the following section.

Surface-Water Inflow and Outflow

During the 2017–22 study, the surface-water inflow (SW_in) term to the Medina and Diversion Lake system was computed from records collected at two continuous-record streamgages upstream from Medina and Diversion Lakes, USGS streamgaging station 08178980 Medina River above English Crossing near Pipe Creek, Tex. (site 1), and USGS streamgaging station 08179110 Red Bluff Creek at Farm to Market Road 1283 near Pipe Creek, Tex. (site 2; installed on December 5, 2017) (fig. 1; table 1), and from streamflow estimates from the ungaged areas that drain into the Medina and Diversion Lake system. Prior to the installation of site 2, the drainage area upstream from site 2 was part of the ungaged contributing areas. After the installation, streamflow records from site 2 were directly included in SW_in.

Streamflow for the ungaged areas was estimated using data collected from three USGS streamgaging stations: 08180586 San Geronimo Creek near Helotes, Tex. (site 3); 08181400 Helotes Creek at Helotes, Tex. (site 4); and 08200977 Middle Verde Creek at State Highway 173 near Bandera, Tex. (site 5) (fig. 1; table 1), and using the drainage-area ratio method suggested by Asquith and others (2006).

The drainage-area ratio method estimates streamflow for an ungaged area using daily streamflow information from a gaged drainage area and accounts for the difference in the drainage areas of the two areas by using the following equation:

Before the installation of the site 2 gage on December 5, 2017, the ungaged area was 177 mi², and it was 119.1 mi² after the gage was installed. For the simplest drainage-ratio method, assumptions are made that the expected value of the estimated streamflow equals the true streamflow value and the exponent ϕ=1 (Asquith and others, 2006). Thus, the daily estimated streamflow of the ungaged area is directly proportional to the daily streamflow at a gaged station.

Asquith and others (2006) computed the exponent values for the 34 streamflow percentile ranges using daily mean streamflow for 712 streamgages in Texas to account for the effects of streamflow probability on the drainage-area ratio method in the State. For this study, the method was modified to only include 130 streamgages from watersheds with similar topography, geology, and streamflow characteristics compared to the streamgages that monitor inflows to Medina Lake to better represent the local hydrologic characteristics (Slattery and Choi, 2024). The selected 130 streamgages are in 17 counties: Mason, Llano, Burnet, Kimble, Gillespie, Blanco, Travis, Hays, Comal, Kendall, Kerr, Bandera, Real, Edwards, Uvalde, Medina, and Bexar, which often are identified as the Texas Hill Country area (Pegasus Planning, 2023). For this study, the exponent values were calculated for 51 streamflow percentile ranges rather than 34 to provide an exponent value for every 2 percentile increment between 0 and 100 using the daily discharge data from the selected 130 streamgages, from October 1, 1915, to October 15, 2022 (table 2).

Using equation 2, estimated daily streamflow of the ungaged area was calculated from the three gaged stations: site 3 (fig. 1; table 1) with a drainage area of 31.1 mi²; site 4 (fig. 1; table 1) with a drainage area of 15 mi²; and site 5 (fig. 1; table 1) with a drainage area of 38.9 mi². The mean of the three streamflow estimates was selected as the final daily streamflow into Medina and Diversion Lakes from the ungaged areas.

Daily mean streamflow data collected during 2017–22 and used in the calculation of SW_in and SW_out are published in the USGS NWIS database (U.S. Geological Survey, 2023). SW_out from the Medina and Diversion Lake system was computed by summing the daily streamflow values recorded at two USGS streamgaging stations: 08180000 Medina Irrigation Canal near Riomedina, Tex. (site 8), and 08180500 Medina River near Riomedina, Tex. (site 10) (fig. 1; table 1, respectively). The daily mean streamflows, the daily estimated discharge of the ungaged areas, and the calculated SW_in and SW_out terms are provided in Slattery and Choi (2024).

Reservoir Storage

Reservoir storage for Medina Lake was computed from continuous lake stage recorded at USGS streamgaging station 08179500 Medina Lake near San Antonio, Tex. (site 7), whereas reservoir storage for Diversion Lake was computed from continuous lake stage recorded at USGS streamgaging station 08180010 Diversion Lake near Riomedina, Tex. (site 9) (fig. 1; table 1), by using the TWDB stage-volume-area tables for each lake (Sullivan and others, 2003). The TWDB stage-volume-area tables for each lake were entered into the USGS NWIS database (U.S. Geological Survey, 2023) to produce a stage-volume relation and continuous calculation of storage from the lake stages. The daily storage is calculated as the sum of the daily mean storage values for Medina and Diversion Lakes. Daily changes in lake storage (∆S) were computed as the difference between the amount of current-day storage and the amount of previous-day storage. Positive values of ∆S represent an increasing amount of water being held in storage in the Medina and Diversion Lake system. Negative values of ∆S represent an increasing amount of water in the Medina and Diversion Lake system being released from storage.

Calculated Seepage_out

The calculated Seepage_out from the Medina and Diversion Lake system provides the best estimate of actual recharge to the Edwards and Trinity aquifers, and it was used as the benchmark for comparing with other methods of estimating recharge. Seepage_out was computed as the residual of all other terms in the water-budget equation (eq. 1) to estimate the seepage loss to the groundwater system underlying the Medina and Diversion Lake system. Seepage_out represents water that is not accounted for by all other terms of the water-budget equation, including any unrecognized errors. Positive values of Seepage_out represent losses from the lake system to the groundwater system (Lambert and others, 2000). Negative Seepage_out values represent gains to the lake system from the groundwater system. The daily calculated Seepage_out values and the individual terms of the water-budget equation used in equation 1 are included in Slattery and Choi (2024).

Contributions From Each Term of the Water-Budget Equation

The calculated Seepage_out (eq. 1) is the key result of the water-budget analysis as explained in the “Groundwater Recharge” section. For the period March 4, 2017–October 6, 2022, the daily calculated Seepage_out ranged from −4,291 to 4,705 acre-ft, with a mean of 110 acre-ft/d (fig. 5; Slattery and Choi, 2024); both the minimum and the maximum values occurred during times of precipitation runoff. A lag between large inflows to the lake system and changes in the Medina Lake stage and groundwater-level altitudes cause brief periods when the Seepage_out is negative; these lags result in transient periods of unaccounted lake inflows or groundwater fluxes. A comparison of the contribution of each of the terms to the water-budget equation is summarized for each year of the study (tables 3 and 4). Table 3 provides a comparison of the annually calculated sum of the individual terms of the water-budget equation, in acre-feet. The largest contributions of individual terms of the water-budget equation to the Medina and Diversion Lake system were from SW_in, SW_out, and Seepage_out, accounting for 357,810; 309,900; and 226,300 acre-ft, respectively. P accounted for 61,280 acre-ft, E accounted for 102,320 acre-ft, and change in lake storage (ΔS) accounted for −219,200 acre-ft. Table 4 provides a summary of the annual relative contribution as a percentage of the total of each of the individual terms of the water-budget equation. For the Medina and Diversion Lake system, SW_in, SW_out, and ΔS were the major terms of the water-budget equation, accounting for 21.1, 22.2, and −21.9 percent, respectively. P accounted for 4.1 percent, E accounted for 7.3 percent, and Seepage_out accounted for 17.5 percent.

Measurement Error for the Terms in the Water-Budget Equation

Water-budget terms that are calculated from more than one measured variable might reflect an accumulation of errors in the measured terms (Lee and Swancar, 1997). If a term is derived as the sum or difference of other measured terms, then the potential error is the sum of the variances in the measured terms (Winter, 1981). For the water-budget equation, each measured term used to calculate Seepage_out was assigned a percentage error to define the confidence limits around the measured values. The percentage error (%ei) was assigned to each term in the water-budget equation based on the method of measurement, accuracy, precision of the instrumentation, and the presumed quality of the hydrologic record (Lee and Swancar, 1997). Records rated as good were assigned a percentage error (%ei) of plus or minus (±) 8 percent; records rated as fair were assigned a percentage error of ±10 percent, and records rated as poor were assigned a percentage error of ±15 percent (Novak, 1985, p. 65).

Records for surface-water inflows (SW_in) measured at sites 1 and 2, records for surface-water outflows (SW_out) measured at sites 8 and 10, and records for precipitation (P) measured at site 6 (fig. 1; table 1) were rated as good with a percentage error of ±8 percent. Records for change in lake storage (ΔS) from sites 7 and 9 were rated as fair with a percentage error of ±10 percent, and evaporation data (E) from site 6 were rated as poor with a percentage error of ±15 percent (Novak, 1985, p. 65). Incorporating the individual errors for each of the measured terms in the water-budget equation, the net error was calculated as the square root of the sum of the individual errors for each term (eq. 3):

The monthly and annual standard error of the Seepage_out term was also calculated. The standard error is the standard deviation of the daily calculated Seepage_out values for a given month or year, divided by the square root of the number of days in the month or year. The standard error represents the standard deviation of the mean within a dataset and serves as a measure of the variation of random variables, providing a measurement of the spread in the dataset. The smaller the spread, the more accurate the dataset (Ott, 1993). Summaries of the net eSeepage_out term, as well as the calculated standard error of the Seepage_out term, are discussed in more detail in the “Measurement Error Associated With the Calculated Recharge” section of this report. The daily calculated net eSeepage_out data are included in Slattery and Choi (2024).

Groundwater Recharge

For this study, seepage loss from the Medina and Diversion Lake system was assumed to provide recharge to the Edwards aquifer and the upper zone of the Trinity aquifer, and the recharge was calculated or estimated using three methods as described in the “Purpose and Scope” section of this report. The first method compiles the daily calculated Seepage_out values from the water-budget equation (eq. 1) into monthly and annual summaries of calculated recharge to the Edwards aquifer and the upper zone of the Trinity aquifer (tables 5 and 6) during March 4, 2017–September 30, 2022, with 2017 and 2022 being partial years of record for the calculated recharge. The second method estimates recharge to the Edwards aquifer and the upper zone of the Trinity aquifer using a new log-log WLS regression equation that relates the stage of Medina Lake to seepage losses from the Medina and Diversion Lake system. Complete years of stage records are available during 2017–22. The equation was used to estimate monthly and annual recharge to the Edwards aquifer and the upper zone of the Trinity aquifer during January 2017–December 2022. The third method is the estimated recharge to the Edwards aquifer and the upper zone of the Trinity aquifer by using the Puente (1978) method, which is presented for comparison with the first and second methods described herein (Puente, 1978; Slattery and Choi, 2023).

Regression Equation Depicting Relation Between Medina Lake Stage and Groundwater Recharge (Method 2)

Results from the 2016 study (Asquith and Slattery, 2016) culminated in a log-log WLS regression equation with prediction intervals and better defined the relation between the Medina Lake stage and recharge compared to the relation between the Medina Lake stage and recharge determined using the Puente method. The study also identified periods where the relation between the Medina Lake stage and the groundwater recharge estimates were not well defined (Asquith and Slattery, 2016). For this study, water-budget periods were calculated over a wide range of stages on Medina Lake, ranging from 987.44 to 1,064.35 ft above NGVD 29, providing a range in lake stages that will better define the statistical relation between the Medina Lake stage and the groundwater recharge estimates and help validate the statistical relation published in 2016.

The selected water-budget periods were calculated from the daily Seepage_out values, during which time the water-budget terms were relatively stable, and the effects of precipitation, stormwater runoff, and changes in reservoir storage were minimal. To identify the stable periods, the mean of the Seepage_out term was calculated for water-budget periods of 10 days, along with the standard deviation of the Seepage_out values. The coefficient of variation is defined as the ratio of the standard deviation to the mean for a given dataset (Helsel and others, 2020). The coefficient of variation was computed for Seepage_out values for each water-budget period. If the coefficient of variation was greater than 0.90, then the period was excluded. Additional periods of 7–12 days where the coefficient of variation was less than or equal to 0.90 were also included from the remaining days. The selection of such periods would presumably minimize errors associated with disequilibrium within the system. Periods of less than 7 days were not evaluated. Periods of less than 7 days would not adequately account for the traveltime of the water through the system and would not provide a reasonable sample size for the computation of the daily calculated Seepage_out value from the water-budget equation. A total of 144 water-budget periods were thus selected between March 15, 2017, and October 6, 2022, representing about 85 percent of the period of record (fig. 5). Data from the 144 selected water-budget periods were then appended to a dataset compiled during a similar previous study (Asquith and Slattery, 2016; Slattery and Miller, 2017) and include the statistical summaries and errors computed for each of the selected water-budget periods. The dataset is available in Slattery and Choi (2024).

For the statistical analysis, data from four time periods (1955–64, 1995–96, 2001–02, and 2017–22) were combined into one dataset (a total of 271 data points) (Asquith and Slattery, 2016; Slattery and Miller, 2017). The daily calculated Seepage_out values range from 6.22 to 199.68 acre-ft/d, with the altitude of the Medina Lake stage ranging from 963.27 to 1,064.35 ft above NGVD 29.

The statistical analysis of Medina Lake stage and Seepage_out data was done by using R scripts (Wood, 2006, 2016a, b; R Core Team, 2023) developed as part of the 2016 study (Asquith and Slattery, 2016; Slattery and Miller, 2017) and modified to incorporate the additional 2017–22 dataset (Slattery and Choi, 2024). A log-log WLS regression equation, including the 75-percent and 90-percent prediction intervals associated with the equation, was derived to model the relation between the Medina Lake stage and Seepage_out data (Helsel and others, 2020). The resulting water-budget equation is expressed as the change in Seepage_out:

${}_{\delta }Seepag{e}_{out}=\delta \times {10}^{\left\{3800.97{\text{log}}_{10}\left(ML\right)-628.27{\left[{\text{log}}_{10}\left(ML\right)\right]}^2-5746.80\right\}}$

(4)

where

_δSeepage_out

is the estimated recharge from the Medina and Diversion Lake system to the Edwards aquifer and upper zone of the Trinity aquifer, in acre-feet per day;

ML

is the Medina Lake stage, in feet above NGVD 29; and

δ

is a bias correction factor that is set to 1.000 or 1.081 during the retransformation of median and mean Seepage_out values, respectively, from log units back to linear units, respectively (a bias correction factor set to 1.000 indicates no correction was applied).

The regression equation is graphically depicted in figure 6. The adjusted R² value for the equation is 0.82, and the residual standard error (in logarithmic, base-10 scale) is 0.14. Faraway (2005, 2006) and Helsel and others (2020) provide detailed descriptions of the methods used to derive the regression equations, adjusted R², residual standard errors, and prediction intervals for regression equations (fig. 6). The results obtained from the log-log WLS regression equation shown in figure 6 were transformed into their original units using the Duan (1983) smearing estimate method, which is explained in detail by Helsel and others (2020). The abbreviations applicable to mathematical functions and statistical terms from the R regression output are provided (fig. 7A), along with the R regression outputs of the log-log WLS regression equation (fig. 7B). The log-log WLS regression equation (eq. 4) developed for the Medina and Diversion Lake system relates the stage in Medina Lake to the seepage loss from the entire lake system (figs. 6 and 7B).

The log-log WLS regression equation (eq. 4) (figs. 6 and 7B) indicates that the estimated seepage loss (_δSeepage_out) increases nonlinearly as the stage in Medina Lake increases, applicable for stages between 963 and 1,059.13 ft above NGVD 29. For stages less than 963 ft above NGVD 29, there are few measured observations, and the relation between the Medina Lake stage and _δSeepage_out is poorly defined. Using equation 4, when the Medina Lake stage reaches 1,059.13 ft above NGVD 29, a maximum _δSeepage_out value of 127.32 acre-ft/d is computed; this value then begins to decline as the Medina Lake stage becomes greater than 1,059.13 ft above NGVD 29, and equation 4 is, therefore, invalid. Decreasing seepage loss occurring when the Medina Lake stage was rising was not observed in the measured data, except during unusually wet periods when the rocks that contain the Edwards and Trinity aquifers become saturated and cannot accept additional recharge (for example, from August 2018 through November 2018, a period of saturated conditions was noted).

Uncertainties not addressed by the statistical reanalysis may be associated with the characteristics of the data themselves. For example, few data are available for certain ranges of Medina Lake stage, particularly for stages less than 970 ft above NGVD 29 and for stages between 980 and 1,015 ft above NGVD 29; the lack of data for these stage ranges is more pronounced for the data collected during 1995–96 and 2001–02, when the Medina Lake stage varied little compared to the larger ranges in stages recorded during 1955–64 and 2017–22 (fig. 6). Differences in data-collection techniques are an additional source of data uncertainty. The water-budget data from the earliest period (1955–64) were collected using different techniques compared to the more recent data, so the accuracy of the Seepage_out data may have varied over time. For example, evaporation during 1955–64 was determined from published evaporation tables by the TWDB (TWDB, 2024), whereas the more recent evaporation from 1995–96, 2001–02, and 2017–22 was determined by using data obtained from USGS-operated meteorological stations temporarily installed on or near Medina Lake.

Data collected during 1995–96 and 2001–02 exhibit a similar distribution compared to data collected from 1955–64 for the same Medina Lake stages. It is reasonable, therefore, to assume that the more recent water-budget analyses, based on the more recent data, would produce results for lower stages (less than 1,030 ft above NGVD 29) that are consistent with the results produced using the data from 1955–64. However, data from 2017–22 indicate a greater mean Seepage_out compared to the three earlier water-budget periods for the same Medina Lake stages, except for Medina Lake stages of about 1,000 ft above NGVD 29 and for stages between 1,020 and 1,040 ft above NGVD 29.

Additional sources of uncertainty not addressed in this regression analysis include the possibilities of serially correlated data, unaccounted for antecedent hydrological conditions, and differences in hydrostratigraphy at different Medina Lake stages that might affect Seepage_out. Serial correlation is the dependence or correlation between residuals for values collected in a time series (Helsel and others, 2020). For the Medina Lake stage data, the possibility of serial correlation means that stage values collected consecutively over time might not be independent. Instead of varying independently, the data might change similarly in response to monthly and annual scale changes in hydrometeorological processes and are, therefore, not randomly distributed in time (Helsel and others, 2020). Accounting for the effects of serial correlation would be difficult and would require more data than available in this study. The antecedent hydrological conditions in the area surrounding the Medina and Diversion Lake system are also not represented in the regression equation. Also not specifically accounted for in the regression equation are differences in hydrostratigraphy that might affect Seepage_out at different stages in either Medina or Diversion Lake (Lambert and others, 2000). Errors associated with the calculation of the Seepage_out term, which account for the potential errors of the individual terms, are summarized in the “Measurement Error Associated With the Calculated Recharge” section of this report.

Puente Method of Estimating Annual Groundwater Recharge From Medina Lake (Method 3)

Published estimates of annual recharge to the Edwards aquifer from the Medina River drainage area during 1934–2022 range from 6,300 acre-ft (1956) to 104,000 acre-ft (1960), with a mean of 61,400 acre-ft/yr (Slattery and Choi, 2023, basin 5) and are based on methodology published by Puente (1978). This method assumes all lake losses recharge the Edwards aquifer before some of the water ultimately recharges the Trinity aquifer.

To estimate recharge to the Edwards aquifer from the Medina and Diversion Lake system, Puente (1978) used a mass-balance analysis method (inflow minus outflow) to account for all inflow to and outflow from Medina Lake and the Medina and Diversion Lake system, including evaporation from the lake surfaces. Using base flow data collected during 1930 as part of a Medina River seepage investigation, Puente (1978) published a set of correlation curves relating groundwater recharge from the Medina and Diversion Lake system to the reservoir contents (storage) in Medina Lake. Puente (1978) reported that recharge during rising lake stages (increasing storage) was greater than recharge during falling stages (decreasing storage); these differences in recharge were attributed to bank-storage losses during rising lake stages and return flows from bank storage during falling stages. Figure 8 contains two modified curves from the curves published by Puente (1978) by substituting Medina Lake stage for storage.

Calculated Total Monthly and Annual Recharge From Seepage_out

The total monthly recharge values calculated from Seepage_out are variable, ranging from −693 acre-ft per month, representing a gain to the lake system from unaccounted for inflows of surface water or groundwater, to 5,490 acre-ft per month, representing recharge from the lake system to the Edwards aquifer and the upper zone of the Trinity aquifer. The total monthly calculated recharge values during March 2017–September 2022 are summarized in table 5 and shown in figure 9. The total annual recharge values calculated from Seepage_out are also listed in tables 5 and 6 and shown in figure 10.

Some of the variability in the monthly calculated recharge values is the result of variable hydrologic conditions. For example, months when the recharge rates were relatively low often corresponded to increases in Medina Lake stage values. During August–October 2018, when the calculated monthly recharge was small, and during November 2018, when the monthly calculated Seepage_out value was negative, the calculated Seepage_out rates were likely affected by rejected recharge where the rocks that contain the Edwards and Trinity aquifers were saturated, as described in the “Geology and Hydrostratigraphy” section of this report. Months when the calculated recharge rates were relatively low were also common when the Medina Lake stage was less than 1,045 ft above NGVD 29 (fig. 9; tables 5 and 7). Months of higher calculated recharge rates generally coincided with hydrologically stable periods with relatively little precipitation and low base flows in the streams impounded by the lake system when the Medina Lake stage was equal to or greater than 1,045 ft above NGVD 29 (fig. 9; tables 5 and 7).

For years with complete periods of record, the calculated annual total recharge calculated from Seepage_out ranged from 34,610 acre-ft in 2021 to 50,880 acre-ft in 2019. During 2019, Medina Lake was nearly full, and the stage values for Medina Lake were consistently among the highest observed for the study period (fig. 10; tables 5, 6, and 7).

Estimated Monthly and Annual Recharge From the Weighted Least-Squares Regression Equation

The estimated monthly and annual totals for recharge during January 2017–December 2022 were estimated using the WLS regression equation (eq. 4) (figs. 9 and 10; tables 5 and 6). The monthly and annual WLS regression estimated recharge totals are shown in figures 9 and 10, respectively.

The monthly and annual recharge totals estimated by using equation 4 (WLS estimated recharge) are less variable compared to the monthly and annual calculated recharge totals. The WLS regression equation monthly recharge rates ranged from 933 acre-ft per month in November and December 2022 to 3,950 acre-ft per month in January and June 2017 and January, March, May, July, August, and October 2019 (fig. 9; table 5). The WLS estimated recharge rates remained nearly constant when the Medina Lake stage ranged from approximately 1,040 to 1,064 ft above NGVD 29 and steadily declined to between 1,010 and 1,040 ft above NGVD 29, with a greater rate of decline observed when the Medina Lake stage decreased to less than 1,010 ft above NGVD 29 (figs. 6 and 10; tables 5 and 7).

The total annual WLS estimated recharge ranged from 19,460 acre-ft in 2022, when the annual mean Medina Lake stage was at its lowest level for the study period, to 46,460 acre-ft in 2019, when the annual mean Medina Lake stage was at its highest levels for the study period (fig. 10; tables 5 and 7). Between 2017 and 2020, WLS estimated recharge remained nearly constant, ranging from 43,940 to 46,460 acre-ft, coinciding with years when the annual mean Medina Lake stage was between 1,045 and 1,062 ft above NGVD 29. The WLS estimated annual recharge decreased by approximately 20 percent in 2021 when the annual mean Medina Lake stage was 1,025 ft above NGVD 29 and decreased again by approximately 40 percent in 2022 when the annual mean Medina Lake stage was 1,000 ft above NGVD 29 (fig. 10; tables 5 and 7).

Estimated Monthly and Annual Recharge—Puente Method

The monthly and annual recharge estimated using the Puente method, as published by the USGS (Slattery and Choi, 2023) (figs. 9 and 10; table 5), is described in the “Puente Method of Estimating Annual Groundwater Recharge From Medina Lake” section. The estimated recharge rates are reported as recharge exclusively to the Edwards aquifer, but for the purpose of this study, recharge estimated by the Puente method is considered as recharge to both the Edwards aquifer and the upper zone of the Trinity aquifer.

The monthly recharge estimated using the Puente method ranged between 2,630 and 9,410 acre-ft per month. The month with the lowest recharge rate (December 2022) (fig. 9; table 5) coincides with the month of the lowest mean Medina Lake stage and with falling lake-stage conditions. The month with the highest recharge rate coincides with the highest monthly mean Medina Lake stage (December 2018), and with rising lake stage conditions. The annually estimated recharge rates by the Puente method ranged from 37,320 acre-ft in 2022, when the lake stage was at its lowest level and declining, to 86,830 acre-ft in 2019, when the lake stage was at its highest level and rising (fig. 10; tables 5 and 6).

Comparison of Recharge Methods

The total monthly recharge estimated using the WLS and the Puente method of estimating recharge were compared to the calculated recharge during two periods: (1) when the Medina Lake stage was rising and (2) when the Medina Lake stage was steady or falling. As described in the section “Calculated Seepage_out,” the calculated Seepage_out is considered to represent the most accurate accounting of the seepage losses from the Medina and Diversion Lake system that provide recharge to the Edwards aquifer and the upper zone of the Trinity aquifer.

Comparisons were made between months when the mean Medina Lake stages were equal to or greater than 1,045 ft above NGVD 29 and months when the mean Medina Lake stages were less than 1,045 ft above NGVD 29. At stages equal to or greater than 1,045 ft above NGVD 29, there is contact between the waters of Medina Lake and the permeable rocks of the Edwards Group that contain the Edwards aquifer; this contact between the lake waters and the permeable rocks that contain the Edwards aquifer is conducive to seepage losses that recharge the groundwater system. As the Medina Lake stages decrease to less than 1,045 ft above NGVD 29, rates of recharge to the Edwards aquifer and the upper zone of the Trinity aquifer decrease because the lake waters are no longer in contact with the rocks that compose the Edwards Group.

Comparison of the Weighted Least-Squares Estimated Recharge and Calculated Recharge Methods

The WLS estimated total recharge was compared to the calculated total recharge for the March 2017–September 2022 period. The WLS estimated total recharge was 0.5 percent less than the calculated recharge during March 2017–September 2022. The total WLS estimated recharge during March 2017–September 2022 was 224,310 acre-ft, whereas the total calculated recharge was 225,400 acre-ft (table 6).

The largest differences between the WLS estimated recharge and the calculated recharge occurred in months with rising Medina Lake stage that coincided with higher precipitation amounts and greater discharges; during these months, the WLS estimated recharge remained relatively constant, but the calculated recharge was much lower for reasons described in the section “Calculated Total Monthly and Annual Recharge From Seepage_out” (fig. 9; tables 5 and 7). The smaller differences between the WLS estimated and calculated recharge occurred during months when the stage of Medina Lake was steady or declining. Months when the stage of Medina Lake was steady or declining coincided with hydrologically stable periods with relatively small amounts of precipitation and base-flow conditions in the Medina River upstream from Medina Lake. The total WLS estimated recharge during September 2018–June 2019, when the Medina Lake stage was generally rising, was 38,250 acre-ft, which was about 24 percent more than the total calculated recharge of 30,750 acre-ft during this period. For months of steady or falling lake-stage conditions (March 2017–August 2018 and July 2019–September 2022), the total WLS estimated recharge was 185,880 acre-ft, which was about 4.5 percent less than the total calculated recharge of 194,650 acre-ft. Only a small difference was observed between the WLS estimated recharge and the calculated recharge when the Medina Lake stages were equal to or greater than 1,045 ft above NGVD 29 and at Medina Lake stages less than 1,045 ft above NGVD 29.

A large difference between the WLS estimated recharge and the calculated recharge was also observed in 2022. During 2022, the Medina Lake stage decreased to less than 1,020 ft above NGVD 29 then continued to steadily decline further (table 7). The large difference between the WLS estimated recharge and the calculated recharge when the Medina Lake stage was less than 1,020 ft above NGVD 29 might indicate a lower limit to the WLS regression equation where the relations between the Medina Lake stage and the groundwater recharge estimates are not well defined. At stages less than approximately 1,020 ft above NGVD 29, fewer water-budget periods are available for use in the statistical regression analysis compared with periods when stages are greater than 1,020 ft above NGVD 29 (fig. 6; table 5).